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A Capacitated Lot Sizing Game with Transshipments, Scarce Capacities, and Player-Dependent Cost Coefficients

  • Julia DrechselEmail author
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Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 644)

Abstract

In this chapter, we investigate a game with cooperative production based on the capacitated lot sizing problem where the available resources of the players may be used jointly. As in the chapters before, two topics will be discussed: Determining the optimal production plan for the grand coalition and allocating the total costs for such a production plan among the players.

Keywords

Master Problem Lagrangean Relaxation Grand Coalition Cost Allocation Cost Coefficient 
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.

References

  1. Billington, P. J., McClain, J. O., & Thomas, L. J. (1983). Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction. Management Science, 29(10), 1126–1141.CrossRefGoogle Scholar
  2. Derstroff, M. C. (1995). Mehrstufige Losgrenplanung mit Kapazittsbeschrnkungen. Physica, Heidelberg.CrossRefGoogle Scholar
  3. Diaby, M., Bahl, H. C., Karwan, M. H., & Zionts, S. (1992). A Lagrangean Relaxation Approach for Very-Large-Scale Capacitated Lot-Sizing. Management Science, 38(9), 1329–1340.CrossRefGoogle Scholar
  4. Drexl, A., & Kimms, A. (1997). Lot Sizing and Scheduling - Survey and Extensions. European Journal of Operational Research, 99(2), 221–235.CrossRefGoogle Scholar
  5. Erlenkotter, D. (1978). A Dual-Based Procedure for Uncapacitated Facility Location. Operations Research, 26(6), 992–1009.CrossRefGoogle Scholar
  6. Fisher, M. L. (1981). The Lagrangean Relaxation Method for Solving Integer Programming Problems. Management Science, 27(1), 1–18.CrossRefGoogle Scholar
  7. Geoffrion, A. M. (1974). Lagrangean Relaxation for Integer Programming. Mathematical Programming Study, 2(1), 81–114.Google Scholar
  8. Goemans, M. X., & Skutella, M. (2004). Cooperative Facility Location Games, Journal of Algorithms, 50(2), 194–214.CrossRefGoogle Scholar
  9. Helber, S., & Sahling, F. (2010). A Fix-and-Optimize Approach for the Multi-Level Capacitated Lot Sizing Problem. International Journal of Production Economics, 123(2), 247–256.CrossRefGoogle Scholar
  10. Held, M., Wolfe, P., & Crowder, H. P. (1974). Validation of Subgradient Optimization. Mathematical Programming, 6(1), 62–88.CrossRefGoogle Scholar
  11. Karimi, B., Fatemi Ghomi, S. M. T., & Wilson, J. M. (2003). The Capacitated Lot Sizing Problem: A Review of Models and Algorithms. Omega, 31(5), 365–378.CrossRefGoogle Scholar
  12. Lang, J. C., & Domschke, W. (2010). Efficient Reformulations for Dynamic Lot-Sizing Problems with Product Substitution. OR Spectrum, 32(2), 263–291.CrossRefGoogle Scholar
  13. Millar, H. H., & Yang, M. (1994). Lagrangean Heuristics for the Capacitated Multi-Item Lot-Sizing Problem with Backordering. International Journal of Production Economics, 34(1), 1–15.CrossRefGoogle Scholar
  14. Pochet, Y., & Wolsey, L. A. (2006). Production Planning by Mixed Integer Programming. Springer, Heidelberg.Google Scholar
  15. Sahling, F., Buschkühl, L., Tempelmeier, H., & Helber, S. (2009). Solving a Multi-Level Capacitated Lot Sizing Problem with Multi-Period Setup Carry-Over via a Fix-and-Optimize Heuristic. Computers & Operations Research, 36(9), 2546–2553.CrossRefGoogle Scholar
  16. Sambasivan, M., & Yahya, S. (2005). A Lagrangean-Based Heuristic for Multi-Plant, Multi-Item, Multi-Period Capacitated Lot-Sizing Problems with Inter-Plant Transfers. Computers & Operations Research, 32(3), 537–555.CrossRefGoogle Scholar
  17. Sox, C. R., & Gao, Y. (1999). The Capacitated Lot Sizing Problem with Setup Carry-Over. IIE Transactions, 31(2), 173–181.Google Scholar
  18. Stadtler, H. (2003). Multilevel Lot Sizing with Setup Times and Multiple Constrained Resources: Internally Rolling Schedules with Lot-Sizing Windows. Operations Research, 51(3), 487–502.CrossRefGoogle Scholar
  19. Tempelmeier, H., & Derstroff, M. (1996). A Lagrangean-Based Heuristic for Dynamic Multilevel Multiitem Constrained Lotsizing with Setup Times. Management Science, 42(5), 738–757.CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.DuisburgGermany

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