Robust order promising - Design and analysis of a capable-to-promise approach including order- and resource-related measures Dissertation zur Erlangung des akademischen Grades Doctor rerum politicarum (Dr. rer. pol.) an der Fakultät Wirtschaftswissenschaften der Technischen Universität Dortmund Sonja Kalkowski Dortmund 2017 II Table of contents List of figures .................................................................................................IV List of tables.................................................................................................... V List of abbreviations .................................................................................... VII List of symbols ...............................................................................................IX Decision variables ....................................................................................... IX Parameters ................................................................................................... X Indices and sets ..........................................................................................XII Superscripts ............................................................................................. XIII 1 Motivation ................................................................................................... 1 1.1 Problem ................................................................................................. 1 1.2 State of the art ........................................................................................ 5 1.2.1 Capable-to-promise approaches ........................................................ 5 1.2.2 Identification of research gaps ........................................................ 18 1.3 Objective and approach ........................................................................ 22 2 Approaches ............................................................................................... 29 2.1 Basic approach with order-related uncertainty ...................................... 29 2.1.1 Introduction ................................................................................... 29 2.1.2 Planning approach .......................................................................... 32 2.1.2.1 Basic model .......................................................................... 32 2.1.2.2 Consideration of adjustment measures .................................. 35 2.1.3 Numerical analysis ......................................................................... 40 2.1.3.1 Test configuration ................................................................. 40 2.1.3.2 Test results ............................................................................ 43 2.1.4 Conclusions ................................................................................... 45 2.2 Extended approach with order- and resource-related uncertainty .......... 47 2.2.1 Introduction ................................................................................... 47 2.2.2 Planning situation ........................................................................... 52 2.2.2.1 Planning object ..................................................................... 52 2.2.2.2 Structure of planning approach.............................................. 54 2.2.3 Planning models ............................................................................. 56 2.2.3.1 First planning stage ............................................................... 56 2.2.3.2 Second planning stage ........................................................... 61 III 2.2.4 Numerical analysis ......................................................................... 64 2.2.4.1 Procedure .............................................................................. 64 2.2.4.2 Test data ............................................................................... 65 2.2.4.3 Test results ............................................................................ 69 2.2.5 Conclusions ................................................................................... 74 Appendix A ............................................................................................. 76 3 Coordination of measures ......................................................................... 77 3.1 Introduction ......................................................................................... 77 3.1.1 Problem description ....................................................................... 77 3.1.2 Literature review ............................................................................ 79 3.1.3 Research focus ............................................................................... 84 3.2 Planning at subordinate level................................................................ 86 3.2.1 Planning situation ........................................................................... 86 3.2.2 Price- and delivery-date-dependent customer behavior ................... 87 3.2.3 Extended planning model ............................................................... 88 3.3 Exploration of CTP model behavior ..................................................... 94 3.3.1 Developing the multi-group path model ......................................... 94 3.3.2 Estimating the multi-group path model ........................................... 99 3.3.2.1 Data basis ............................................................................. 99 3.3.2.2 Evaluation ........................................................................... 101 3.4 Coordination at superordinate level .................................................... 108 3.4.1 Procedure of the limited search .................................................... 108 3.4.2 Quality of the limited search ........................................................ 110 3.5 Conclusions ....................................................................................... 112 Appendix A: Data basis for CTP model tests ............................................ 114 Appendix B: Verification of multi-group path models ............................... 114 Appendix C: Intermediate results of limited search ................................... 119 Appendix D: Detailed results of quality evaluation ................................... 121 4 Conclusions ............................................................................................. 122 References .................................................................................................... 128 IV List of figures Figure 1.1.1: Basic structure of a batch CTP approach ......................... 4 Figure 1.2.1: Classification of order specifications ............................. 11 Figure 1.3.1: Basic structure of the dissertation .................................. 22 Figure 2.1.1: CTP classification and profile of the proposed approach........................................................................ 30 Figure 2.1.2: Relevant approaches ...................................................... 31 Figure 2.1.3: Tested parameter constellations ..................................... 41 Figure 2.1.4: Production-related data .................................................. 42 Figure 2.1.5: Generated profits ........................................................... 43 Figure 2.1.6: Robustness index ........................................................... 44 Figure 2.1.7: Capacity utilization ....................................................... 45 Figure 2.2.1: Structure of the supply chain ......................................... 53 Figure 2.2.2: Structure of the planning approach ................................ 55 Figure 2.2.3: Scenarios to be analyzed ............................................... 68 Figure 2.2.4: Generated profits of non-interactive order promising ..... 70 Figure 2.2.5: Generated profits of interactive order promising ............ 71 Figure 2.2.6: Penalty costs in representative capacity scenario IV ...... 73 Figure 3.1.1: Combined deductive-inductive CTP approach ............... 84 Figure 3.4.1: Flow-chart for measure parameterization ..................... 109 V List of tables Table 1.2.1: Relevant modelling approaches ....................................... 6 Table 2.2.1: Overview of relevant CTP approaches and applied preventive adaptation measures ..................................... 49 Table 2.2.2: Original order data ........................................................ 65 Table 2.2.3: Defined and estimated capacity situations...................... 66 Table 2.2.4: Varied parameters of adaptation measures ..................... 67 Table 2.2.5: Coefficients of variation of planning data and generated profits ............................................................ 72 Table 3.1.1: Batch CTP approaches including robustness-generating measures ....................................................................... 80 Table 3.3.1: Modeling the implementation of robustness-generating measures and prevailing conditions by exogenous variables.................................................. 95 Table 3.3.2: Modeling the impact of robustness-generating measures by endogenous variables ................................ 96 Table 3.3.3: Matrix of formula-conditioned and hypothetical relations .................................................... 97 Table 3.3.4: Standardized direct causal effects in the partially restricted model R .................................... 102 Table 3.3.5: Standardized direct causal effects in the partially restricted model E .................................... 103 Table 3.3.6: Validity of hypotheses concerning the influencing variables .............................................. 104 Table 3.3.7: Validity of hypotheses concerning the moderating variables .............................................. 105 Table 3.3.8: Standardized total causal effects in the partially restricted models R and E ........................ 106 Table 3.3.9: Systematization of robustness-generating measures by means of their impacts ............................................ 107 Table 3.4.1: Determined parameter values for each constellation .... 110 Table 3.4.2: Average shares of dominating solutions, efficiency values and relative objective-achievement-degrees ...... 112 Table A.1: Order data ................................................................... 114 VI Table A.2: Capacity data ............................................................... 114 Table A.3: Parameters varied for MS ............................................ 114 Table B.1: Limitations in the unrestricted and partially restricted models ......................................................... 115 Table B.2: Standardized direct causal effects in the individually partially restricted model R ................ 116 Table B.3: Standardized direct causal effects in the individually partially restricted model E ................ 117 Table B.4: Harmonization of releases and its impact on model fits .................................................................... 119 Table C.1: Average efficiency values for an average CN-configuration and varying safety factor ................. 119 Table C.2: Average efficiency values for a predefined safety factor and varying costs for utilizing premium capacity ........................................................ 120 Table C.3: Average efficiency values for a predefined safety factor, predefined costs for utilizing premium capacity and varying shares of premium capacity ........ 120 Table D.1: Shares of dominating solutions, efficiency values and relative objective-achievement-degrees of DP-solutions (lower 0.5 quantile of DP-solutions’ efficiency values) .................................. 121 Table D.2: Shares of dominating solutions, efficiency values and relative objective-achievement-degrees of DP-solutions (upper 0.5 quantile of DP-solutions’ efficiency values) .................................. 121 VII List of abbreviations ad. adaptation AGFI Adjusted-Goodness-of-Fit-Index AP acceptance probability ATP available-to-promise B batch C cost minimization CCR Charnes-Cooper-Rhodes CMIN minimum discrepancy CN capacity nesting CS customer satisfaction maximization CTP capable-to-promise CTPM capable-to-promise model CV coefficient of variation D demand DEA Data Envelopment Analysis DF degrees of freedom DT delivery time minimization DP detected parameter E increased order-related uncertainty F formula-conditioned relation GFI Goodness-of-Fit-Index H hypothetical relation I intermediate variable L adaptation of delivery dates LP linear programming max. maximization MGA multi-group analysis min. minimization MIP mixed-integer programming VIII MS proposing modified order specifications MTO make-to-order MTS make-to-stock N no use of adaptation measures ns non-significant OV order volume maximization P profit maximization PC penalty costs PD partial deliveries PP production progressiveness maximization QPD demand quantity depending on price and delivery time R regular order-related uncertainty RM robustness maximization RT real-time rel. released res. restricted RMSEA Root Mean Square Error of Approximation S supply SC safety capacity TW time window U uncertainty WL workload maximization WO work overload minimization Z objective IX List of symbols Decision variables B inventory quantity C random variable of available capacity D delivery date J random variable of interarrival time K random variable of costs M quantity to be delivered P production quantity  random variable of price Q consumption quantity Q random variable of order quantity u auxiliary variable for linearization V deviation from requested delivery time interval/ contractually fixed delivery date y auxiliary variable for linearization Z acceptance decision    response function  auxiliary variable for tardy/ premature delivery  discount X Parameters a replenishment quantity b production coefficient e efficiency value eˆ average efficiency value C deterministic production capacity d number of allowed partial deliveries d  share of dominating solutions F probability distribution of available capacity G weighting factor delivery time deviation (premature delivery) H weighting factor discount (premature delivery) k cost ratio M weighting factor delivery time deviation (tardy delivery) MS shifting between order promising steps II and III N weighting factor discount (tardy delivery) p significance value q order quantity QI quality indicator QI average quality indicator kr index value of first externally procured material at current planning period z number of relevant criteria ZV objective value  sufficiently large number  acceptance probability r regression weight  penalty costs  upper limit of step interval in the response function  share of premium capacity  weighting function XI  chance constraint probability value  time span for revision of production decisions  capacity requirements per piece  mean value  product price  standard deviation  length of batch interval  robustness index  maximum discount  lead time deferral XII Indices and sets Indices c product configuration i orders ( 1,..., )i I l steps of customers’ response function ( 1,..., )l L P solution with detected parameters ( [1,..., ])P S r materials ( 1,..., )r R s included data sets ( 1,..., )s S t time periods ( 1,..., )t T Sets A order inquiries that arrived in the batch interval A order inquiries with a profit chance / currently acceptable orders Aˆ previously accepted, but not yet fulfilled orders A rejected or completely fulfilled orders A fulfilled orders A finally rejected orders A provisionally rejected orders / orders to be modified XIII Superscripts c contractually fixed cap capacity situation CP consecutive planning runs des desired delivery time interval e early FP finished product l late L inventory M manufacturing max maximum min minimum P premium capacity PD partial delivery pr planning run prev previous R material real realized compared to contractually fixed delivery date S standard capacity Tr transportation UL upper limit of desired delivery time interval 1 1 Motivation 1.1 Problem In economic research, the decision regarding order acceptance or rejection has been discussed for a long time1). For make-to-order (MTO) production the order ac- ceptance decision is an essential part of order promising which is characterized by in- teractive negotiations concerning order specifications with customers.2) Nowadays, the ability to define economically advantageous order specifications represents a key success factor for companies and can induce long-term competitive advantages. Thereby customers’ increasing request for shorter delivery times, more reliable com- pletion dates as well as high levels of flexibility in changing order specifications, have to be considered.3) MTO companies have a particularly high level of latitude for determining order specifications, since the majority of production decisions only have to be made after the receipt of an order inquiry4). Hence, the efficient design of order promising provides a high potential to fulfill growing customer requirements and to obtain a high degree of customer satisfaction in the long run. In this context, it should be noted that the interests of the company and customers do not necessarily have to correspond; accordingly, requested order specifications may partially remain unsatisfied. Due to prevailing conflicts between the involved negoti- ating parties, the establishment of compromises and trade-offs are consequently in the focus of interest.5) The company faces the challenge of balancing its own sched- ule with that of its customers. Furthermore, uncertainty concerning the future order and resource situation considerably complicates this problem6). Thereby, uncertainty 1) Cf. e.g. Adam (1969); Friedman (1956); Goodman/Baurmeister (1976); Jacob (1971); Laux (1971); Schwendiger (1979); Stark/Mayer (1971); Wallace/Daugherty (1987). 