Literature Review

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 636)


This chapter reviews the literature on lot-sizing with substitution and related fields of research. In Sect. 4.1, we briefly review the literature on and highlight applications of assortment problems, which can be seen as a tactical/medium-term counterpart to dynamic lot-sizing problems with substitution. Sect. 4.2 describes three existing production planning models with substitution/flexible BOM. Related topics, amongst others stochastic inventory control with substitution and flexible bills-of-materials, are briefly discussed in Sect. 4.3.


Revenue Management Initial Inventory Substitution Cost Demand Class Variable Production Cost 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Aissaoui, N., Haouari, M., & Hassini, E. (2007). Supplier selection and order lot sizing modeling: A review. Computers & Operations Research, 34(12), 3516–3540.CrossRefGoogle Scholar
  2. Archibald, T. W. (2007). Modelling replenishment and transshipment decisions in periodic review multilocation inventory systems. Journal of the Operational Research Society, 58(7), 948–956.CrossRefGoogle Scholar
  3. Balakrishnan, A., & Geunes, J. (2000). Requirements planning with substitutions: Exploiting bill-of-materials flexibility in production planning. Manufacturing & Service Operations Management, 2(2), 166–185.CrossRefGoogle Scholar
  4. Ball, M. O., Chen, C.-Y., & Zhao, Z.-Y. (2003). Material compatibility constraints for make-to-order production planning. Operations Research Letters, 31(3), 420–428.CrossRefGoogle Scholar
  5. Bassok, Y., Anupindi, R., & Akella, R. (1999). Single-period multiproduct inventory models with substitution. Operations Research, 47(4), 632–642.CrossRefGoogle Scholar
  6. Begnaud, J., Miller, L., & Benjaafar, S. (2006). The multilevel lot sizing problem with flexible production sequences (Working paper). Minnesota: Industrial and Systems Engineering Department of Mechanical Engineering, University of Minnesota, MN.Google Scholar
  7. Birge, J. R., Drogosz, J., & Duenyas, I. (1998). Setting single-period optimal capacity levels and prices for substitutable products. International Journal of Flexible Manufacturing Systems, 10(4), 407–430.CrossRefGoogle Scholar
  8. Bitran, G. R., & Dasu, S. (1992). Ordering policies in an environment of stochastic yields and substitutable demands. Operations Research, 40(5), 999–1017.CrossRefGoogle Scholar
  9. Chen, C., Zhao, Z., & Ball, M. (2001). Quantity and due date quoting available to promise. Information Systems Frontiers, 3(4), 477–488.CrossRefGoogle Scholar
  10. Chen, J. (2003). Component allocation in multi-echelon assembly systems with linked substitutes. Computers & Industrial Engineering, 45(1), 43–60.CrossRefGoogle Scholar
  11. DeCroix, G., & Zipkin, P. (2005). Inventory management for an assembly system with product or component returns. Management Science, 51, 1250–1265.CrossRefGoogle Scholar
  12. Denton, B., & Gupta, D. (2004). Strategic inventory deployment in the steel industry. IIE Transactions, 36(11), 1083–1097.CrossRefGoogle Scholar
  13. Dickersbach, J. T. (2006). Supply chain management with APO: Structures, modelling approaches, and implementation of MySAP SCM 4.1 (2nd edn.). Berlin: Springer.Google Scholar
  14. Domschke, W., & Scholl, A. (2005). Grundlagen der Betriebswirtschaftslehre (3rd edn.). Berlin: Springer.Google Scholar
  15. Drezner, Z., Gurnani, H., & Pasternack, B. A. (1995). An EOQ model with substitutions between products. The Journal of the Operational Research Society, 46(7), 887–891.Google Scholar
  16. Duenyas, I. P., & Tsai, C. Y. P. (2000). Control of a manufacturing system with random product yield and downward substitutability. IIE Transactions, 32(9), 785–795.Google Scholar
  17. Erlenkotter, D. (1978). A dual-based procedure for uncapacitated facility location. Operations Research, 26(6), 992–1009.CrossRefGoogle Scholar
  18. Fleischmann, B., & Meyr, H. (2003). Customer orientation in Advanced Planning Systems. In H. Dyckhoff, R. Lackes, & J. Reese (Eds.), Supply chain management and reverse logistics (pp. 297–322). Berlin: Springer.Google Scholar
  19. Gallego, G., Katircioglu, K., & Ramachandran, B. (2006). Semiconductor inventory management with multiple grade parts and downgrading. Production Planning & Control, 17(7), 689–700.CrossRefGoogle Scholar
  20. Gallego, G., & Phillips, R. (2004). Revenue management of flexible products. Manufacturing & Service Operations Management, 6(4), 321–337.CrossRefGoogle Scholar
