Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
권호 표지

Distribution Planning for a Two-Echelon Distribution System under Fill Rate Constraints

Fill Rate 제약이 존재하는 2단계 분배형 시스템에서의 분배 계획

  • 권익현 (고려대학교 정보통신기술연구원) ;
  • 김성식 (고려대학교 정보경영공학부) ;
  • 김창욱 (연세대학교 정보산업공학과)
  • Published : 2006.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper considers a periodic review, two-echelon inventory system with one central warehouse and several re-tailers facing normally distributed demand. The goal is to attain target fill rates, while the systemwide total holding costs are minimized. An important aspect of this problem is material rationing in the case of shortages. If a central warehouse has insufficient inventory to deliver all replenishment orders to retailers, all order quantities are should be adjusted according to some rationing rule. A simple but efficient rationing rule is proposed and compared with the Balanced Stock (BS) rationing as introduced by Heijden which is known to be the best rationing policy in the literature. Numerical results show that the proposed rationing rule is more cost effective than BS rationing, especially for the differences in holding costs between retailers are large.

Keywords

References

  1. 권익현, 김성식, '2단계 시리얼 시스템의 Fill Rate 만족 방안', 한국경영과학회지, 제31권, 제1호(2006),,p.105-116
  2. Axsater, S., Inventory Control, Kluwer Academic Publishers, Boston, 2000
  3. Axsater, S., 'Note: Optimal Policies for Serial Inventory Systems under Fill Rate Constraints,' Management Science, Vol.49 , No.2(2003), pp.247-253 https://doi.org/10.1287/mnsc.49.2.247.12746
  4. Clark, A.J. and H. Scarf, 'Optimal Policies for a Multiechelon Inventory Problem,' Management Science, Vol.6, No.4(1960), pp.475-490 https://doi.org/10.1287/mnsc.6.4.475
  5. Deuermeyer, B.L. and L.B. Schwarz, 'A Model for the Analysis of System Service Level in Warehouse- Retailer Distribution Systems : The Identical Retailer Case,' in : Schwarz, L.B. (Ed.), Multi-Level Production/Inventory Contrd Systems : Theory and Practice, TIMS Studies in the Management Sciences 16, North-Holland, Amsterdam, 1981, pp.163-193
  6. Diks, E.B., A.G. de Kok, and A.G. Lagodimos, 'Multi-Echelon Systems: A Service Measure Perspective,' European Journal of Operational Research, Vol.95, No.2(1996), pp. 241-263 https://doi.org/10.1016/S0377-2217(96)00120-8
  7. Diks, E.B. and A.G. de Kok, 'Optimal Control of a Divergent Multi-Echelon Inventory System,' European Journal of Operational Research, Vol.111, No.1(1998), pp.75-97 https://doi.org/10.1016/S0377-2217(97)00327-5
  8. Diks, E.B. and A.G. de Kok, 'Computational Results for the Control of a Divergent N-Echelon Inventory System,' International Journal of Production Economics, Vol.59, No.1-3(1999), pp.327-336 https://doi.org/10.1016/S0925-5273(98)00023-1
  9. Donselaar, K. van and J. Wijngaard, 'Commonality and Safety Stocks,' Engineering Costs and Production Economics, Vol.12, No.1-4(1987), pp.197-204 https://doi.org/10.1016/0167-188X(87)90078-4
  10. Eppen, G. and L. Schrage, 'Centralized Ordering Policies in a Multi - Warehouse System with Lead Times and Random Demand,' in : Schwarz, L.B. (Ed.), MultiLevel Production-Inventory Control Systems : Theory and Practice, TIMS Studies in the Management Sciences 16, NorthHolland, Amsterdam, 1981, pp.51-67
  11. Federgruen, A. and P.H. Zipkin, 'Approximations of Dynamic Multilocation Production and Inventory Problems,' Management Science, Vol.30, No.1(1984), pp.69-84 https://doi.org/10.1287/mnsc.30.1.69