2) Cf. Mansouri et al. (2012), p. 25. 3) Cf. Grillo et al. (2016), p. 239; Mansouri et al. (2012), p. 25. 4) Cf. e.g. Seitz/Grunow (2016), p. 658. 5) Cf. Mansouri et al. (2012), p. 25. 6) For a distinction between order- and resource-related uncertainties see e.g. Choi et al. (2016), p. 382 and Vilko et al. (2014), p. 4. 2 is generally understood as the difference between information already available and information necessary to fulfill the task1). To offer order specifications which are reliable and competitive from the customer’s, as well as the company’s, point of view and thus meet the needs of both parties, irre- spective of existing uncertainty, this dissertation focuses on robust order promising. The term robustness, in general, describes the insensitivity of a system to random changes2). The following two robustness dimensions are used to clarify this term3): (1) planning robustness and (2) solution robustness. The term planning robustness is applied in case of dynamic decision fields (e.g. roll- ing planning)4). Receipts of customer inquiries, the non-availability of material, or in- ternal factors like machine failures, cause revisions of production or delivery date decisions; which usually involve additional costs5). In order promising, a high degree of planning robustness is present if plans are created in which the extent of plan revi- sions induced by order- and resource-related uncertainty is low6). A high degree of robustness is therefore achieved, from the customer’s point of view, if only a few ad- justments of promised order specifications are necessary. On the other hand, a high level of solution robustness is present if changes in the planning data have an insig- nificant effect on the planning objective7). In this case, uncertain planning data only causes small fluctuations in the company’s achievement of objectives (e.g. profit maximization, cost minimization, etc.), so that the long-term continuance of the company can be ensured through a high degree of solution robustness. 1) Cf. Galbraith (1973), p. 5. 2) Cf. Scholl (2001), p. 93. 3) An overview of additional robustness criteria can be found in Roy (2010), pp. 629 ff. 4) Cf. Kimms (1998), p. 355; Scholl (2001), pp. 108 ff. 5) Cf. Pujawan/Smart (2012), p. 2253; Sridharan et al. (1988), pp. 148 ff. 6) Cf. Kimms (1998), pp. 355 ff. 7) Cf. Herroelen/Leus (2004), p. 1602; Mulvey et al. (1995), p. 265. 3 In the literature, capable-to-promise (CTP) approaches are in particular proposed to support order promising in MTO production environments1). These approaches are generally used to determine reliable responses to customer inquiries based on the available resources2). Thereby, order receipts trigger a detailed verification whether the start of production can ensure an on-time delivery with regard to material and ca- pacity limitations. Thus, CTP approaches in general guarantee a high precision of or- der promises.3) According to the response time4) of the system, real-time and batch CTP approaches can be distinguished5): - In real-time approaches, customers receive a response immediately after the arri- val of their orders; - whereas a main characteristic of batch approaches is the initial collection of cus- tomer inquiries during a predefined time interval (batch interval). Planning of or- der acceptance, quantities to be delivered and/or delivery dates is done simultane- ously after the expiration of the time interval for all order inquiries which arrived during the past batch interval.6) The decision for/against one of the entitled modes needs to be made industry- specifically. In the present dissertation a batch approach, whose basic structure is visualized in figure 1.1.1, is chosen to support order promising. As visualized in the figure, in standard batch CTP approaches, decisions on the acceptance of orders ar- riving in the past batch interval, are made according to the principles of rolling plan- ning7) by taking into account available resources as well as orders accepted in a pre- 1) Cf. Kilger/Meyr (2008), p. 187. 2) Cf. Ball et al. (2004), p. 449. 3) Cf. Fischer (2001), p. 33; Jung (2010), p. 369; Kilger/Meyr (2008), p. 187. 4) Different classification approaches can for example be found in Ball et al. (2004), pp. 455 ff.; Framinan/Leisten (2010), pp. 3091 ff.; Jung (2010), pp. 369 ff.; Kilger/Meyr (2008), pp. 181 ff.; Pibernik (2002), pp. 349 ff. or Pibernik (2005), pp. 241 ff. 5) Cf. e.g. Ball et al. (2004), p. 456; Chen et al. (2001), p. 478; Chen et al. (2002), p. 425; Framinan/Leisten (2010), pp. 3083 f.; Jung (2010), p. 370; Jung (2012), p. 1780; Pi- bernik (2002), p. 351; Pibernik (2005), p. 242; Robinson/Carlson (2007), p. 283. 6) Cf. Ball et al. (2004), p. 456; Chen et al. (2001), p. 478; Chen et al. (2002), p. 425; Fra- minan/Leisten (2010), pp. 3083 f.; Pibernik (2002), p. 351; Pibernik (2005), p. 242. 7) Cf. Scholl (2001), pp. 33 f. 4 vious planning run. Thus, those of the previously accepted orders, which have not been completely fulfilled yet, need to be considered and therefore still influence pro- duction. The delivery dates and quantities for all orders are determined, wherein the revision of already taken production decisions is permitted. Due to the fact that the next planning run is not carried-out until the expiration of another batch interval, the production plan is fixed for the periods of the next batch interval but is only of pre- liminary nature for the remaining periods of the planning horizon. Figure 1.1.1: Basic structure of a batch CTP approach Outlining the basic idea of CTP approaches illustrates the fundamental suitability of these planning approaches for supporting order promising under uncertainty. In par- ticular, opportunities for revising taken decisions and consequently options, for end of planning horizon current period futurepast planned delivery dates and quantities of currently accepted orders (and previously accepted orders) Planning run in t irrevocable plan preliminary plan implemented plan fulfilled orders accepted orders, available resources, customer enquiries batch interval end of planning horizon current period futurepast planned delivery dates and quantities of currently accepted orders (and previously accepted orders) Planning run in t+1 irrevocable plan preliminary plan implemented plan fulfilled orders accepted orders, available resources, customer enquiries batch interval 5 adapting planning decisions to the change in uncertain environmental situations, are revealed. However, a largely unrestricted revision of decisions contradicts the in- tended robustness concept of order promising. Since basic options to implement an order promising, which is planning and solution robust at the same time, consist of integrating temporal and/or quantitative buffers or courses of action for possible events1), the identification and integration of problem-related adaptation measures is recommendable. For this reason, the aim of the present dissertation is to extend a standard batch CTP approach to a robust planning model by integrating and coordi- nating order- and resource-related adaptation measures to handle uncertainty. 1.2 State of the art 1.2.1 Capable-to-promise approaches Although the origin of CTP approaches is connected to statements made by Schwendinger in 19792), currently only a few quantitative CTP approaches exist3). A taxonomy of these approaches is presented in table 1.2.1. The applied criteria serve for revealing research focuses and deficits related to general characteristics of the approaches, the type of considered uncertainty, the consideration of order- and re- source-related measures to cover uncertainty and the interaction with customers. With respect to the general characteristics, the type of CTP approach can be consid- ered for classifying the approaches. Thereby a distinction between batch (B) and re- al-time (RT) approaches is made. The selection of a specific mode depends on the objectives and characteristics of the company being considered. 1) Cf. Herroelen/Leus (2004), pp. 1602 ff.; Seitz/Grunow (2016), p. 657; Vorst/Beulens (2002), p. 412. 2) Cf. Fischer (2001), p. 11. See Schwendinger (1979) for a definition of the closely related concept available-to-promise. 3) Cf. Chen et al. (2001), p. 478; Chen et al. (2002), p. 426; Gao et al. (2012), p. 773; Halim/Muthusamy (2012), p. 4535; Jung (2010), p. 369; Pibernik (2002), p. 354, Pi- bernik (2005), p. 240; Zhao et al. (2005), p. 68. 6 General characteristics Considered uncertainty Measures related to orders resources T yp e of C T P ap pr oa ch O bj ec ti ve SC s tr uc tu re O rd er -r el at ed R es ou rc e- re la te d O rd er r ej ec tio n D ev ia tin g or de r sp ec if ic at io ns R es ch ed ul in g R es ou rc e ne st in g Sa fe ty c ap ac it y In te ra ct io n w ith cu st om er s Aouam/Brahimi (2013) B C - x x x - - x x - Charnsirisakskul et al. (2004) B P - x - x x x - - - Charnsirisakskul et al. (2006) B P - x - x x x - - - Chen/Dong (2014) B P x x - x x x - x - Chen/Dong (2014) RT P x x - x x x x x - Chen et al. (2001) B P x x - x x x x - - Chen et al. (2002) B P x x - x x x - - - Chiang/Wu (2011) RT P - x - x - x x - - Gao et al. (2012) B P - x - x - x x - - Guillén et al. (2005) B P/CS x x - - x - - - o Halim/Muthusamy (2012) B C x x x x x x - x - Hempsch et al. (2013) B C/DT x x - o x x - - o Jeong et al. (2002) RT PP x x - x x x - - - Jung (2010) B C x x - o x x - - - Jung (2012) B C x x x o x x - x - Lečić-Cvetković et al. (2010) RT OV - x - x x x x - - Lim/Halim (2011) B RM x x x x x x - x - Lin et al. (2010) B P x x - x x x - - - Manavizadeh et al. (2013) B C/WO x x - x x x x - o Pan/Choi (2016) B C - x x o x x x - o Pibernik (2002, 2005) RT OV - x - x x - - - - Pibernik (2002, 2005) B P - x - x x - - - - Pibernik/Yadav (2008) RT OV - x - x - x x x o Renna/Argoneto (2010) RT P x x - - x x x - o Robinson/Carlson (2007) RT C - x - x - x - - - Seitz/Grunow (2016) RT P - x x x x x - - - Taylor/Plenert (1999) B OV - x - - - x - - - Wu/Liu (2008) B WL - x - x - x - - - Xiong et al. (2003) RT OV x x - - - x - - - Yang/Fung (2014) B P/OV x x - x x x - - - Zhao et al. (2005) B C - x - o x x - - - Table 1.2.1: Relevant modelling approaches (with x: considered, -: not considered, o: partially considered) 7 While response times to customer inquiries are shorter for real-time approaches, in- teractions between incoming orders can only be considered to a limited extent since order acceptance decisions are made separately. In case of periodic batch approaches, longer response times are tolerated in favor of capturing interdependencies between incoming orders.1) The particular suitability of the mode needs to be verified with re- spect to the regarded industry sector. Although a batch CTP approach is developed in the course of the dissertation, it is recommendable to simultaneously include real- time approaches into the literature review. The justification for the latter is that inde- pendently of the chosen mode, all described CTP approaches intend an availability- oriented support of order promising and consider different measures to cover uncer- tainty. Closely linked to the implemented mode are the objectives pursued in different pa- pers whereby both monetary (maximization of profit (P); minimization of costs (C)) and non-monetary (maximization of order volume (OV), workload (WL), production progressiveness (PP), robustness (RM) or customer satisfaction (CS); minimization of delivery time (DT), work overload (WO)) objectives are focused. The overview table reveals that batch approaches primarily aim at monetary objectives in the form of a single- or multi-criteria objective optimization. Solely non-monetary objectives can be found in the approaches of Taylor and Plenert2) as well as Wu and Liu3); whereby a maximization of the order volume and a high workload of the production system are intended. Furthermore, Lim and Halim are the only authors who explicitly pursue the non-monetary objective of robustness maximization by maximizing the certainty degree of the solution while ensuring a predefined aspiration level. Howev- er, economic implications of their procedure are not adequately taken into account.4) The partly algorithmized real-time approaches pursue monetary and non-monetary 1) Cf. Jung (2012), p. 1780. 2) Cf. Taylor/Plenert (1999), pp. 50 ff. 3) Cf. Wu/Liu (2008), pp. 2258 ff. 4) Cf. Lim/Halim (2011), pp. 302 f. 8 objectives in a balanced manner. Of particular note is that especially younger publi- cations aim at fulfilling monetary objectives1). Due to their cross-functional character, CTP approaches are suitable for capturing the multi-tiered nature of supply chains and allow for a better coordination between forecast-driven push-activities as well as order-driven pull-activities along the supply chain2). In the considered planning approaches, the specific structure of the supply chain is taken into account in different ways: According to Jung3), Hempsch et al.4) or Yang and Fung5) one possibility is to model product- or order-related production and transport flows which take place across multiple locations and may take time due to limited capacity availability. In a similar way, Chen and Dong6), Guillén et al.7) as well as Jeong et al.8) consider one sub-aspect of relations between goods in supply chains by examining product-related transports between multiple plants of a produc- tion company as well as various sales regions and distribution centers. Alternatively, multistage production processes are modeled by means of production coefficients in the approaches of Halim and Muthusamy9) as well as Lim and Halim10), whereby dif- ferent suppliers provide the individual components. Renna and Argoneto11) also in- corporate various suppliers during a multi-agent-based negotiating process, but do not capture the product structure. In contrast, Chen et al.12), Lin et al.13) as well as 1) See e.g. Chen/Dong (2014), Chiang/Wu (2011), Renna/Argoneto (2010) or Seitz/Grunow (2016). 2) Cf. Chen et al. (2001), p. 478; Gao et al. (2012), p. 771; Zhao et al. (2005), p. 66. 3) Cf. Jung (2010), pp. 371 ff.; Jung (2012), pp. 1786 ff. 4) Cf. Hempsch et al. (2013), pp. 27 ff. 5) Cf. Yang/Fung (2014), pp. 4255 ff. 6) Cf. Chen/Dong (2014), pp. 6719 ff. 7) Cf. Guillén et al. (2005), pp. 7407 ff. 8) Cf. Jeong et al. (2002), pp. 193 ff. 9) Cf. Halim/Muthusamy (2012), pp. 4536 ff. 10) Cf. Lim/Halim (2011), pp. 300 ff. 11) Cf. Renna/Argoneto (2010), pp. 75 ff. 12) Cf. Chen et al. (2001), pp. 480 ff.; Chen et al. (2002), pp. 427 ff. 13) Cf. Lin et al. (2010), pp. 722 ff. 9 Manavizadeh et al.1) take an individualized product structure for each order into ac- count which is based on bills of material and specifies components as well as poten- tial component suppliers or qualities. By additionally including lead times for each production stage, Xiong et al.2) apply a dynamic bill of material in their planning ap- proach and thereby allow for an easier estimation of the delivery date. However, this estimation ignores the influence of limited capacity on the lead-time and may there- fore cause infeasible plans. In addition to examining the general characteristics of relevant CTP approaches, the type of considered uncertainty is also investigated. Since, in the order-promising process, uncertainty is mainly caused by incoming orders and necessary production resources, the consideration of order- and resource-related uncertainty is focused. The analysis of relevant approaches reveals that almost all papers solely consider or- der-related uncertainty (e.g. in terms of uncertain order quantities, product configura- tions or delivery dates) and assume deterministic resource availability. In particular, the more realistic simultaneous consideration of order- and resource-related uncer- tainty is only done in the minority of approaches3). Due to the underlying robustness-oriented problem definition and the resulting need for taking into account the underlying uncertainty situation, the literature review con- sequently further focuses on adaptation measures considered to cover uncertainty. Thereby, emphasis is placed on the following order- and/or resource-related adapta- tion measures: - Order-related measures: - Rejection of orders - Deviation from requested order specifications (e.g. temporal, quantitative or qualitative) 1) Cf. Manavizadeh et al. (2013), pp. 2535 ff. 2) Cf. Xiong et al. (2003), pp. 136 ff. 3) Cf. Auoam/Brahimi (2013), p. 508; Halim/Muthusamy (2012), p. 4538; Jung (2012), p. 1782; Lim/Halim (2011), p. 302; Pan/Choi (2016), pp. 546 f.; Seitz/Grunow (2016), pp. 660 ff. 10 - Order- and resource-related measure: - Revision of production and delivery date decisions - Resource-related measures: - Resource nesting - Providing safety capacity Order-related adaptation measures refer to the order-driven pull-activities along the supply chain. In this context the rejection of orders is discussed as a first measure. If the fulfillment of customer inquiries is economically disadvantageous under the cho- sen objective, e.g. due to scarce production capacities and/or insufficient material availability, order inquiries are rejected in the multitude of papers. The following planning approaches are exceptions: - Analogously to Xiong et al.1), Taylor and Plenert2) include all incoming orders in the production plan. The afore-mentioned