  21. Gerchak, Y., & Grosfeld-Nir, A. (1999). Lot-sizing for substitutable, production-to-order parts with random functionality yields. International Journal of Flexible Manufacturing Systems, 11(4), 371–377.CrossRefGoogle Scholar
  22. Geunes, J. (2003). Solving large-scale requirements planning problems with component substitution options. Computers & Industrial Engineering, 44(3), 475–491.CrossRefGoogle Scholar
  23. Gunasekaran, A., & Ngai, E. (2005). Build-to-order supply chain management: A literature review and framework for development. Journal of Operations Management, 23(5), 423–451.CrossRefGoogle Scholar
  24. Gurnani, H., & Drezner, Z. (2000). Deterministic hierarchical substitution inventory models. Journal of the Operational Research Society, 51(1), 129–133.Google Scholar
  25. Hale, W., Pyke, D. F. P., & Rudi, N. (2000). An assemble-to-order system with component substitution (Working paper). Hanover, NH / Rochester, NY: Amos Tuck School, Dartmouth College / The Simon School, University of Rochester.Google Scholar
  26. Hardung, B., & Kollert, T. (2005). Optimisation of the variant combination of control units considering the order history. In H.-D. Haasis, H. Kopfer, & J. Schönberger (Eds.), Operations research proceedings 2005. Berlin: Springer.Google Scholar
  27. Henrich, P., Land, M., & Gaalman, G. (2007). Semi-interchangeable machines: Implications for workload control. Production Planning & Control, 18(2), 91–104.CrossRefGoogle Scholar
  28. Hsu, A., & Bassok, Y. (1999). Random yield and random demand in a production system with downward substitution. Operations Research, 47(2), 277–290.CrossRefGoogle Scholar
  29. Hsu, V. N., Li, C. L., & Xiao, W. Q. (2005). Dynamic lot size problems with one-way product substitution. IIE Transactions, 37, 201–215.CrossRefGoogle Scholar
  30. Jones, P. C., Lowe, T. J., Muller, G., Xu, N., Ye, Y., & Zydiak, J. L. (1995). Specially structured uncapacitated facility location problems. Operations Research, 43(4), 661–669.CrossRefGoogle Scholar
  31. Karakul, M., & Chan, L. (2008). Analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem. European Journal of Operational Research, 190, 179–204.CrossRefGoogle Scholar
  32. Lang, J. C., & Domschke, W. (2008). Efficient reformulations for dynamic lot-sizing problems with product substitution. OR Spectrum. doi:10.1007/s00291-008-0148-1.Google Scholar
  33. Liu, J., & Lee, C. G. (2007). Evaluation of inventory policies with unidirectional substitutions. European Journal of Operational Research, 182, 145–163.CrossRefGoogle Scholar
  34. Minner, S., Silver, E. A., & Robb, D. J. (2003). An improved heuristic for deciding on emergency transshipments. European Journal of Operational Research, 148(2), 384–400.CrossRefGoogle Scholar
  35. Nahmias, S. (1982). Perishable inventory theory: A review. Operations Research, 30(4), 680–708.CrossRefGoogle Scholar
  36. Ozturan, C. (2004). Network flow models for electronic barter exchanges. Journal of Organizational Computing and Electronic Commerce, 14(3), 175–194.CrossRefGoogle Scholar
  37. Pentico, D. W. (1988). The discrete two-dimensional assortment problem. Operations Research, 36(2), 324–332.CrossRefGoogle Scholar
  38. Pentico, D. W. (2008). The assortment problem: A survey. European Journal of Operational Research, 190(2), 295–309.CrossRefGoogle Scholar
  39. Poltroniere, S., Poldi, K., Toledo, F., & Arenales, M. (2008). A coupling cutting stock-lot sizing problem in the paper industry. Annals of Operations Research, 157(1), 91–104.CrossRefGoogle Scholar
  40. Quante, R., Meyr, H., & Fleischmann, M. (2009). Revenue management and demand fulfillment: Matching applications, models, and software. OR Spectrum, 31(1), 31–62.CrossRefGoogle Scholar
  41. Ram, B., Naghshineh-Pour, M., & Yu, X. (2006). Material requirements planning with flexible bills-of-material. International Journal of Production Research, 44(2), 399–415.CrossRefGoogle Scholar
  42. Rao, U. N., Swaminathan, J. N., & Zhang, J. (2004). Multi-product inventory planning with downward substitution, stochastic demand and setup costs. IIE Transactions, 36(1), 59–71.CrossRefGoogle Scholar
  43. Sadowski, W. (1959). A few remarks on the assortment problem. Management Science, 6(1), 13–24.CrossRefGoogle Scholar
  44. Shumsky, R. A., & Zhang, F. (2007). Dynamic capacity management with substitution (Working paper). Hanover, NH: Tuck School of Business, Dartmouth College.Google Scholar
  45. Varian, H. (2007). Intermediate microeconomics: A modern approach (7th edn.). New York: WW Norton.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Law, Business and Economics Chair of Operations ResearchTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations