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Fill-Rate Optimization in a One-Warehouse N-Identical Retailer Distribution System

Author

Listed:
  • Leroy B. Schwarz

    (Krannert Graduate School, Purdue University, West Lafayette, Indiana 47907)

  • Bryan L. Deuermeyer

    (Department of Industrial Engineering, Texas A&M University, College Station, Texas 77843)

  • Ralph D. Badinelli

    (School of Business, University of Kentucky, Louisville, Kentucky 40506)

Abstract

This paper examines the system fill-rate of a one-warehouse N-identical retailer distribution system as a function of warehouse and retailer safety stock. Using the approximation model of Deuermeyer and Schwarz (Deuermeyer, B. L., L. B. Schwarz. 1981. A model for the analysis of system service level in warehouse/retailer distribution systems: the identical retailer case. Chapter 8 in Multi-Level Production/Inventory Control Systems: Theory and Practice. North-Holland, Amsterdam.) we examine the problem of maximizing system fill-rate subject to a constraint on system safety stock. Optimal safety stock policy is characterized to be the intersection of a fill-rate policy line and the safety stock budget line. Properties of fill-rate policy lines are given. These properties may be used to provide managerial insight into system optimization and as the basis for heuristics. One heuristic, the vertical heuristic, based on the corresponding deterministic version of the problem, yields trivially simple and near-optimal policies.

Suggested Citation

  • Leroy B. Schwarz & Bryan L. Deuermeyer & Ralph D. Badinelli, 1985. "Fill-Rate Optimization in a One-Warehouse N-Identical Retailer Distribution System," Management Science, INFORMS, vol. 31(4), pages 488-498, April.
    • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:4:p:488-498
    DOI: 10.1287/mnsc.31.4.488
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    Cited by:

    1. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    2. Noordhoek, Marije & Dullaert, Wout & Lai, David S.W. & de Leeuw, Sander, 2018. "A simulation–optimization approach for a service-constrained multi-echelon distribution network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 292-311.
    3. Whybark, D. Clay & Yang, Shitao, 1996. "Positioning inventory in distribution systems," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 271-278, August.
    4. Chiu, Yuan-Shyi Peter & Chen, Yung-Chung & Lin, Hong-Dar & Chang, Huei-Hsin, 2014. "Combining an improved multi-delivery policy into a single-producer multi-retailer integrated inventory system with scrap in production," Economic Modelling, Elsevier, vol. 39(C), pages 163-167.
    5. Takahashi, Katsuhiko & Aoi, Takahiko & Hirotani, Daisuke & Morikawa, Katsumi, 2011. "Inventory control in a two-echelon dual-channel supply chain with setup of production and delivery," International Journal of Production Economics, Elsevier, vol. 133(1), pages 403-415, September.
    6. Sarker, Bhaba R. & Diponegoro, Ahmad, 2009. "Optimal production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers," European Journal of Operational Research, Elsevier, vol. 194(3), pages 753-773, May.
    7. Erenguc, S. Selcuk & Simpson, N. C. & Vakharia, Asoo J., 1999. "Integrated production/distribution planning in supply chains: An invited review," European Journal of Operational Research, Elsevier, vol. 115(2), pages 219-236, June.
    8. David Simchi-Levi & Yao Zhao, 2005. "Safety Stock Positioning in Supply Chains with Stochastic Lead Times," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 295-318, December.
    9. Chiu, Singa Wang & Lin, Li-Wen & Chen, Kuang-Ku & Chou, Chung-Li, 2013. "Determining production–shipment policy for a vendor–buyer integrated system with rework and an amending multi-delivery schedule," Economic Modelling, Elsevier, vol. 33(C), pages 668-675.
    10. Gérard P. Cachon, 2001. "Exact Evaluation of Batch-Ordering Inventory Policies in Two-Echelon Supply Chains with Periodic Review," Operations Research, INFORMS, vol. 49(1), pages 79-98, February.
    11. Monthatipkul, Chumpol & Yenradee, Pisal, 2008. "Inventory/distribution control system in a one-warehouse/multi-retailer supply chain," International Journal of Production Economics, Elsevier, vol. 114(1), pages 119-133, July.
    12. B Desmet & E-H Aghezzaf & H Vanmaele, 2010. "A normal approximation model for safety stock optimization in a two-echelon distribution system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 156-163, January.
    13. Karaman, Abdullah & Altiok, Tayfur, 2009. "Approximate analysis and optimization of batch ordering policies in capacitated supply chains," European Journal of Operational Research, Elsevier, vol. 193(1), pages 222-237, February.
    14. Ahire, Sanjay L. & Schmidt, Charles P., 1996. "A model for a Mixed Continuous-Periodic Review One-Warehouse, N-Retailer inventory system," European Journal of Operational Research, Elsevier, vol. 92(1), pages 69-82, July.
    15. Aydin Alptekinoglu & Arunava Banerjee & Anand Paul & Nikhil Jain, 2013. "Inventory Pooling to Deliver Differentiated Service," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 33-44, September.
    16. Garg, D. & Narahari, Y. & Viswanadham, N., 2006. "Achieving sharp deliveries in supply chains through variance pool allocation," European Journal of Operational Research, Elsevier, vol. 171(1), pages 227-254, May.
    17. Verrijdt, J. H. C. M. & de Kok, A. G., 1995. "Distribution planning for a divergent N-echelon network without intermediate stocks under service restrictions," International Journal of Production Economics, Elsevier, vol. 38(2-3), pages 225-243, March.
    18. Bollapragada, rinivas & Akella, Ram & Srinivasan, Ramesh, 1998. "Centralized ordering and allocation policies in a two-echelon system with non-identical warehouses," European Journal of Operational Research, Elsevier, vol. 106(1), pages 74-81, April.
    19. Tseng, Chao-Tang & Wu, Mei-Fang & Lin, Hong-Dar & Chiu, Yuan-Shyi Peter, 2014. "Solving a vendor–buyer integrated problem with rework and a specific multi-delivery policy by a two-phase algebraic approach," Economic Modelling, Elsevier, vol. 36(C), pages 30-36.
    20. Agrawal, Vipul & Chao, Xiuli & Seshadri, Sridhar, 2004. "Dynamic balancing of inventory in supply chains," European Journal of Operational Research, Elsevier, vol. 159(2), pages 296-317, December.
    21. Chiu, Yuan-Shyi Peter & Huang, Chao-Chih & Wu, Mei-Fang & Chang, Huei-Hsin, 2013. "Joint determination of rotation cycle time and number of shipments for a multi-item EPQ model with random defective rate," Economic Modelling, Elsevier, vol. 35(C), pages 112-117.
    22. Markus Ettl & Gerald E. Feigin & Grace Y. Lin & David D. Yao, 2000. "A Supply Network Model with Base-Stock Control and Service Requirements," Operations Research, INFORMS, vol. 48(2), pages 216-232, April.

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