authors thereby consider the option to integrate alternative materials for order fulfillment by means of a bill-of-material explosion. - Guillén et al.3) also do not implement the possibility of rejecting order inquiries but chose offers from the set of Pareto-optimal combinations of order specifica- tions, which result from the considered divergent objective criteria named profit and customer satisfaction. - Renna and Argoneto4), Hempsch et al.5) as well as Pan and Choi6) develop strate- gies for avoiding order rejections within the scope of multi-agent-systems. In the paper of Renna and Argoneto, a supplier agent places counteroffers in each nego- tiation round as long as customers’ order specification requests cannot be fulfilled. In this process the decision about acceptance or rejection as well as the request of another counteroffer is up to the customer. Similarly, in the papers of Pan and Choi as well as of Hempsch et al. a negotiation agent places counteroffers which have to be evaluated in several negotiation rounds. Thereby, Pan and Choi reject 1) Cf. Xiong et al. (2003), pp. 138 ff. 2) Cf. Taylor/Plenert (1999), pp. 50 ff. 3) Cf. Guillén et al. (2005), pp. 7412 ff. 4) Cf. Renna/Argoneto (2010), pp. 75 ff. 5) Cf. Hempsch et al. (2013), pp. 33 ff. 6) Cf. Pan/Choi (2016), pp. 543 f. 11 customer inquiries after the expiration of a predefined negotiation period. In con- trast, Hempsch et al. only involve those order inquiries for which an insufficient contribution to objective achievement was determined by a CTP model and order rejection was recommended as a consequence. The need for avoiding final order rejection is based on the argumentation that rejected customers might turn to competitors and a permanent impairment of customer relationship might result1). - Furthermore, Jung2), as well as Zhao et al.3), intend to avoid order rejections by taking into account penalty costs for early or tardy (partial) delivery. Rejections only occur at the end of the planning horizon since options for further shifting or- ders no longer exist. Moreover, additional strategies to prevent negative consequences of order rejections are pointed out in the presented CTP approaches. Even though Pibernik4) and Jeong et al.5) implement the measure of order rejection, they demand for an examination of several options for action so that order rejection has to be seen as a last option. An al- ternative approach is proposed by Lečić-Cvetković et al.6) whereby inadequately ful- filled orders are assigned higher priority values for the next planning iteration to in- crease the probability of order fulfillment. Figure 1.2.1: Classification of order specifications 1) Cf. Hempsch et al. (2013), p. 31. 2) Cf. Jung (2010), pp. 371 ff.; Jung (2012), p. 1788. 3) Cf. Zhao et al. (2005), pp. 70 ff. 4) Cf. Pibernik (2002), pp. 365 ff.; Pibernik (2005), pp. 246 ff. 5) Cf. Jeong et al. (2002), p. 201. 6) Cf. Lečić-Cvetković et al. (2010), pp. 789 f. Order specifications Non-monetary Quantity Time Quality Monetary Basic price Payment arrangements Surcharges/ Discounts 12 Another order-related adaptation measure consists in deviating from requested order specifications. Basic options for implementing this measure can be derived from the classification of order specifications shown in figure 1.2.1. The deviation from non-monetary order specifications can thus occur with respect to quantity, time and quality. Investigating the considered quantitative CTP approaches reveals that in particular the options of quantitative and temporal deviation are wide- ly used. In the event of quantitative deviations, the alternatives of a complete or par- tial deviation from the requested order quantity are implemented. While a lower quantity than requested is delivered in case of complete quantitative deviation1), mul- tiple partial deliveries, for which a minimum quantity per delivery can be described2), take place in the event of partial deviations3). To limit the occurrence of quantitative deviations, some approaches additionally consider penalty costs if requested order quantities are not met4). Analog options of complete or partial deviations exist in the temporal dimension. In the first-mentioned case the (in)complete quantity is deliv- ered at a deviating delivery date5), whereas a partial deviation from the requested de- livery date is present in the second case since (un)punctual sub-quantities are deliv- ered6). Thereby, the alternatives of a quantitative/temporal deviation are considered 1) Cf. Charnsirisakskul et al. (2006), pp. 156 ff.; Chen et al. (2001), pp. 480 ff.; Chen et al. (2002), pp. 427 ff.; Halim/Muthusamy (2012), p. 4536; Lečić-Cvetković et al. (2010), pp. 786 ff.; Lim/Halim (2011), p. 301; Lin et al. (2010), pp. 724 ff.; Pibernik (2002), p. 365; Pibernik (2005), pp. 246 ff.; Renna/Argoneto (2010), pp. 76 ff.; Seitz/Grunow (2016), p. 663; Yang/Fung (2014), pp. 4255 ff. 2) Cf. Pibernik (2002), pp. 359 ff.; Pibernik (2005), pp. 244 ff. 3) Cf. Charnsirisakskul et al. (2004), pp. 699 ff.; Chen/Dong (2014), pp. 6722 ff.; Jung (2010), pp. 371 ff.; Jung (2012), pp. 1782 ff.; Zhao et al. (2005), pp. 69 ff. 4) See e.g. Charnsirisakskul et al. (2006), pp. 156 ff.; Chen/Dong (2014), pp. 6722 ff.; Ha- lim/Muthusamy (2012), p. 4536 ; Lim/Halim (2011), p. 301. 5) Cf. Charnsirisakskul et al. (2006), pp. 156 ff.; Chen et al. (2001), pp. 480 ff.; Guillén et al. (2005), pp. 7412 ff.; Hempsch et al. (2013), pp. 35 ff.; Jeong et al. (2002), pp. 196 f.; Pan/Choi (2016), pp. 539 ff.; Renna/Argoneto (2010), pp. 77 f.; Seitz/Grunow (2016), p. 659; Yang/Fung (2014), pp. 4255 ff. 6) Cf. Charnsirisakskul et al. (2004), pp. 699 ff.; Chen/Dong (2014), pp. 6722 ff.; Jung (2010), pp. 371 ff.; Jung (2012), pp. 1782 ff.; Manavizadeh et al. (2013), pp. 2534 ff.; Pibernik (2002), pp. 359 ff.; Pibernik (2005), pp. 244 ff.; Zhao et al. (2005), pp. 69 ff. 13 with and without adherence to given intervals of accepted deviations from the re- quested date and/or quantity1). In addition to the so far examined deviations from non-monetary order specifica- tions, the option of deviating from the requested product quality further exists. Chen and Dong consider qualitative deviations by substituting specified products up to a maximum quantity defined by the customer and by taking into account penalty costs2). Analogously, Pibernik permits access to substitute products provided that on- ly insufficient quantities of requested products are available at the selected location3). Deviations from the requested quality are alternatively modeled by involving substi- tute components. Thus, Chen et al. define a customer-specific set of suppliers from whom substitute components may be ordered if necessary4). Accordingly, Lin et al. as well as Manavizadeh et al. model deviating product qualities by considering alter- native bills of material5). Besides the previously mentioned options, Hempsch et al. make offering value-added services a subject of discussion. Thereby, the authors em- phasize that this qualitative adaptation measure provides the opportunity to compen- sate for a tardy delivery and/or reduced order quantity and thus can increase custom- er satisfaction6). On the monetary level, the following order specifications can be distinguished: basic price, surcharges (e.g. obligatory fees, service charges) / discounts and payment ar- rangements (e.g. payment deadlines, means of payment, interest, debt retirement). However, additional fees or payment arrangements are primarily investigated in marketing (e.g. drip pricing, partitioned pricing) as well as financial literature and 1) Delivery time intervals are for example specified by the customers in Charnsirisakskul et al. (2004), pp. 699 ff.; Charnsirisakskul et al. (2006), pp. 156 ff.; Chen et al. (2001), pp. 480 ff.; Guillén et al. (2005), pp. 7412 ff.; Pibernik (2002), pp. 359 ff.; Pibernik (2005), pp. 244 ff. or Yang/Fung (2014), pp. 4255 ff. 2) Cf. Chen/Dong (2014), pp. 6722 f. 3) Cf. Pibernik (2002), pp. 365 ff.; Pibernik (2005), pp. 246 ff. 4) Cf. Chen et al. (2001), pp. 480 ff. 5) Cf. Lin et al. (2010), pp. 724 ff.; Manavizadeh et al. (2013), pp. 2533 ff. 6) Cf. Hempsch et al. (2013), p. 32. 14 are not in the focus of this dissertation.1) Instead, basic price, potential surcharg- es/discounts or payment arrangements are considered to be aggregated in the product price. Sole exception from this aggregation is a deviation from the product price which compensates the customer’s loss of utility induced by deviations from request- ed non-monetary order specifications. Consequently, the literature review of CTP approaches focuses on such deviations from the product price. So far, this adaptation measure has been increasingly used in negotiations with customers: - Guillén et al. develop a negotiating process for determining delivery-date-price combinations, which represent compromises made from the customers’ and com- pany’s point of view. For this purpose, both negotiating partners specify starting prices, which represent preferred sales or purchase prices and customarily define the upper/lower limit of the finally negotiated price.2) - Renna and Argoneto, Hempsch et al. as well as Pan and Choi negotiate product prices in multi-agent-systems. While the first-mentioned authors place counterof- fers in terms of alternative delivery-date-quantity-price combinations3), Hempsch et al. derive counteroffers e.g. utilizing reduced prices, offering value-added ser- vices or reducing delivery time4). In contrast, Pan and Choi model a two-stage ne- gotiating process whereby the due date is negotiated at the first stage. Accrued in- termediate losses of one negotiating partner are compensated at the second stage while determining the corresponding price.5) Furthermore, Charnsirisakskul et al. propose an approach which customizes product prices by allocating individual prices to customers according to the corresponding order quantity and delivery time. Thereby, the price accepted by the customer is modeled in accordance with the maximum willingness to pay.6) Additionally, Manav- izadeh et al. implement an option for deviating from requested monetary order speci- 1) Cf. e.g. Bertini/Wathieu (2008), pp. 237 ff.; Carlson/Weathers (2008), pp. 724 ff.; Greenleaf et al. (2016), pp. 106 ff.; Pesch (2010), pp. 217 ff.; Robbert/Roth (2014), pp. 413 ff. 2) Cf. Guillén et al. (2005), pp. 7412 f. 3) Cf. Renna/Argoneto (2010), pp. 75 ff. 4) Cf. Hempsch et al. (2013), pp. 34 ff. 5) Cf. Pan/Choi (2016), pp. 542 ff. 6) Cf. Charnsirisakskul et al. (2006), pp. 156 f. 15 fications by granting discounts depending on the order volume and the chosen prod- uct configuration.1) In contrary to the exclusively order-related adaptation measures, the option of revis- ing production and delivery date decisions simultaneously relates to orders and re- sources. This measure acknowledges the fact that it is not possible to completely cover the uncertainty emerging during the order promising and fulfillment process from an economic stand point. Rather, it must be assumed that in the course of order fulfillment, revisions of production and delivery date decisions are induced by order and/or resource-related uncertainty. The majority of current CTP approaches consid- er this aspect with respect to production decisions2). The opportunity of revising pre- vious contractually fixed-delivery-dates is only occasionally discussed; although this measure can be economically advantageous if currently present lucrative orders can thus be accepted3). Resource-related adaptation measures refer to forecasting-driven push activities of a supply chain. In general, the option of resource nesting serves for allowing only lu- crative orders to get access to a predefined share of resources. If such orders are not present in the current planning situation, the reserved resources can be used for ful- filling future, as yet unknown lucrative orders. For the adaptation measure, a differ- entiation needs to be made between limiting access to consumable (e.g. materials) as well as to non-consumable (e.g. capacity) resources. In CTP approaches, Chen et al. implement nesting of consumable resources by reserving a certain level of compo- nents necessary for producing future lucrative orders4). Chen and Dong as well as Gao et al. simultaneously impede access to consumable and non-consumable re- sources. Taking into account penalty costs, Chen and Dong only allow highly priori- 1) Cf. Manavizadeh et al. (2013), pp. 2534 ff. 2) See e.g. Chiang/Wu (2011), pp. 764 ff.; Lin et al. (2010), p. 724; Pibernik/Yadav (2008), p. 602 or Zhao et al. (2005), p. 72. 3) See e.g. Seitz/Grunow (2016), p. 666. 4) Cf. Chen et al. (2001), p. 481. 16 tized orders to utilize reserved production capacity and needed components1). In con- trast, Gao et al. consider pseudo orders for reserving resources for potential lucrative orders2). On the other hand, Aouam and Brahimi3), Chiang and Wu4), Lečić-Cvetković et al.5), Manavizadeh et al.6), Pan and Choi7), Pibernik and Yadav8) as well as Renna and Argoneto9) implement strategies for nesting of non-consumable resources. For example, Chiang and Wu design a dynamic capacity-rationing strategy to protect ca- pacity for high-prioritized orders. In contrast, Renna and Argoneto, Manavizadeh et al., as well as Pan and Choi, reserve resources by distinguishing between the capacity utilization costs in case of standard and over working time. Besides resource nesting, providing safety capacity is also related to the resources of the production process. Due to a conservative capacity estimation, only as much ca- pacity is involved in the planning process as necessary to fulfill capacity constraints according to a predefined probability level. In the context of present CTP approach- es, Aouam and Brahimi, Lim and Halim, Halim and Muthusamy as well as Pibernik and Yadav, consider a corresponding idea by formulating service level constraints for meeting capacity restrictions10). Analogously, Jung models providing safety ca- pacity by reducing the actual available capacity for planning purposes according to a predefined factor11). In contrast, Chen and Dong develop a separate pre-allocation model for determining the level of required safety capacity aiming at being able to 1) Cf. Chen/Dong (2014), pp. 6724 ff. 2) Cf. Gao et al. (2012), pp. 773 ff. 3 Cf. Aouam/Brahimi (2013), pp. 509 ff. 4) Cf. Chiang/Wu (2011), pp. 767 ff. 5) Cf. Lečić-Cvetković et al. (2010), pp. 786 ff. 6) Cf. Manavizadeh et al. (2013), pp. 2535 ff. 7) Cf. Pan/Choi (2016), pp. 537 ff. 8) Cf. Pibernik/Yadav (2008), pp. 594 ff. 9) Cf. Renna/Argoneto (2010), p. 79. 10) Cf. Aouam/Brahimi (2013), pp. 507 ff.; Halim/Muthusamy (2012), pp. 4538 f.; Lim/Halim (2011), pp. 302 f.; Pibernik/Yadav (2008), pp. 598 ff. 11) Cf. Jung (2012), pp. 1790 ff. 17 handle differences between the forecasted and actually incoming demand of the next period1). In addition to order- and/or resource-related adaptation measures, the interaction with customers is discussed in the following. The previous literature review has re- vealed that customer behavior and customers’ responses to proposed order specifica- tions influence the order promising process in a decisive manner. Nevertheless, basic concepts for considering the interaction with customers can so far only be detected in the following approaches: - In the context of model tests Pibernik and Yadav consider an order placement probability which decreases with increasing deviation from the requested delivery date. The impacts of different courses of this function are analyzed during their model tests.2) - Manavizadeh et al. also assume that not all customer inquiries are produced with certainty. Due to this reason, they take into account the customer’s acceptance probability, which is evaluated based on previous data and market studies, and solely capture the expected work load of an order. The specific resource allocation is only done after the proposed order specifications are accepted by the customer.3) - Renna and Argoneto model customer behavior in a multi-agent-based negotiating process by using an additive utility function which reflects the degree of customer satisfaction as percentage difference between requested and offered specifications. Counteroffers are accepted as long as they exceed a calculated utility threshold value. Thereby, counteroffers are determined based on decisions previously made about potential production alternatives.4) In a comparable way, Hempsch et al. model potential customer responses by means of conditional utility functions. Based on the results of a CTP model, counteroffers are adjusted within each round of an isolated negotiating process.5) Moreover, Pan and Choi implement an inter- 1) Cf. Chen/Dong (2014), pp. 6719 ff. 2) Cf. Pibernik/Yadav (2008), pp. 608 f. 3) Vgl. Manavizadeh et al. (2013), pp. 2537 ff. 4) Cf. Renna/Argoneto (2010), pp. 75 ff. 5) Cf. Hempsch et al. (2013), pp. 39 ff. 18 active negotiating process between a manufacturer agent and a supplier agent whose behavior is modeled by means of non-linear utility functions.1) - Guillén et al. include interaction with customers by intending to find a trade-off between the objectives of maximizing profit and customer satisfaction. For esti- mating customers’ responses, scoring functions are used which are approximated by means of linear functions to capture the deviation from the requested delivery date or product price. The resulting satisfaction values are assumed to be inde- pendent of each other and are thus aggregated to a total value using an additive function.2) 1.2.2 Identification of research gaps In an entire view, the state of the art reveals that quantitative CTP approaches, suita- ble to support order promising in an uncertain environment, have already been pro- posed in the literature. Thus, the following tendencies concerning main research fo- cuses can be derived: - Approaches for less complex supply chain structures are predominantly formulat- ed. Flows of goods and information between the stages of the supply chain are on- ly captured occasionally and in aggregated form. - Often a production-oriented perspective is chosen in the approaches. Customers’ perspectives are neglected in most cases. - Adaptation measures for handling upcoming uncertainty are integrated in the planning approaches. Most commonly adaptation measures are implemented which either focus order- or resource-related uncertainty. -- Widely used order-related adaptation measures are the rejection of order in- quiries, as well as temporal and/or quantitative deviations from requested or- der specifications. However, expected customer responses to these measures are ignored most of the time. -- As a resource-oriented measure, resource nesting is increasingly addressed in the literature. In the CTP context providing safety capacity so far has only been investigated in a few approaches. 