Abstract
This paper considers a one-warehouse multi-retailer inventory system that faces discrete stochastic demand of the customers. Under the so-called balance assumption (also known as the allocation assumption), base stock policies are optimal. Our main contribution is to show that the optimal base stock levels satisfy newsvendor characterizations, which are in terms of inequalities, and to extend the newsvendor equalities known for the continuous demand model. These characterizations are appealing because they (i) are easy to explain to nonmathematical oriented people like managers and MBA students, (ii) contribute to the understanding of optimal control, (iii) help intuition development by providing direct relation between cost and optimal policy parameters.
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References
Aviv Y, Federgruen A (2001) Capacitated multi-item inventory systems with random and seasonally fluctuating demands: implications for postponement strategies. Manag Sci 47: 512–531
Axsäter S (2003) Supply Chain Operations: Serial and Distribution Inventory Systems. In: de Kok AG, Graves SC (eds) Handbook in operations research and management science, volume 11: design and analysis of supply chains. Elsevier, Amsterdam, pp 525–559
Chen F (2000) Optimal policies for multi-echelon inventory problems with batch ordering. Oper Res 48: 376–389
Chen F, Zheng YF (1994) Lower bounds for multi-echelon stochastic inventory problems. Manag Sci 40: 1426–1443
Clark AJ, Scarf H (1960) Optimal policies for a multi-echelon inventory problem. Manag Sci 6: 475–490
de Kok AG (1989) A moment-iteration method for approximating the waiting-time characteristics of the GI/G/1 queue. Prob Eng Inf Sci 3: 273–287
de Kok AG, Fransoo JC (2003) Planning supply chain operations: Definition and comparison of planning concepts. In: Kok AG, Graves SC (eds) Handbook in operations research and management science, volume 11: design and analysis of supply chains. Elsevier, Amsterdam, pp 597–675
Diks EB, de Kok AG (1998) Optimal control of a divergent N-echelon inventory system. Eur J Oper Res 111: 75–97
Doğru MK (2006) Optimal control of one-warehouse multi-retailer systems: an assessment of the balance assumption. Ph.D. thesis, Beta Research School, D77, Technische Universiteit Eindhoven, Eindhoven
Doğru MK, van Houtum GJ, de Kok AG (2008) Newsboy characterizations for optimal reorder levels of serial inventory systems with fixed batch sizes. Oper Res Lett 36: 551–556
Doğru MK, de Kok AG, van Houtum GJ (2010) A numerical study on the effect of the balance assumption in one-warehouse multi-retailer inventory systems. Flex Serv Manuf J 21: 114–147
Eppen G, Schrage L (1981) Centralized Ordering Policies in a Multi-Warehouse System with Lead Times and Random Demand. In: Schwarz LB (ed) Multi-level production-inventory control systems: theory and practice. North-Holland, Amsterdam, pp 51–67
Everett H (1963) Generalized lagrange multiplier method for solving problems of optimum allocation of resources. Oper Res 11: 399–417
Federgruen A, Zipkin P (1984a) Approximations of dynamic, multi-location production and inventory problems. Manag Sci 30: 69–84
Federgruen A, Zipkin P (1984b) Computational issues in an infinite-horizon, multi-echelon inventory model. Oper Res 32: 818–836
Fox B (1966) Discrete optimization via marginal analysis. Manag Sci 13: 210–216
Gross OA (1956) Notes on linear programming: a class of discrete-type minimization problems. Tech. rept. RM-1644. RAND Corporation, Santa Monica
Lee HL, Tang CS (1997) Modelling the costs and benefits of delayed product differentiation. Manag Sci 43: 40–53
Rogers DF, Tsubakitani S (1991) Inventory positioning/partitioning for backorders optimization for a class of multi-echelon inventory problems. Decis Sci 22: 536–558
Saaty TL (1970) Optimization in integers and related extremal problems. McGraw-Hill, New York
van Houtum GJ (2006) Multi-echelon production/inventory systems: Optimal policies, heuristics, and algorithms. In: Johnson MP, Norman B, Secomandi N (eds) INFORMS tutorials in operations research series. INFORMS, Hanover, pp 163–199
van Houtum GJ, Zijm WHM (1991) Computational procedures for stochastic multi-echelon production systems. Int J Prod Econ 23: 223–237
van Houtum GJ, Scheller-Wolf A, Yi J (2007) Opimal control of serial inventory systems with fixed replenishment intervals. Oper Res 55: 674–687
Wijngaard J (1982) On aggregation in production planning. Eng Costs Prod Plan 6: 259–265
Zipkin P (2000) Foundations of inventory management. McGraw-Hill, Boston
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Doğru, M.K., de Kok, A.G. & van Houtum, G.J. Newsvendor characterizations for one-warehouse multi-retailer inventory systems with discrete demand under the balance assumption. Cent Eur J Oper Res 21, 541–559 (2013). https://doi.org/10.1007/s10100-012-0246-7
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DOI: https://doi.org/10.1007/s10100-012-0246-7