  12. Federgruen, A and P.H. Zipkin, 'Allocation Policies and Cost Approximations for Multilocation Inventory Systems,' Naval Research Logistics Quarterly, Vol.31, No.1(1984), pp. 97-129 https://doi.org/10.1002/nav.3800310112
  13. Hadley, G. and T. Whitin, Analysis of Inventory Systems, Prentice-Hall, Englewood Cliffs, NJ, 1963
  14. Heijden, M.C. van der, 'Supply Rationing in Multi-Echelon Divergent Systems,' European Journal of Operational Research, Vol. 101, No.3(1997), pp.532-549 https://doi.org/10.1016/S0377-2217(96)00187-7
  15. Heijden, M.C. van der, E.B. Diks, and A.G. de Kok, 'Stock Allocation in General MultiEchelon Distribution Systems with (R,S) Order-up-to Policies,' International Journal of Production Economics, Vol.49, No.2(1997), pp.157-174 https://doi.org/10.1016/S0925-5273(97)00005-4
  16. Heijden, M.C. van der, 'Near Cost-Optimal Inventory Control Policies for Divergent Networks under Fill Rate Constraints,' International Journal of Production Economics, Vol.63, No.2(2000), pp.161-179 https://doi.org/10.1016/S0925-5273(99)00008-0
  17. Houtum, G.J. van, K. Inderfurth, and W.H.M. Zijm, 'Material Coordination in Stochastic Multi-Echelon Systems,' European Journal of Operational Research, Vol.95, No.1(1996), pp.1-23 https://doi.org/10.1016/0377-2217(96)00080-X
  18. Johnson, M.E., H.L. Lee, T. Davis, and R. Hall, 'Expressions for Item Fill Rates in Periodic Inventory Systems,' Naval Research Logistics, Vol.42, No.1 (1995), pp.57-80 https://doi.org/10.1002/1520-6750(199502)42:1<57::AID-NAV3220420107>3.0.CO;2-2
  19. Kok, A.G. de, Hierarchical Production Planning for Consumer Goods,' European Journal of Operational Research, Vol.45, No.1 (1990), pp.55-69 https://doi.org/10.1016/0377-2217(90)90156-6
  20. Kok, A.G. de and J.C. Fransoo, 'Planning Supply Chain Operations: Definition and Comparison of Planning Concepts,' in: Kok, A.G. de and S.C. Graves (Eds.), Supply Chain Management: Design, Coordination and Operation, Handbooks in Operations Research and Management Science 11, Elsevier Publishing Company, 2003, pp.597-676
  21. Lagodimos, A.G., 'Multi-Echelon Service Models for Inventory Systems under Different Rationing Policies,' International Journal of Production Research, Vol.30, No.4 (1992), pp.939-958 https://doi.org/10.1080/00207543.1992.9728466
  22. Sherbrooke, C.C., 'METRIC: A Multi-Echelon Technique for Recoverable Item Control,' Operations Research, Vol.16, No.1(1968), pp,122-141 https://doi.org/10.1287/opre.16.1.122
  23. Sobel, M.J., 'Fill Rates of Single-Stage and Multistage Supply Systems,' Manufacturing & Service Operations Management, Vol.6, No.1(2004), pp.41-52 https://doi.org/10.1287/msom.1030.0027
  24. Verrijdt, J,H.C.M. and A.G. de Kok, 'Distribution Planning for a Divergent N-Echelon Network without Intermediate Stocks under Service Restrictions,' International Journal of Production Economics, Vol.38, No.2-3 (1995), pp.225-243 https://doi.org/10.1016/0925-5273(94)00097-T
  25. Verrijdt, J,H.C.M. and A.G. de Kok, 'Distribution Planning for a Divergent Depotless Two-Echelon Network under Service Constraints,' European Journal of Operational Research, Vol.89, No.2(1996), pp.341-354 https://doi.org/10.1016/0377-2217(94)00242-8
  26. Zipkin, P.H., 'On the Imbalance of Inventories in Multi-Echelon Systems,' Mathematics of Operations Research, Vol.9, No.3 (1984), pp.402-423 https://doi.org/10.1287/moor.9.3.402