1) Cf. Pan/Choi (2016), pp. 542 ff. 2) Cf. Guillén et al. (2005), pp. 7412 ff. 19 -- Currently very few approaches take both sources of uncertainty into account. Detailed, situation-specific analyses of interactions between adaptation measures therefore hardly exist. In summary, research is required with regard to the following thematic fields: - interaction with customers during order promising; - consideration of multiple adaptation measures to simultaneously cover order- and resource-related uncertainty; - analysis of measure interactions, as well as - coordination of parameter values of the measures. To some extent, initial ideas for fulfilling required research are already available in the current literature. But although some papers exist, which include interactions with customers, central aspects remain yet to be considered: - Pibernik and Yadav capture customer behavior solely in the course of model tests. Thereby, the authors neglect the opportunity to directly incorporate information about customer feedback in the planning approach.1) - Manavizadeh et al. directly consider the customer’s acceptance probability in the decision model. However, interactions between order specifications to be deter- mined and the customer’s acceptance probability are not explicitly captured.2) - Analogously, Renna and Argoneto do not directly use customer feedback infor- mation when generating production alternatives. Instead, production is planned separately before counteroffers are derived based on these plans. However, au- thors do not explain to which extent empirical evidence is available for customer behavior modeled by means of utility functions in this process.3) - In analogy to Renna and Argoneto, Hempsch et al. develop a multi-agent-based negotiating process using utility functions. Again this process is not directly con- sidered in the CTP model, but counteroffers are rather adjusted in each round of the negotiating process. Since customer response is consequently not anticipated 1) Cf. Pibernik/Yadav (2008), pp. 608 f. 2) Cf. Manavizadeh et al. (2013), pp. 2533 ff. 3) Cf. Renna/Argoneto (2010), pp. 75 ff. 20 in the planning model itself, reorganizations of the entire supply chain follow suc- cessful negotiations.1) - Pan and Choi capture interactions between a manufacturer and a supplier within the scope of a multi-agent-system. Thereby, order specifications required by the customer are considered in the manufacturer’s negotiating model, but direct inter- action with the customer does not occur.2) - Guillén et al. directly incorporate customer behavior in their planning approach. Thereby, the authors assume an independency of satisfaction values which result from differences between requested and offered delivery dates or product prices.3) Opportunities to compensate for multiple deviations from desired specifications therefore remain unconsidered. Additionally, due to the chosen multi-objective optimization approach, immediate impacts of satisfaction values on the profit are not captured in the decision model. It therefore appears that a stronger connection between production and customer per- spective is to be pursued to meet the objectives and needs of both, company and cus- tomer. Customer’s response to suggestions of order specifications needs to be direct- ly anticipated during the order promising process in order to avoid subsequent revi- sions of production and order specification decisions. Further research is also required regarding the analysis of measure interactions. Cur- rently, the majority of approaches either take measures for covering order-, or re- source-related uncertainty into account so that the effectivity of proposed measures is often only proved in isolated analyses. However, in general, it cannot be assumed that measure impacts, induced by multiple sources of uncertainty, unfold inde- pendently. Nevertheless, interactions between considered measures have been only occasionally investigated so far: - Chen and Dong analyze their planning approach, with respect to a combined ap- plication of designed adaptation measures, based on different constellations of measure parameters. Key figures of the analysis are the overall profit, the order 1) Cf. Hempsch et al. (2013), pp. 39 ff. 2) Cf. Pan/Choi (2016), pp. 535 ff. 3) Cf. Guillén et al. (2005), pp. 7412 ff. 21 fulfillment rate as well as the profit contribution of each unit of production capaci- ty/components.1) - Chen et al. study the effects of varying batch interval lengths and of implementing their material reservation strategy, whereby the tangible (no record of penalty costs) profit, the overall profit as well as costs for order rejection, are chosen as key figures. Interactions are analyzed by generating scenarios with different batch interval lengths, in case of varying material scarcity as well as permitted ranges of the delivery date interval.2) - Pibernik and Yadav deduce indications for an economically advantageous specifi- cation of measure parameters by extensively analyzing their planning approach. Thereby, they primarily concentrate on the key figures of the achieved service levels for high-prioritized orders, as well as fulfillment rates of required delivery dates for low/high prioritized orders and the whole system.3) - Renna and Argoneto analyze the adaptation measures implemented in the multi- agent-system with respect to the average customer/supplier benefit as well as the unbalanced profit between the suppliers; which is defined as the difference be- tween profits at most and at least achieved by suppliers. Purpose of the analysis is less an analysis of interactions between implemented measures, but rather the de- duction of a performance estimation of an e-marketplace with different dynamic framework conditions.4) Consequently, it has to be concluded that to some extent analyses of interactions be- tween order- and resource-related adaptation measures have already been performed. But in an entire view, these analyses concentrate on a sub-quantity of identified ad- aptation measures and mainly focus on profit as well as cost effects. Impacts on the robustness of planning results are only occasionally addressed5). As soon as multiple adaptation measures are applied in a combinative way and com- pany-specific objectives are simultaneously pursued, apart from a pure analysis of 1) Cf. Chen/Dong (2014), pp. 6730 ff. 2) Cf. Chen et al. (2001), pp. 484 ff. 3) Cf. Pibernik/Yadav (2008), pp. 604 ff. 4) Cf. Renna/Argoneto (2010), pp. 81 ff. 5) See e.g. Aouam/Brahimi (2013), p. 509; Lim/Halim (2011), p. 303; Seitz/Grunow (2016), pp. 665 ff. 22 measure interactions, the deduction of findings concerning objective-oriented meas- ure coordination becomes obligatory. Since analyses related to existing interactions have been only occasionally focused in the literature, there is a substantial need for further research regarding the downstream coordination of measures. In particular, there is a need for extending previous research results with respect to suggesting measure parameters; which may contribute to accomplish the robustness-oriented ob- jective of a company in case of a combined measure application. In an entire view, the following research-leading questions result from the identified research gaps: - Which measures for handling order- and resource-related uncertainty are suitable for being integrated in a CTP model, if a high level of robustness and high profit- ability are strived for during order promising? - How can customers’ responses to order specifications suggested by the company be stronger focused at the same time? - How do these measures need to be coordinated with respect to the objectives of robustness and profit, taking into account their interactions? 1.3 Objective and approach The objective of this dissertation is to develop and analyze an extended batch CTP approach which helps to guarantee a high level of robustness of planning results from the customer’s and company’s point of view, as well as a high level of profitability. Figure 1.3.1: Basic structure of the dissertation 2) Tactical decision-making Ex ante parameterization of order- and resource-related adaptation measures 1) Operative decision-making Design of a decision model with order- and resource-related adaptation measures for supporting robust order promising 23 To achieve this overall aim, a hierarchical procedure has been chosen which can be divided into an operative and a tactical section according to the influence on decision making (cf. figure 1.3.1). In accordance with the operative character of the order promising process as a first step, an existing standard batch CTP approach is extended by robustness generating adaptation measures which are suitable for handling order- and resource-related un- certainty. In addition to adaptation measures already established in literature, a new adaptation measure for directly considering customer interaction during planning is thereby focused. Since considered adaptation measures cannot be assumed to unfold their impacts independently, their coordination is required with respect to the objec- tives of profitability, as well as planning and solution robustness. As a consequence, on the tactical level of decision-making, there is a need for ex ante coordinating order- and resource-related adaptation measures to balance the trade-off between the considered objectives. For this purpose, a detailed analysis of interac- tions between previously identified measures is substantial. Therefore, the aim of the tactical level is to recommend situation-specific combinations of measure parame- ters; which are judged to be economically advantageous with respect to balancing profitability as well as planning and solution robustness. Hence, it is not only intend- ed to measure robustness of order promising but also to control robustness impacts. This hierarchical procedure is successively developed within the following three pa- pers of the cumulative dissertation. In the second chapter, the robustness-oriented CTP approach is designed in the course of the first two papers to support the opera- tive decision process: Section 2.1 provides the first paper, in which a basic CTP model is developed in con- formity with assumptions common in CTP literature. To obtain first insights into the general behavior of the model, as well as into the impacts of different adaptation measures, only the presence of order-related uncertainty has been assumed. Analo- 24 gously to the wide-spread argumentation of assuming certain resources due to the short-term character of operative planning1), resource availability is supposed to be deterministic. Given these central conditions, the advantageousness of the established measures of quantitative deviation from order specifications (partial deliveries), as well as capacity nesting, is herein investigated. Furthermore, customer responses to order specifications, which deviate from requested delivery dates (proposal of deviat- ing delivery dates), are directly integrated into the planning approach. Following Pibernik and Yadav (2008), a discrete function is modeled capturing the fact that customer’s acceptance probability decreases with an increasing deviation from the desired delivery date. The first paper is therefore structured as follows: Subsequent to a short introduction to the problem (2.1.1), the basic model is developed based on the batch CTP ap- proach of Chen et al. (2002). Thereby, the approach is successively extended by the adaptation measures of partial deliveries, capacity nesting as well as proposing devi- ating delivery dates (2.1.2). The impacts of these measures on solution times, profits, capacity utilization as well as planning robustness are subsequently analyzed during a numerical analysis (2.1.3). Planning robustness is quantified by means of a robust- ness measure developed according to Kimms (1998), which captures the extent of production plan adjustments made during planning. The main results, as well as fur- ther research needs, are finally summarized in a conclusion of the first paper (2.1.4). The results of the first paper reveal the fundamental suitability of the planning ap- proach for supporting the robustness-oriented objective. In particular the interaction with customers has always been advantageous from an economic stand point, where- as the advantageousness of the remaining measures strongly seemed to depend on the choice of measure parameters. However, as further research is required regarding the impact of different sources of uncertainty, results need to be verified for a simultane- ous incorporation of uncertainty related to orders and resources. Due to previous framework conditions, delivery dates have always been met in the model experi- 1) See e.g. Ball et al. (2004), p. 449; Chen et al. (2001), p. 480. 25 ments of the first paper so that robustness was only considered with respect to pro- duction decisions but not to customer requirements. A more differentiated view of the robustness concept therefore needs to be established in further research work. Concerning the individual measure impacts on robustness, it became apparent that the option of partial deliveries can enhance planning robustness, whereas, under the given conditions, the remaining measures may have negative impacts on robustness. Nevertheless, further investigations indicated that proposing deviating delivery dates as well as capacity nesting are probably advantageousness in situations with uncer- tain production resources. Based on the results obtained in the first paper, in section 2.2 an extension of the basic CTP model is made within the scope of the second paper. Thereby, the simul- taneous occurrence of order- and resource-related uncertainty is assumed. To further increase the authenticity of the decision model and to allow for a more differentiated consideration of the robustness concept, revisions of previous contractually fixed- delivery-date decisions are permitted. Due to the changes in environmental condi- tions, the selection of adaptation measures, suitable for handling uncertainty, was critically scrutinized: To take account of resource-related uncertainty, following Pibernik and Yadav (2008) or Charnes and Cooper (1959), the adaptation measure of providing safety capacity is modeled besides capacity nesting. Furthermore, the iden- tified high economical potential of customer interaction as well as assumed positive impacts on robustness unfolding in the event of resource-related uncertainty, substan- tiate the ongoing consideration of proposing deviating delivery dates. In contrast, the quantitative deviation from order specifications (partial delivery) is no longer stud- ied, since the functionality of this measure is similar to that of proposing modified delivery dates. In case of partial deliveries, the delivery date is modified for part of the order. Thereby, it is assumed that customers certainly accept this modified deliv- ery date, and the high potential of an explicit interaction with customers is not con- sidered. Since the effectiveness of proposing deviating delivery dates, capacity nesting and proving safety capacity so far has only been proven in isolated analysis, the aim of the second paper is to examine measure interactions with respect to the objectives of 26 profitability as well as planning and solution robustness. For this purpose, the second paper is structured as follows: After a short introduction to the problem (2.2.1), a de- tailed explanation of the underlying planning situation is provided in the second sec- tion (2.2.2). Thereby, the considered planning object is discussed before the structure of the developed planning approach is further specified. Based on these insights, a decision model is developed in the course of the third section (2.2.3); which takes in- to account the robustness-generating measures capacity nesting, proposing deviating delivery dates as well as providing safety capacity. Another research focus of the pa- per is placed on the subsequent extensive numerical analysis (2.2.4). Following an initial clarification of the overall procedure, the underlying test data is revealed and scenarios to be analyzed are deduced. In total, there are 3,960 test constellations which have been studied with respect to generated profits as well as production and solution robustness. The mentioned robustness criteria are measured by means of the pursuing