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The Multilocation Multiperiod Inventory Problem: Bounds and Approximations

Author

Listed:
  • Uday S. Karmarkar

    (Graduate School of Management, University of Rochester, Rochester, New York 14627)

Abstract

The multilocation inventory problem can be thought of naturally as an extension of the single location "newsboy" problem to multiple locations with transshipment possible between locations. Previous work has established the form of optimal policies; however, computational results have been limited to the one-period case or to special structures. This paper develops lower- and upper-bounds for the general multiperiod problem. These also suggest approximations to the optimal solution. Computational methods are discussed and tested on small problems.

Suggested Citation

  • Uday S. Karmarkar, 1987. "The Multilocation Multiperiod Inventory Problem: Bounds and Approximations," Management Science, INFORMS, vol. 33(1), pages 86-94, January.
    • Handle: RePEc:inm:ormnsc:v:33:y:1987:i:1:p:86-94
    DOI: 10.1287/mnsc.33.1.86
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    Cited by:

    1. Tiacci, Lorenzo & Saetta, Stefano, 2011. "Reducing the mean supply delay of spare parts using lateral transshipments policies," International Journal of Production Economics, Elsevier, vol. 133(1), pages 182-191, September.
    2. Nils Rudi & Sandeep Kapur & David F. Pyke, 2001. "A Two-Location Inventory Model with Transshipment and Local Decision Making," Management Science, INFORMS, vol. 47(12), pages 1668-1680, December.
    3. Xiaohong Yu & Sujuan Wang & Xindong Zhang, 2019. "The Impact of Fairness Concerns on the Formation of Retailers Alliance with Consideration of Transshipment," Sustainability, MDPI, vol. 11(3), pages 1-19, January.
    4. Satya S. Malladi & Alan L. Erera & Chelsea C. White, 2021. "Managing mobile production-inventory systems influenced by a modulation process," Annals of Operations Research, Springer, vol. 304(1), pages 299-330, September.
    5. Bitran, Gabriel R. & Leong, Thin-Yin., 1989. "Deterministic approximations to co-production problems with service constraints," Working papers 3071-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    6. Rong Li, 2020. "Reinvent Retail Supply Chain: Ship‐from‐Store‐to‐Store," Production and Operations Management, Production and Operations Management Society, vol. 29(8), pages 1825-1836, August.
    7. Wong, H. & van Houtum, G.J. & Cattrysse, D. & Oudheusden, D. Van, 2006. "Multi-item spare parts systems with lateral transshipments and waiting time constraints," European Journal of Operational Research, Elsevier, vol. 171(3), pages 1071-1093, June.
    8. Amiya K. Chakravarty & Jun Zhang, 2007. "Lateral capacity exchange and its impact on capacity investment decisions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 632-644, September.
    9. Eberly, Janice C. & Van Mieghem, Jan A., 1997. "Multi-factor Dynamic Investment under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(2), pages 345-387, August.
    10. Xinxin Hu & Izak Duenyas & Roman Kapuscinski, 2008. "Optimal Joint Inventory and Transshipment Control Under Uncertain Capacity," Operations Research, INFORMS, vol. 56(4), pages 881-897, August.
    11. Tiacci, Lorenzo & Saetta, Stefano, 2011. "A heuristic for balancing the inventory level of different locations through lateral shipments," International Journal of Production Economics, Elsevier, vol. 131(1), pages 87-95, May.
    12. Sumit Kunnumkal & Huseyin Topaloglu, 2008. "A duality‐based relaxation and decomposition approach for inventory distribution systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 612-631, October.
    13. Huseyin Topaloglu & Sumit Kunnumkal, 2006. "Approximate dynamic programming methods for an inventory allocation problem under uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 822-841, December.
    14. Xu, Kefeng & Evers, Philip T. & Fu, Michael C., 2003. "Estimating customer service in a two-location continuous review inventory model with emergency transshipments," European Journal of Operational Research, Elsevier, vol. 145(3), pages 569-584, March.
    15. Seifert, Ralf W. & Thonemann, Ulrich W. & Sieke, Marcel A., 2006. "Integrating direct and indirect sales channels under decentralized decision-making," International Journal of Production Economics, Elsevier, vol. 103(1), pages 209-229, September.
    16. H Wong & G J van Houtum & D Cattrysse & D Van Oudheusden, 2005. "Simple, efficient heuristics for multi-item multi-location spare parts systems with lateral transshipments and waiting time constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(12), pages 1419-1430, December.
    17. Chew, Ek-Peng & Huang, Huei-Chuen & Johnson, Ellis L. & Nemhauser, George L. & Sokol, Joel S. & Leong, Chun-How, 2006. "Short-term booking of air cargo space," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1979-1990, November.
    18. Zhang, Jiaqi & Archibald, Thomas W., 2011. "A semi-Markov model with holdout transshipment policy and phase-type exponential lead time," European Journal of Operational Research, Elsevier, vol. 211(3), pages 650-657, June.
    19. Felipe Caro & Jérémie Gallien, 2007. "Dynamic Assortment with Demand Learning for Seasonal Consumer Goods," Management Science, INFORMS, vol. 53(2), pages 276-292, February.
    20. Yale T. Herer & Michal Tzur, 2001. "The dynamic transshipment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(5), pages 386-408, August.
    21. Kumar Rajaram & Uday S. Karmarkar, 2002. "Product Cycling With Uncertain Yields: Analysis and Application to the Process Industry," Operations Research, INFORMS, vol. 50(4), pages 680-691, August.
    22. Hui Zhao & Jennifer K. Ryan & Vinayak Deshpande, 2008. "Optimal Dynamic Production and Inventory Transshipment Policies for a Two-Location Make-to-Stock System," Operations Research, INFORMS, vol. 56(2), pages 400-410, April.

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