indicators: (1) In the form of penalty costs, weighted average deviations be- tween contractually fixed and reached delivery dates serve for quantifying robustness from the customer’s point of view (planning robustness)1). (2) In contrast, robustness from the company’s point of view (solution robustness) is captured by comparing coefficients of variation of generated profits along with input data (order/capacity da- ta). Subsequent to the presentation and interpretation of test results, the paper closes with a summarizing conclusion (2.2.5). Analyzing the extended planning approach reveals that, as expected, order- and re- source-related measures are not able to completely cover uncertainty from an eco- nomic stand point. However, an advantageous area is identifiable within which prof- itability, as well as planning and solution robustness, can be simultaneously in- creased by applying adaptation measures in a coordinated way. Since outside the ad- vantageous area, there is a trade-off between the objectives of profitability and ro- bustness, an essential need for research becomes apparent concerning the necessity of coordinating the measures. An isolated investigation of integrated measures fur- 1) Cf. Sridharan et al. (1988), pp. 148 ff. 27 ther indicates that, in particular, the measure of proposing deviating delivery dates is suitable for increasing and stabilizing generated profits. These research results con- sequently motivate further investigations corresponding to the interaction between customer and company. Taking into account the results of the second paper, the measure of proposing deviat- ing delivery dates is at first generalized in the third paper to meet the identified high potential of this measure. While only customers’ responses to deviating delivery dates were anticipated in the previous contributions, the current aim is to extend the measure by a dynamic time-related price differentiation1). Consequently, the measure of proposing deviating order-specifications relates to the dimensions delivery time and price. The remaining measures of capacity nesting and providing safety capacity are still taken into account without any changes. Apart from the outlined extension of the operative CTP model, the last paper additionally focuses the design of the super- ordinate tactical level of decision-making. Ex-ante parameter recommendations shall be derived for coordinating the measures with respect to the objectives of profitabil- ity as well as planning and solution robustness by means of a statistically substantiat- ed procedure. The following structure of the third paper has been chosen to achieve these aims: Subsequent to the explanation of the underlying problem (3.1.1), a literature review is given (3.1.2) before the research focus of the paper is summarized (3.1.3). Subse- quently, the previous operative planning model is extended by the generalized meas- ure of proposing deviating order specifications (3.2). Thereby, the underlying plan- ning situation is described first (3.2.1), before assumptions made during modeling price- and delivery-date-dependent customer behavior are substantiated (3.2.2). The focus of the next section is on resulting implications for the planning model (3.2.3). The remainder of the paper addresses the tactical level of decision-making, whereby the aim of deriving situation-specific recommendations for choosing measure param- eters is pursued. Due to previous results of model experiments, it cannot be assumed 1) For dynamic time-related price differentiation see e.g. Talluri/Ryzin (2005). 28 that the complex causal relations between the measures can be completely identified by means of a deductive analytical procedure. Therefore, an inductive statistical pro- cedure has instead been chosen. For this reason, a parameterization model is de- signed in the third section of the contribution (3.3) which applies the statistical meth- od of structural equation modeling, or more precisely, of path analysis. In this con- text, first of all, a suitable multi-group path model as well as corresponding research hypotheses are derived (3.3.1). For the subsequent estimation of the developed path model (3.3.2), quantifying measure impacts with respect to the objectives is inevita- ble. One possibility for this quantification is to optimize the CTP model of the opera- tive decision level in an extensive numerical study, whereby systematically- generated parameter combinations (24,000 constellations) are tested, and to record realized values of the objective values. Details of this procedure are presented while describing the resulting data basis of the multi-group path model (3.3.2.1). Based on the corresponding data basis, and the subsequent application of the multi-group path model, research hypotheses are verified (3.3.2.2). Obtained findings are afterwards used to deduce recommendations for a multi-criteria setting of measure parameters (3.4). For this purpose, a limited search for advantageous parameter combinations is proposed (3.4.1), before the quality of suggested parameter values is evaluated (3.4.2). Final conclusions summarize the main results of the paper (3.5). After presenting the individual papers, the dissertation concludes with an overall summary in which given answers to initially formulated research questions are criti- cally discussed and starting points for further research are pointed out. Thereby, the extent of how the identified adaptation measures can contribute to an enhancement of robustness from the customer’s and company’s point of view, is reviewed. In particu- lar, the focus lies on the intended concentration on the customer’s perspective by evaluating the potential of proposing modified order specifications while simultane- ously anticipating customers’ responses. Critically summarizing the analysis of measure interactions, the derived procedure for coordinating the adaptation measures is subsequently examined. Finally, the dissertation concludes with an illustration of options for further extending research directions. 29 2 Approaches 2.1 Basic approach with order-related uncertainty1) Abstract: Increasing production requirements have strengthened the academic inter- est for planning approaches that generate reliable delivery promises. An extended batch capable-to-promise approach is presented in this paper which includes preven- tive and reactive measures to increase planning robustness. We extend existing ap- proaches by considering both, proposals for delivery dates that deviate from the orig- inal order specifications and customers’ reactions to these modifications, in the mod- el. To verify the impacts of the extended planning approach it is numerically an- alyzed on the basis of real-world data of a manufacturer of customized leisure prod- ucts. 2.1.1 Introduction In the literature different capable-to-promise approaches are suggested to generate relevant information for reaching agreements on delivery dates with customers. Usu- ally a production-oriented perspective is chosen, while customers’ reactions on sug- gested delivery dates and their adherence are often ignored. Paying attention to these two aspects more reliable statements about feasible delivery dates already can be given in the contract award process. Furthermore, deviations from promised delivery dates can yet be minimized in the order fulfillment process. As a result a higher cus- tomer satisfaction and loyalty is attainable in the long run. Therefore, the aim of this paper is to extend an existing capable-to-promise approach (Chen et al. 2002) in such a way that it allows for meeting promised delivery dates and quantities to the greatest possible extent even though uncertain environmental situations (e.g. order situation) might occur. 1) Gössinger, R.; Kalkowski, S.: Order promising - A robust customer-oriented approach, in: Logistics Management. Products, Actors, Technology - Proceedings of the German Academic Association for Business Research, Bremen 2013, ed. by J. Dethloff et al., Cham et al. 2015, pp. 135-149. To ensure consistency, notations were adapted to disser- tation style. 30 Capable-to-promise (CTP) approaches generalize available-to-promise (ATP) ap- proaches that determine whether customer orders can be fulfilled, at which delivery date and in what quantity. In particular the generalization consists in the integration of additional information about capacities and intermediate product inventories in multi-stage production systems (Pibernik 2005). The existing CTP approaches can be classified according to the criteria and characteristic values represented in figure 2.1.1. Criterion Characteristic value Trigger of the planning process incoming order (real-time) defined time interval (batch) Objective economic technical profit max. cost min. max. order ac- ceptance min. due date deviation max. workload Order rejection not considered considered Deviation from order conditions not considered considered Adaptation (ad.) measures no ad. time ad. intensity ad. quantity ad. quality ad. Capacity policy global nested Figure 2.1.1: CTP classification and profile of the proposed approach The characteristic values of the approach to be discussed in this paper are marked in grey. Existing approaches with similar intentions can be characterized as shown in figure 2.1.2. The overview reveals that none of the existing approaches completely fits with the characteristics of the approach to be analyzed. Thus the considerations underlying the individual characteristics have to be explicated. To model the two options of possible customer reactions on deviating delivery date proposals (placement or refusal of orders) Pibernik and Yadav (2008) integrate an order placement possibility that decreases with increasing deviation from the deliv- ery date (reaction function) and analyze the impacts of different types of reaction functions. In the present paper their idea is adopted, but information about custom- ers’ reactions is integrated in the planning process itself. 31 Criteria Authors B at ch / R ea l- tim e O bj ec ti ve O rd er re je ct io n D ev ia tio n/ ad ap ta ti on N es te d ca pa ci ty Chen et al. (2002) B profit max. x - x Gao et al. (2012) B profit max. x - x Halim/Muthusamy (2012) B cost min. x x - Lim/Halim (2011) B cost min. x x - Jeong et al. (2002) RT cost min. x x - Jung (2012) B cost min. - x - Lečić-Cvetković et al. (2010) RT max. order acceptance x x - Pibernik (2005) RT max. order acceptance x x - B profit max. x - - Pibernik/Yadav (2008) RT max. order acceptance x - x Robinson/Carlson (2007) RT cost min. x - - Zhao et al. (2005) B cost min. - x - Figure 2.1.2: Relevant approaches Additionally, different adaptation measures are analyzed with regard to their impacts on robustness. To extend the degrees of freedom in planning and to gain a lower sen- sitivity towards changes of the order situation the option of partial deliveries (Piber- nik 2005), where delivery dates are met for sub-quantities, will be considered. The second measure integrated in the planning approach, is the idea of a nested policy of capacity utilization (Harris and Pinder 1995, Jacob 1971). Access to a certain amount of capacity or inventory is only given to exceptionally profitable orders. If such or- ders are not present in the relevant planning situation, this reservation can be used for yet unknown future profitable orders. In summary, planning robustness is to be achieved by the following features: - Consideration of customers’ reactions on delivery date proposals that deviate from delivery dates requested by the customers. - Integration of measures to adapt to changing order situations. For this purpose a two-stage CTP-approach is derived based on the capable-to- promise approach proposed by Chen et al. (2002) (section 2.1.2). At the first stage 32 the decision about order acceptance or preliminary rejection of the orders is made. At the second stage alternative delivery date suggestions are generated for preliminarily rejected orders. Implications of this approach on the reliability of the delivery dates are analyzed numerically in chapter 2.1.3 by means of the AIMMS environment us- ing real-world data of a manufacturer of customized products. Finally in chapter 2.1.4 we summarize the main results of the paper and give an outlook on our future research in this field. 2.1.2 Planning approach 2.1.2.1 Basic model Starting point of our considerations are successively arriving orders with a specified desired delivery time interval [ , ]e li it t and a quantity iq of a product with a unit price i . The quantities .i rb of material r ( 1,..., )r R required to produce one unit of or- der i , the associated material costs Rrk and inventory holding costs .L R rk and .L FP ik for materials and finished products, given per quantity and time unit, are known. Ad- ditionally, information about the replenishment times and quantities of material stock . R r ta , the lead time deferrals 1 and 2 for products made in-house  1( 1,..., )kr r re- spectively externally ( ,..., )kr r R procured materials  2 1( ) is available. Fur- thermore, the capacity requirements  i per unit of a finished product, the capacity C of the production system and the quantity and order independent transport costs Trk are known. A rolling horizon with discrete time intervals and a length of T periods is the under- lying planning procedure. At the beginning of the current planning period at orders are scheduled that arrived in between the periods at and 1at (batch interval). The next planning run takes place at the beginning of planning period at for or- ders that arrived in between the periods at and  1at . Therewith in each planning run the planning horizon shifts by  periods. Since the order fulfillment process co- vers multiple periods, the following order sets are to be distinguished at the begin- ning of the current planning period at : - A : Set of orders that arrived in between the periods at and 1at . 33 - Aˆ: Set of orders that were accepted before period at but are not completely ful- filled yet. - A: Set of orders that were rejected or completely fulfilled before period at . In the basic model order- and resource-related decisions have to be made. With re- gard to orders it has to be determined whether to accept ( 1)iZ or to reject ( 0)iZ a present order that has not been considered up to period at . In case of order ac- ceptance a delivery date .i tD is specified as well as the quantities .i tM to be deliv- ered to the customer in period t . Decisions on resources are related to input quanti- ties . . R i r tQ of individual material types, production quantities .i tP of finished products and inventories . R r tB , . FP i tB of materials and finished products. The decision field is re- stricted by the order specifications of the customers, the production conditions and logical requirements of the rolling horizon. Customer-related constraints are: - The delivery quantity .i tM equals the ordered quantity iq . - The delivery date .i tD fits the desired delivery time interval [ , ] e l i it t . The following constraints are determined by the production system: - The production capacity C cannot be exceeded by the capacity demand  i in- duced by the production of finished products .i tP required to fulfill the order. - The quantities of the finished products .i tP to be produced determine the material consumption . . R i r tQ in the preceeding periods according to the production coeffi- cients .i rb and the lead time deferrals 1 and 2 . - The inventories . R r tB , . FP i tB for material and finished products result from incoming quantities . R r ta respectively .i tP and outgoing quantities . . R i r tQ respectively .i tM . - In order to avoid a higher production quantity as needed for delivery, an empty stock of finished products at the end of the planning horizon is postulated. Because of the rolling horizon, at the current planning period orders may exist that were accepted in previous planning periods but are not completed yet. Therefore in- ventories, production quantities, promised delivery dates and quantities from the pre- vious planning run need to be considered as parameters of the current planning run. 34 In accordance with the operative character of the planning problem to decide about order acceptance and delivery dates, the usual objective of profit maximization is pursued. Thereby, the revenue is a positive component, while material, inventory holding and transportation costs are negative components. Several approaches sug- gested in literature (e.g. Chen et al. 2002, Halim and Muthusamy 2012, Lim and Halim 2011, Pibernik 2005, Robinson and Carlson 2007) take penalty costs for order rejection into account. These penalty costs are opportunity costs resulting from future lost sales due to former order rejections which were induced by decisions at the tacti- cal level (capacity planning, customer acquisition). Due to this indirect relation pen- alty costs for order rejection are not considered in the proposed approach. On the other hand order rejection at the first stage of the planning approach is only of pre- liminary nature, since the attempt to accept these orders with deviating conditions is made at the second planning stage. The resulting linear mixed-integer problem can be formulated as follows: (1)                         . ˆ . . . . .1 . .1 max a T RL FP FP Tr R R i t i i i t i t r i r tt t i A A r R L R R r r tr M k B k D k Q k B subject to - Customer-related constraints (2)  . .i t i i tM q D   at t T , i A (3)    . l i e i t i t i it t M q Z i A (4)   . e i l i t i t it t D Z i A (5)   . a T i t it t D Z i A - Production-related constraints (6)      ˆ .i t ii A A P C   at t T (7)  1. . . . R i r i t i r tb P Q    ˆi A A ,  1, , r 1kr ,  at t T 35 (8)  2. . . . R i r i t i r tb P Q    ˆi A A ,  , ,kr r R ,  at t T (9)       ˆr.t 1 . 1 . . .R R R Rr t i r t r ti A AB a Q B r ,  at t T (10)    .t 1 . . i. FP FP i i t i t tB P M B    ˆi A A ,  at t T - Logical requirements (11) . . prev i t i tM M   ˆi A ,  at t T (12) . . prev i t i tD D   ˆi A ,  at t T (13)   . . 1 . 1a a R prevR r t r tB B r (14)   . i. 1 i. 1a a FP prevFP t tB B   ˆi A (15)  i. 1 0a FP tB  i A (16) i. 0 FP TB    ˆi A A (17) . 0i tP  i A ,    1( 1)a at t t (18) . . prev i t i tP P   ˆi A ,    1( 1)a at t t - Domain of decision variables (19)   0,1iZ i (20) . . ., , 0 FP i t i t i tM P B  ,i t (21) . 0 R r tB  ,r t (22)  . 0,1i tD  ,i t (23) . .t 0 R i rQ  , ,i r t 2.1.2.2 Consideration of adjustment measures One essential result revealed through the application of the basic model is the infor- mation about the orders to be accepted, their corresponding delivery dates as well as the orders to be preliminarily rejected. Reasons for order rejection can be order con- 36 ditions that cannot be handled technically (e.g. desired delivery is before the earliest possible completion date) and/or that are economically not favourable (e.g. the order competes for scarce resources with more or less profitable orders that were already bindingly accepted). In the context of economically disadvantageous order condi- tions the producer can reduce the probability of occurrence (prevention) or adapt to these situations (reaction). Both opportunities aim at making robust delivery date de- cisions. The nested policy of capacity utilization and partial deliveries are considered as preventive measures that generalize the basic model. These measures enlarge the number of planning options in such a way that some of the otherwise appearing re- source conflicts can be avoided. In contrast to these preventive measures the oppor- tunity to adapt the desired delivery dates is considered as a reactive measure at the succeeding planning stage. At this second stage alternative delivery date proposals are generated for preliminarily rejected orders and customers decide on the accepta- bility of these suggestions. Preventive measures: In the simplest form of a nested policy of capacity utilization the total capacity is splitted up into standard and premium capacity, and a cost pre- mium for accessing premium capacity is introduced (Jacob 1971). As a result, pre- mium capacity can only be used by more profitable orders. If these orders do not ex- ist yet, it is reserved for profitable orders arriving in future. Implications for planning are on the one hand that the decision maker has ex ante to specify two additional pa- rameters: the share of premium capacity  and the costs Pk for utilizing premium capacity. On the other hand the basic model has to be extended by additional deci- sions, constraints and objective components. Additional decisions arise in the context of utilized units of standard . S i tP and premium . P i tP capacity. Therefore it is necessary to reformulate capacity constraint (6) for both capacity types (6a, 6b) and to ensure that the sum of capacity units used by an order equals its capacity requirements (6c). Finally the objective function (1) must be extended by the component of premium costs (1’). Formally these modifications can be formulated as follows: (1’)                              . ˆ . . . . . . . .1 1 max a T L FP FP Tr i t i i i t i tt t i A A R RR R P P L R R r i r t i t i r r tr r M k B k D k Q k P k B 37 (6a)        ˆ .Pi t ii A A P C   at t T (6b)          ˆ . 1Si t ii A A P C   at t T (6c)  . . . P S i t i t i tP P P   at t T ,   ˆi A A Additional degrees of freedom result, if the desired order quantities are fulfilled by multiple deliveries. Pibernik’s approach (Pibernik 2005) to allow two partial deliver- ies, is going to be extended to the allowance of d deliveries with a defined minimum quantity of PDiq . Partial deliveries are possible for a relation of / 2 PD i iq q between order size iq and minimum quantity PD iq , while the customer can avoid partial deliv- eries by specifications in the range of / 2  PDi i iq q q . Although there is no need for extending the basic model with regard to decisions and constraints partial deliveries imply slight modifications of constraints: - Individual partial deliveries contain at least the minimum quantity specified by the customer and - delivery dates may not lie outside the desired time interval. Formally the following changes are relevant: (2a)  . .i t i i tM q D   at t T , i A (2b)  . . PD i t i i tM q D   at t T , i A (3a)    . l i e i t i t i it t M q Z  i A (3b)    . a T i t i it t M q Z  i A (4a)   . l i e i t i t it t D Z  i A (4b)          . l i e i t i i t it t PD i q D Z q  i A (5’)          . a T i i t it t PD i q D Z q  i A 38 Adaptation of delivery dates as a reactive measure: For preliminarily rejected orders the second planning stage tries to find out which delivery dates outside the given de- livery time interval can be met. The adjusted delivery dates are proposed to the cus- tomers and they decide themselves about whether to accept or reject the order. So the final order acceptance decisions are made by the customers. In this case a detailed distinction within order set A is necessary at the beginning of planning period at : - A : Set of orders that were completely fulfilled before period .at - A : Set of orders that were finally rejected before period .at - A : Set of orders that were preliminarily rejected before period .at It is assumed that the producer has collected empirical data concerning customers’ reactions on modified order conditions during past order negotiations. Furthermore, a function of acceptance probabilities depending on the extent of deviation from the given delivery time interval can be derived on the basis of this data by means of sta- tistical tools. This reaction function  ( )ULiV describes a non-increasing acceptance in case of increasing deviation (delay) ULiV of the delivery date from the upper limit l it of the delivery time interval. It is modelled as a discrete distribution with L levels and maximum/minimum acceptance  max ,  min at the first/last level:                     max max 1 max max 1 min max 1 : (V ) : ; 2, , 1 : UL i UL UL i l l i l UL L i V V l L V  i A with     max max 10 l l ,     10 1l l and    .[ ; ]maxa UL l i i t it t T V D t t Since the final decision of order acceptance under modified conditions is made by the customer order-related decisions in the basic model reduce to decisions concern- ing delivery dates and quantities of preliminarily rejected orders ( A ). The resource- related decisions in the basic model (input quantities, production quantities, invento- ries) still have to be made for order sets Aˆ and A . With regard to the decision field those customer-related decisions are omitted that were linked with the order ac- 39 ceptance decision and the adherence of the delivery time interval (3a, 4b). An addi- tional easing of constraints arises because of the facts that - the order acceptance by the producer is given (   1 iZ i A , in constraints 3b and 5’) and - the delivery is permitted in the interval in between the earliest delivery date speci- fied by the customer and the end of the planning horizon (4a’). Under the assumption of a robustness oriented planning behavior the impact of scheduling preliminarily rejected orders on capacity and material requirements are considered in such a way that all adjusted delivery dates can be met even though all corresponding customers agree with these dates (no overbooking). Therefore it is not necessary to modify the constraints of the production system and the rolling horizon approach. Two implications for the objective function result from the new planning situation. On the one hand the omission of the order acceptance decision induces the irrele- vance of success components that are solely affected by this decision. On the other hand customers’ reactions to modified order conditions are uncertain. Thus, the ob- jective function includes an additional uncertain component for orders with proposed deviating delivery dates ( )A . This component captures delivery date dependent ex- pected values of revenues as well as inventory holding, material requirements, trans- portation and premium costs. In case of already confirmed orders Aˆ delivery dates respective quantities and material requirements are specified. But the contingent scheduling of preliminarily rejected orders may reveal that modified dates or quanti- ties of the finished products manufacturing, the storage of materials and finished products as well as a modified utilization of premium capacity induce lower costs. In comparison to the basic model a reduced deterministic (certain) component is there- fore relevant in the objective function. The allocation of material inventory holding costs to both components cannot be made according to the principle of causation, since the material inventory is affected by the interaction of consumed materials of both order sets ( A and Aˆ). For estimating the expected inventory holding costs, the 40 stock is hence considered in equivalence to the proportion of material requirements in both components. Formally these circumstances can be formulated as follows: (1’’)                                          . . ˆ . .t . .1 . . .t . . . . . . .1 max (V ) a T RL FP FP P L R R i i t i i r i r tt t i A r UL L FP FP Tr P P i i t i i i i t i t ii A R R R L R R r i r t r i r tr k B k k B M k B k D k P k Q k B with               . ˆ . ˆ .. . : 0 0 : otherwise i i r i i ri A AR i i ri r t i A A q b q b q bB    ˆi A A , r , t (4a’)   . 1e i T i tt t D  i A Because of the dependency of the acceptance probability and the delivery dates being planned as well as their multiplicative linkage in the objective function a nonlinear mixed-integer programming model results. 2.1.3 Numerical analysis 2.1.3.1 Test configuration Within the numerical analysis the suitability of the proposed two-stage planning ap- proach is analyzed based on real-world data of a manufacturer of customized leisure products. For this purpose plans with regard to order acceptance and termination of order quantities to be delivered are generated on the basis of order and resource data in a rolling horizon approach. The different model formulations are tested for varying simulated developments of reality in order to discuss the following questions: - How do preventive and reactive measures affect the reliability of delivery dates? - To which extent does the second planning stage influence the solution quality of the planning approach? Starting point of the tests was a preliminary assessment of a planning horizon which is suitable according to the criteria solution time and profit. The planning horizons to be studied resulted from the latest delivery date accepted plus a share of the estimat- 41 ed maximum time necessary to complete all orders to be planned. For the present da- ta constellation best results were obtained for a share of 10 percent. In order to analyze impacts of preventive and reactive measures on planning robust- ness, the following parameter constellations are combined in the planning approach and tested for 5 order scenarios: Partial deliveries (PD) Capacity Nesting (CN) Adaptation of delivery dates Description Value of PD iq Description Value of ( , Pk ) No PD (N) iq No CN (N) (0, 0) No adaptation (N) Average number of PD (PD1)  min ,3iq Low level of CN (CN1) (1/3, 2900) Adaptation (L) Maximum num- ber of PD (PD2) 1 High level of CN (CN2) (2/3, 3500) Figure 2.1.3: Tested parameter constellations Real order data (scenario 1) from a period of three months was taken as the basis of the tests as well as realistically generated order data (scenario 2 to 5). The generated order data is a realization of random variables with regard to intermediate arrival times and order quantities that follow a normal distribution according to the parame- ters (expected value, standard deviation) revealed by the real data. A uniform two- week delivery time interval that starts with the period of the order receipt was as- sumed to be relevant for all orders. Furthermore, the reaction function has been em- pirical-qualitatively (expert survey) estimated:             10 : 01.0 : 0 100.6 (V ) : 10 250.2 : 251 10 UL i UL iUL i UL i UL i V V V V Within the planning process this function is applied and after a planning run the cus- tomer decision is simulated as a random variable with a probability value according to this function. Real data of the 7 best-selling product configurations was taken as a basis for production-related data: 42 Materials (A-parts) Capacity Prices/Costs (in €)  56R ,  45kr  3C  59 Trk ,    2599, 5750i ,   6.71,125.21Rrk  1 3 ,  2 2   1i .L FP ik , .L R rk : 0.25% of invested capital per piece Figure 2.1.4: Production-related data Planning is done on a daily basis at the beginning of each week with a rolling hori- zon and an underlying batch interval of 5 days. The planning model was implement- ed in the AIMMS 3.13 environment. Plans at the first level (order acceptance, deliv- ery dates and quantities for accepted orders) are exact solutions of the linear mixed- integer model determined by the solver CPLEX 12.5. In order to generate plans at the second level (delivery date and quantity suggestions for preliminarily rejected or- ders) locally optimal solutions are created with the “AIMMS Outer Approximation Algorithm”, because of the nonlinearity of the mixed-integer model (Roelofs and Bisschop 2016). To avoid inacceptable computation times the maximum computa- tion time permitted was set on 100 s per iteration and the amount of iterations was limited to 15. Following Kimms (1998) a measure for planning robustness is considered to judge the reliability of delivery dates. In the discussed planning problem, robustness will be the higher the less production decisions .i tP have to be revised because of changing information between the planning runs. Then the robustness measure refers to - those customer orders, that are planned to be processed in consecutive planning runs (set CPA ) and - overlapping time periods (set CPT ) in consecutive planning runs 1pr and pr :       ( 1) ( ) ( 1) ( )min ; ,...,min ;CP pr pr pr pra aT t t T T For a normalized robustness index the cumulative changes in production quantities in between planning run 1pr and pr are set in relation to the cumulated production quantities in planning run 1pr . Additionally the weighting function  t takes into account that - from an economic point of view - plan modifications in the distant fu- ture are less important than those that lie close to the current planning period. The 43 lower the index  ( )pr is, the higher is the robustness between the planning runs 1pr and pr . For the robustness of the whole planning the worst value indicated in all planning runs is considered:    ( )max pr pr with                    ( ) ( 1) . .( ) ( 1) .max ;1 CP CP CP CP pr pr t i t i tpr i A t T pr t i ti A t T P P P   1pr and       ( 1) ( ) 1 min ; 1t pr pra at t t       ( 1) ( ) ( 1) ( )min ; min ;pr pr pr pra at t t T T 2.1.3.2 Test results To point out the impacts of the second planning stage onto solution quality, the aver- age values of computation times and profits achieved at the first and at both planning stages are compared. With regard to computation times it becomes obvious that alt- hough the nonlinear problem at the second stage (deviating delivery date sugges- tions) induces a higher computational effort (maximum time: 500 s) than the linear problem (order acceptance according to desired delivery dates) at the first stage (maximum time: 0.3 s), all computation times lie within an acceptable range. In order to ensure comparable profits, the generated profits (see figure 2.1.5) were adjusted by the access costs on premium capacity. Figure 2.1.5: Generated profits ((a) one-stage and (b) two-stage planning approach) 44 The observation of these profits reveals that alternative delivery date suggestions considering customers’ reactions are always economically advantageous. Regarding partial deliveries and nested policy of capacity utilization a heterogeneous picture emerges. In the majority of investigated parameter constellations profits can be in- creased by partial deliveries, whereas the nested policy mainly reduces profits. Therefore it can reasonably be assumed that the economic benefits of these measures are dependent on the fit between the chosen parameter values and the order situation. Concerning the reliability of promised/suggested delivery dates it has to be pointed out that all planned delivery dates and quantities are met, because of the underlying certain resource and capacity availability. Although unexpected capacity or resource shortages were so far not directly taken into account, statements about the degree of reliability can be derived by consideration of the robustness measure and the average capacity utilization per period. As the one- and two-stage planning approaches achieve robustness values significantly below 0.5 (see figure 2.1.6), only few adap- tions of production decisions caused by varying order situations are necessary. Pro- duction decisions are more robust, if only the first planning stage with partial deliver- ies is applied. The nested policy as well as the suggestion of modified delivery dates reduces planning robustness. Figure 2.1.6: Robustness index ((a) one-stage and (b) two-stage planning approach) 45 Figure 2.1.7: Capacity utilization ((a) one-stage and (b) two-stage planning approach) On the other hand these measures provide flexibility to react to modified order situa- tions by causing a low average level of capacity utilization (see figure 2.1.7). In the first case premium capacity leads to the opportunity to revise production decisions in favour of accepting additional orders. The consideration of orders with modified de- livery dates in the latter case induces the uncertainty that customers do not accept deviating conditions and cancel the orders. With the released capacity it is possible to assign more advantageous production dates to accepted orders or to accept additional orders without endangering previously promised delivery dates. 2.1.4 Conclusions In the present paper an extended capable-to-promise approach was developed and analyzed with the intention not only to generate high profits through order ac- ceptance, but also to promise reliable delivery dates. The extensions refer to a nested policy of capacity utilization and partial deliveries as preventive measures and to the suggestion of modified delivery dates as a reactive measure. During the planning of modified delivery dates customers’ reactions were considered with the help of an ac- ceptance probability in dependency of the deviation from the originally desired de- livery date. This approach can be seen as a significant extension of planning ap- proaches proposed in the literature. Using real-world data of a manufacturer of customized leisure products and several deduced test cases the solution quality and computational effort as well as impacts of 46 the preventive and reactive measures on delivery reliability were numerically ana- lyzed. It became apparent that - all promised delivery dates could be met, - suggesting modified delivery dates is economically advantageous and the benefit of the two other measures is dependent on the parameter choices, - the computation time is acceptable and dependent on the application of the partic- ular measures, - partial deliveries directly increase planning robustness and - the nested policy of capacity utilization and the suggestion of alternative delivery dates are additional options that can be used when deviating production situations occur. Since material and capacity availabilities were assumed to be certain in the tests, the gained statements need to be verified in further analyses while considering stochastic influences. Furthermore, statements about optimal parameter choices for the different measures need to be generated in this context. 47 2.2 Extended approach with order- and resource-related uncertainty1) Abstract: One important way to differentiate from competitors is to promise reliable delivery dates. Therefore, order promising not only aims at maximizing short-term profits, but also at achieving an acceptable degree of robustness. In capable-to- promise (CTP) approaches proposed for answering to customer order inquiries the order- and resource-related uncertainty is taken into account by several preventive measures. Up until now, the effectiveness of these measures has been proven in iso- lated analyses. Although they are directed to different uncertainty types it cannot be concluded that the observed impacts unfold independently. In this paper a CTP ap- proach is presented and analyzed for the case of order- and resource-related uncer- tainty. Robustness is achieved by the preventive adaptation measures of capacity nesting, providing safety capacity and proposal of alternative delivery dates. Plan- ning occurs at two stages: (1) order acceptance according to the order specifications requested by the customer or provisionally order rejection, and (2) proposal of alter- native delivery dates for provisionally rejected orders. As a major extension to the current literature customers’ response on alternative delivery dates is anticipated and considered at this stage. In contrast to currently existing approaches the suitability of this new approach, the impacts of preventive measures on profit and robustness and the interactions between the measures are systematically evaluated in a numerical analysis. 2.2.1 Introduction Order promising comprises the decisions on order acceptance and order specification that are made during the contract awarding process interactively by customer and producer (Mansouri et al. 2012). The set of accepted orders in the company’s point of view forms a master production schedule which has to maximize the expected profit with respect to order- and resource-related uncertainty as well as adaptation measures that are available to cope with uncertainty. Order acceptance decisions are studied as single-player auctions with a long tradition in economic research (cf. the reviews from Engelbrecht-Wiggans 1980, King and Mercer 1988 or the bibliography 1) Gössinger, R.; Kalkowski, S.: Robust order promising with anticipated customer feed- back, in: International Journal of Production Economics, Vol. 170 (2015), pp. 529-542. To ensure consistency, notations were adapted to dissertation style. 48 provided by Stark and Rothkopf 1979). More recently the increasing importance of reliable order delivery dates led to a growing interest in developing planning instru- ments for enhancing on-time deliveries (e.g. Stevenson et al. 2005). In the context of make-to-order supply chains capable-to-promise (CTP) approaches are suggested to determine delivery dates and quantities based on the available resources (Pibernik 2005). Thereby normally a deterministic resource availability is assumed, substanti- ated by the short-term planning horizon of CTP approaches (Ball et al. 2004, Chen et al. 2001). But despite the operative focus of these approaches, in particular order- and resource-related uncertainty arises in practice (Pujawan and Smart 2012) and hampers the endeavors to achieve more reliable delivery dates. The intention to propose reliable delivery dates can be operationalized with the aim to create plans that are characterized by robustness in two dimensions (cf. Roy 2010 for multiple robustness dimensions): (1) A risk-averse planning behavior prefers that changes in the planning data have a minimum impact on the value of the planning objective (solution robustness, Mulvey et al. 1995). (2) Plan revisions necessary to restore an optimal plan in case of updated planning data are accompanied by addi- tional implementation costs (e.g. due to the nervousness of recently started distribu- tion, production and procurement processes; Pujawan and Smart 2012, Sridharan et al. 1988). This motivates to generate plans in such a way that the extent of revisions is low (planning robustness, Kimms 1998). In order to achieve an order promising that is both, solution robust and planning robust, the general approaches for robust- ness generation, to provide temporal and quantitative buffers as well as to set up con- tingency plans that consider all possible courses of actions (Herroelen and Leus 2004), have to be put into problem-specific terms. In the present paper a CTP approach is developed and analyzed that generates ro- bustness by considering multiple adaptation measures during the order promising process. Different adaptation measures to cover uncertainty have been proposed in the CTP literature (see table 2.2.1). The overview reveals that the measures are most- ly applied either to cover order- or resource-related uncertainty but the need for cov- ering both uncertainty types is often neglected. Up to now the effectiveness of the adaptation measures is therefore solely proven in isolated analyses. But although the 49 adaptation measures are related to different sources of uncertainty it cannot be as- sumed that their impacts unfold independently. Hence, one contribution of this paper is to give insight into the impacts of a joint measure application on profit, solution robustness and planning robustness. Type of CTP approach Batch Real-time C he n/ D on g (2 01 4) C he n et a l. (2 00 1) G ao e t a l. (2 01 2) G ui llé n et a l. (2 00 5) H al im /M ut hu sa m y (2 01 2) Ju ng ( 20 12 ) Pi be rn ik ( 20 05 ) Z ha o et a l. (2 00 5) C he n/ D on g (2 01 4) C hi an g/ W u (2 01 1) C hr is to u/ Po ni s (2 00 9) Je on g et a l. (2 00 2) L eč ić -C ve tk ov ić e t a l. (2 01 0) Pi be rn ik ( 20 05 ) Pi be rn ik /Y ad av ( 20 08 ) R en na /A rg on et o (2 01 0) Order-related uncertainty X X X X X X X X X X X X X X X X Resource-related uncertainty X X X X X X A da pt at io n m ea su re s Nesting of non-consumable resources* X X X X X X X X Nesting of consumable resources X X X X Safety capacity* X Proposal of deviating delivery quantities X X X X X X X X X X Proposal of deviating delivery dates* X X X X X X X X X X Considering customer response* O O O Table 2.2.1: Overview of relevant CTP approaches and applied preventive adaptation measures Due to the results of previous studies in literature the adaptation measures highlight- ed by asterisks seem to be particularly suitable to unfold notable impacts on robust- ness and profit. In order to analyze the interaction of adaptation measures in the pres- ence of resource- and order-related uncertainty the batch CTP approach proposed in this paper applies these asterisked measures. Therefore as a second contribution, in comparison to the existing literature a more comprehensive approach results. In the following review of current CTP approaches we concentrate on the preventive measures of capacity nesting (nesting of non-consumable resources), providing safe- ty capacity and proposal of alternative delivery dates while considering customer re- sponse. 50 Capacity nesting (Harris and Pinder 1995, Jacob 1971) is applied in CTP approaches to cover order-related uncertainty (Chen and Dong 2014, Chiang and Wu 2011, Christou and Ponis 2009, Gao et al. 2012, Lečić-Cvetković et al. 2010, Pibernik and Yadav 2008). The underlying idea is to set protection levels by splitting up the total capacity in multiple segments (e.g. in standard and premium capacity) and defining segment-specific costs for utilizing capacity. Hence, the access to a share of capacity is made more expensive and thus this share can only be used by more profitable (lu- crative) orders. That is, the discrimination between less profitable and more profita- ble orders is defined by the utilization cost difference. On this basis the risk of hav- ing to reject future lucrative orders can be covered. A greater share of premium ca- pacity and higher utilization costs hinder the acceptance of low profitable orders and extend the chance for being able to accept lucrative orders in the future. Safety capacity is provided to handle resource-related uncertainty. By a risk-averse estimation of availability only as much capacity is considered in the plan as it is nec- essary to meet capacity constraints with an economically acceptable probability (chance constraint, Charnes and Cooper 1959). In the CTP literature only Pibernik and Yadav (2008) consider this concept to cope with resource-related uncertainty. As emphasized in literature the interaction with customers is of great significance in order promising. While in other research fields contributions concerning negotiations exist (see e.g. Renna and Argoneto 2010), there is a lack of CTP approaches taking into account customers’ response in the order awarding process. Although the im- portance of methodologies directly incorporating customers is highlighted by deci- sion makers with industrial experience, recently still a lack between the optimization techniques developed in literature and the decision support needed in practice can be observed (Mansouri et al. 2012). However, taking customers’ response on suggested deviating delivery dates appropriately into account can enable the identification of more reliable delivery dates. In a long-term perspective this may lead to an increas- ing customer satisfaction and loyalty. Pibernik and Yadav (2008) consider a corre- sponding aspect in the tests of their CTP model by assuming an order acceptance probability that decreases with increasing delivery date deviation (response func- tion). This response function is a specific case of probability distributions that have 51 been proposed in the context of competitive bidding for orders with non-price fea- tures (Simmonds 1968) and have been made applicable for planning of make-to- order production by means of strike rate matrices (Kingsman et al. 1993, Kingsman and Mercer 1997). Recently, Thürer et al. (2014) have analyzed the implications of considering strike rates for workload control by means of simulations. Thereby strike rates are assumed to be independent from due dates and are used as a parameter which is systematically varied for different simulation runs. Renna and Argoneto (2010) consider the order promising situation my means of a Multi Agent System. Customer behavior is simulated with a customer negotiation agent that tries to max- imize a utility function depending on proposed due date, order quantity and price. A utility threshold that varies with the number of negotiation rounds and the utility de- velopment implicitly models an acceptance probability. Since this behavior is not an- ticipated by the Supplier Negotiation Agent and the Supplier Production Agent the tested negotiations reveal similar results as the previously mentioned simula- tions/tests. In the stochastic model to support order promising before bargaining starts Guillén et al. (2005) consider customer behavior with an expected customer satisfaction. This construct is measured by means of a scoring system reflecting the distance between proposed order specification and values for delivery date and price preferred by the customer. Offers with a high customer satisfaction are expected to have a high acceptance probability in the subsequent bargaining process. However, the impact of this procedure to the profit generated with order promising is not ana- lyzed. In contrast to this, in the approach developed in the present paper the response function builds a central element of the planning model in order to enhance the de- grees of freedom and to increase the robustness of the plan. As a substantial exten- sion to current approaches, the option of proposing delivery dates that deviate from those requested by the customers in the contract awarding process is considered. Thereby customers’ response on proposed deviating delivery dates is anticipated in the planning process by means of a probability distribution. One possibility to handle order-related and resource-related uncertainty in a reactive manner and to facilitate the application of preventive adaptation measures is to revise the delivery date and production decisions of past contract awarding processes by a 52 rescheduling of orders under contract. The majority of papers consider this aspect with regard to production decisions (Chen et al. 2001, Halim and Muthusamy 2012, Jeong et al. 2002, Jung 2012, Lečić-Cvetković et al. 2010, Robinson and Carlson 2007, Zhao et al. 2005). Nevertheless it can also be advantageous to revise already contracted delivery dates and take upcoming penalty costs into account, in order to accept pending lucrative orders (Jung 2012, Pibernik 2005). The remainder of this paper is organized as follows: The underlying planning situa- tion is described in section 2.2.2. First the considered supply chain is characterized before the structure of the two-stage planning approach is explained. In section 2.2.3 the decision models are developed step-by-step, whereby the proceeding at the first stage is addressed first. Necessary modifications for the second planning stage fol- low. In a numerical analysis (section 2.2.4) the joint impacts of the considered adap- tation measures on robustness and profit are analyzed for different order and capacity scenarios based on real data. Finally the main results and implications as well as di- rections of future research are summarized in section 2.2.5. 2.2.2 Planning situation 2.2.2.1 Planning object The structure of the considered supply chain supplemented by corresponding sym- bols of decision variables and parameters is illustrated in figure 2.2.1. Planning is fo- cused on the make-to-order part of a linear supply chain which comprises the pro- cesses of manufacturing, intermediate storing and delivering of customer-ordered fi- nal product quantities that fulfill demand (D). These processes are initiated by order requests submitted from individual customers (dotted line) and controlled by deci- sions on order acceptance, delivery dates as well as production quantities (preselec- tion and order promising). The upstream make-to-stock part of the supply chain is considered insofar as required materials (produced in-house or externally procured) are taken out from stock with different lead times. The rest of the supply side (S) is taken into account by periodical material stock replenishments. 53 Figure 2.2.1: Structure of the supply chain For reasons of planning five order sets have to be distinguished. Set A: order inquir- ies that arrived in the batch interval; set A: order inquiries with a profit chance; set Aˆ: orders that have been accepted before the batch interval has started, but that are not yet fulfilled; set A : rejected orders; set A : fulfilled orders. All accepted orders have to be fulfilled. With an order inquiry i ( 1,..., )i I a customer specifies a product that needs to be delivered with quantity iq during the time interval [ , ] e l i it t at a price i . Given the product specification the company is aware of the order specific production coeffi- cients .i rb of materials r ( 1,..., )r R as well as capacity requirements per piece  i . The lead time deferrals 1 for products made in-house and 2 for externally pro- cured materials as well as exogenous given material replenishments . R r ta are deter- ministic parameters. Cost rates relevant for decision making are transportation costs Trk , inventory holding costs for materials .L Rrk and finished products .L FP ik , costs for utilizing premium capacity Pk and manufacturing costs Mrk (material and prime costs). For already accepted orders ˆ( )A the delivery date . c i tD and the penalty costs per planning period for premature  ei or tardy  l i delivery are contractually fixed. Based on this deterministic data the producer decides on a preselection of orders A with a situation-independent positive margin (price – manufacturing costs – transpor- tation costs). The actual margin of these orders is dependent from the specific capaci- ty supply and demand (order sets A and Aˆ) situation in the planning horizon antici- pated during order processing. Due to possibly induced costs of inventory holding and of deviating from contractually fixed delivery dates, it will not exceed the situa- tion-independent margin. Hence, preselected orders have a profit chance. Since the no S D . FP i tB. R r tB , , , , ,M Pt i rC k k   Trk .L FP ik .L R rk .i rb .i tD. ., , S P i t i t iP P Z , , ,e li i i iq t t  desiV,l ei i  1 2,  . R r ta order promising pre- selection no yes yes A A A Aˆ A A 54 residual requests \A A will never be profitable for the company they are finally re- jected and not considered in the planning process. According to the common practice of CTP approaches for order promising a rolling planning horizon of length T is applied. Each planning run is carried out after  pe- riods (batch interval) starting with the current planning period at . In addition uncer- tain information about the future is considered: - Experiences with customer inquiries in the past allow for an estimation of cus- tomers’ response to proposed deviations from the delivery time interval desiV in the form of a discrete probability function   desiV . On the basis of statistical data on past order inquiries the stream of inquiries expected for the future can be de- scribed by positive random variables of interarrival time J , order quantity Q , price  and manufacturing costs  MK . - The available capacity tC is uncertain and modelled as a tF -distributed random variable. That is, the distribution can be put in a concrete time-dependent form in such a way that the standard deviation increases with increasing distance from at . The realization of this random variable is completely known for the current plan- ning period at . Specific distributions tF are taken as a basis for the remaining pe- riods of the batch interval. These distributions are characterized by non-decreasing standard deviations as well as not necessarily identical expected values. For peri- ods after the batch interval a probability distribution TF with a constant expected value and standard deviation is assumed. 2.2.2.2 Structure of planning approach In order to take the different adaptation measures into account a two-stage planning approach is proposed (see figure 2.2.2). At both planning stages the adaptation measures of capacity nesting and safety capacity are applied to cover order- and re- source-related uncertainty. At the first planning stage “order acceptance by the company” basically the common idea of batch CTP approaches is implemented: A set of customer requests is present and only those orders are accepted that can be fulfilled by means of the expected non-dedicated capacity within the specified delivery time interval in the most profit- able way. For each accepted order delivery date, delivery quantity and penalty costs for premature/tardy delivery are contractually fixed and the order fulfillment process 55 is started. In any case these orders utilize a share of standard capacity. In situations where the standard capacity is not sufficient and lucrative orders are present addi- tionally a share of premium capacity is utilized. In contrast to conventional CTP ap- proaches the other share of orders is not finally, but provisionally rejected. Figure 2.2.2: Structure of the planning approach Provisionally rejected orders are included in the process at the second planning stage “proposal of modified order specification”. Although the set of these orders contains only orders with a profit chance, in the current situation and with respect to the de- sired delivery time interval they can be valued as to be in the range from not yet prof- itable via barely profitable up to lucrative. Since capacity supply and demand fluctu- ate randomly and the accuracy of information about the situation in a future period improves over time this valuation may be different when the delivery date proposed for such an order deviates from the desired interval. Therefore, the producer gener- ates promises for provisionally rejected orders that do not take requested delivery time intervals and contractually fixed delivery dates as hard constraints into account. Instead of this on the one hand for provisionally rejected orders an anticipated cus- tomer response (acceptance probability) to delivery dates deviating from requests is Orders accepted according to modified specifications Order promising Order acceptance by company Orders with modified delivery dates Proposal of modified order specification Customer requests with a profit chance Anticipated customer response Order acceptance by customer Orders accepted according to requests Provisionally rejected orders yes no R es ch ed ul in g Orders finally rejected by the customer yes no first planning stage second planning stage C on tr ac t Order processing 56 considered. On the other hand for already accepted orders penalty costs for devia- tions from contractually fixed delivery dates are taken into account. Under these as- sumptions practicable delivery dates are determined that balance expected costs of displacing orders from their most beneficial processing period and expected costs of losing profit chances due to customers’ rejections. The two stage approach enables a simple interaction with clients whose order re- quests could be accepted with a deviating delivery date. The decision whether orders with a modified specification are accepted is no longer up to the company but to the individual customers. If one decides to reject this modification his order is finally re- jected, otherwise the new order specifications are accepted. For orders accepted at the second stage the terms of contract (see first planning stage) are fixed. Just like at the first planning stage accepted orders in particular utilize a share of standard capac- ity and only if this is not sufficient for fulfilling lucrative orders additionally a share of premium capacity is dedicated to these orders. In contrary to a comprehensive single-stage approach where decisions on acceptance and (modified) delivery dates of all orders are made simultaneously this two-stage structure enables a faster reaction to order inquiries which can exactly be met accord- ing to the customer specification, because customers’ response is not necessary. On the other hand such a single-stage approach would allow for a higher expected value of profit. Since in this case acceptance and delivery dates of all orders cannot be con- firmed until the customers’ response to all deviating delivery dates is received com- pletely the response time is indeterministic and longer by tendency. So, this proce- dure would only be preferable if the customers are willing to tolerate longer response times to their requests. 2.2.3 Planning models 2.2.3.1 First planning stage On the basis of the order and resource situation at the time of planning and the or- ders’ profitabilities, the company decides about the acceptance or provisional rejec- tion   0,1iZ of each newly arrived order request. In the first-mentioned case addi- 57 tionally the period  . 0,1i tD in which the order is to be delivered with quantity  0iq as well as production quantities .i tP need to be determined. For already ac- cepted, but not yet fulfilled orders these decisions have already been made in former planning runs, but can be revised, except the acceptance decision ( 1)iZ . The decision field is restricted by customer-, production- and measure-related con- straints as well as logical requirements of the rolling horizon. Customer-related con- straints for newly arrived order inquiries with a profit chance (2, 3) ensure the deliv- ery of the whole requested quantity within the desired delivery time interval, if the order will be accepted (Chen et al. 2001). In the event of revising delivery dates of accepted, but not yet fulfilled orders, adjusted delivery dates can be set within the considered planning horizon (4). The agreed delivery time of an accepted order is a soft constraint. Violations are quantified (5) and penalized with contractually fixed costs in the objective function (1). Since there are different costs for delivery date deviations  ei ,  l i a distinction between premature ( 0 real iV   0)i and tardy ( 0realiV   1)i delivery is to be made (6, 7), where  is a sufficiently large number. Constraints of the production system result from the available capacity tC , the in- ventory of finished products . FP i tB that is increased/decreased by production .i tP / de- livery  .i i tq D (8) and the inventory of materials . R r tB that is increased/decreased by exogenous given replenishments . R r ta / material consumption by manufacturing pro- cesses . . M i r tQ required to fulfill accepted orders (9). Materials produced in-house  ( 1,..., 1)kr r and materials procured from external sources ( ,..., )kr r R are pro- vided with different lead times 1 or 2  1 2( ) , respectively (10, 11). Measure-related constraints (12-14) result from considering preventive adaptation measures. The available capacity is split up into standard . S i tP and premium capacity . P i tP according to share  . With additional costs Pk for utilizing premium capacity the option of capacity nesting reserves capacity for highly profitable (lucrative) or- ders and thus handles order-related uncertainty. Both parameters have to be set in ac- cordance to the uncertain order and resource situation. Due to multiple sources of uncertainty and interactions between the parameters it is unlikely that closed form 58 analytical expressions do exist for an optimum parameter setting in the general case. Hence, one way of determining good parameter constellations is a grid search in which both parameters are varied systematically with respect to the evaluation of achieved planning results. Providing safety capacity serves as a measure to cope with uncertainty about the available capacity. On the basis of a risk-averse estimation of the capacity the capacity utilization is planned in such a way that capacity constraints are fulfilled with a given probability   0.5 . In this case the factual available capac- ity exceeds estimated values most of the time. For the opposite situation it is assumed that the feasibility of the plan is reached by applying operative adjustment measures that are not explicitly modelled. The value of parameter  has to be chosen in such a way that the trade-off between capacity idle time costs and costs of delayed order fulfillment due to scarce capacity is balanced. Since both cost components contain a share of opportunity costs they cannot always be measured with acceptable effort. In such cases a reasonable  -value is predefined that covers the set of possible capacity situations with a high percentage. The rolling horizon requires logical consistency. Data of already started order ful- fillment processes need to be transferred from the last to the current planning run, whereby production decisions can be revised with respect to the lead time of required materials (15). That is, producing a higher quantity than originally planned is not permitted for those periods in which already started material supply processes are not yet finished. On the other hand, for order inquiries production quantities are zero in the first planning periods (16) and the finished product inventory is zero too (17). Additionally, the inventory data . 1a R r tB and . 1a FP i tB need to be transferred (18, 19). In order to avoid higher production quantities than necessary to fulfill the orders, the stock of finished products should be zero at the end of the planning horizon (20). Fi- nally, domains of decision variables and auxiliary variables are specified (21-27). The decisions on acceptance (21) and delivery date (22) as well as the identification of the decisions’ directions (23) are binary. Planned deviations are integer-valued (24). Decisions on manufacturing quantities (25), capacity utilization and inventory levels (26, 27) are non-negative real-valued. 59 The planning approach aims at maximizing the profit generated within the planning horizon. Due to the distinction of order sets, the objective function is split up into three deterministic components (1). For newly arrived order inquiries the revenue is diminished by holding costs of finished products .L FPik , transportation costs Trk , costs for utilizing premium capacity Pk as well as manufacturing costs Mrk . In case of already accepted orders only inventory holding costs of finished products and ma- terials as well as costs for utilizing premium capacity are relevant. Additionally, the costs of the realized deviation realiV from the contractually agreed delivery date . c i tD need to be considered. Although these penalty costs are included, considering the cost for inventory holding of finished products .L FPik is still necessary since produc- ing the whole requested order quantity might not be possible in one planning period. The remaining success-related components are fixed, since the order acceptance de- cisions have already been made. As a third component inventory holding costs of materials .L Rrk are jointly taken into account for all present orders. The following mixed-integer, quadratic decision model results: (1)                                                          . . .ˆ ˆ . . . . . . .1 . .1 max 1 a a a T L FP FP P P i i t i t it t i A real e real l i i i i i ii A T RL FP FP Tr P P M M i i i t i i t i t i t i r i r tt t r i A T R L R R r r tt t r k B k P V V q D k B k D k P k Q k B subject to: - Customer-related constraints: -- Newly arrived order inquiries with a profit chance: (2)   . l i e i t i t it t D Z   i A (3)   . a T i t it t D Z   i A -- Accepted, but not yet fulfilled orders: (4) a T i tt t D   . 1   ˆi A (5)  . .1 Treal c i i t i tt V D D t       ˆi A 60 (6)     1reali iV   ˆi A (7)   reali iV   ˆi A - Production-related constraints: (8)     . 1 . . . FP FP i t i t i i t i tB P q D B    ˆi A A ,  at t T (9)       . 1 . 1 . . .ˆ R R M R r t r t i r t r ti A A B a Q B   at t T ,  1,...,r R (10)  1. . . . M i r i t i r tb P Q    ˆi A A ,  at t T ,  1,..., 1kr r (11)  2. . . . M i r i t i r tb P Q    ˆi A A ,  at t T ,  ,...,kr r R - Measure-related constraints: (12)           .ˆProb( )Pi t i ti A A P C   at t T (13)             .ˆProb( 1 )Si t i ti A A P C   at t T (14)  . . . S P i t i t i tP P P    ˆi A A ,  at t T - Logical requirements of the rolling horizon: (15)       . .a a a a t t prev i t i tt t t t P P   ˆi A ,    10,..., 1 (16) . 0i tP   i A ,     1 1a at t t (17) a FP i tB  . 1 0   i A (18)   . . 1 . 1a a FP FP prev i t i tB B   ˆi A (19)   . . 1 . 1a a R R prev r t r tB B   1,...,r R (20) . 0 FP i TB    ˆi A A - Domains of decision variables and auxiliary variables: (21)   0,1iZ   i A (22)  . 0,1i tD    ˆi A A ,  at t T 61 (23)    0,1i   ˆi A (24) realiV    ˆi A (25) . . 0 M i r tQ    ˆi A A ,  at t T ,  1,...,r R (26) . . . ., , , 0 P S FP i t i t i t i tP P P B    ˆi A A ,  at t T (27) . 0 R r tB   at t T ,  1,...,r R 2.2.3.2 Second planning stage If the solution of the first planning stage leads to a non-empty set of provisionally re- jected orders, the planning process is continued at the second planning stage. Now, proposals for deviating delivery dates are generated for provisionally rejected orders with respect to anticipated customers’ response. Therefore as a subset of order set A the set A has to be defined as the set of customer orders which were provisionally rejected at the beginning of planning period at . Thus, order sets Aˆ and A are rele- vant for planning at the second stage. The decision about the acceptance of a suggested delivery date is no longer up to the company, but to the customer. In order to include customers’ acceptance probability into the planning process, it is assumed that historical data about customers’ response on deviating delivery date proposals is available. Furthermore, the decision maker is capable to derive a discrete response function   desiV depending on the extent of the deviation desiV from the desired delivery time interval. Thereby a distinction be- tween premature ( 0)desiV , punctual ( 0) des iV and tardy ( 0) des iV delivery is made (28-32): (28) . a Te e i i t it t V D t t      i A (29) . a T l l i i t i t t V D t t      i A (30) ' min( ,0)e ei iV V  i A (31) ' max( ,0)l li iV V  i A 62 (32) ' 'des l ei i iV V V   i A Customers’ response is modeled as a discrete function with L steps, whereby the values  1,..., L represent the probability of accepting deviating delivery dates (33). Abstracting from further dimensions of order specification (e.g. price, partial deliver- ies) an acceptance probability of one can be assumed for punctual deliveries, whereas the remaining probability values for positive or negative deviations lie in the interval  0,1 : (33)                     1 1 1 1 : V : V , 2,..., 1 :