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A Multi-period Profit Maximization Policy for a Stochastic Demand Inventory System with Upward Substitution
Authors: Soma Roychowdhury
Abstract:This paper deals with a periodic-review substitutable inventory system for a finite and an infinite number of periods. Here an upward substitution structure, a substitution of a more costly item by a less costly one, is assumed, with two products. At the beginning of each period, a stochastic demand comes for the first item only, which is quality-wise better and hence costlier. Whenever an arriving demand finds zero inventory of this product, a fraction of unsatisfied customers goes for its substitutable second item. An optimal ordering policy has been derived for each period. The results are illustrated with numerical examples. A sensitivity analysis has been done to examine how sensitive the optimal solution and the maximum profit are to the values of the discount factor, when there is a large number of periods.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070105Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1103
 I. Duenyas and C.Y. Tsai, Optimal Control of a Manufacturing System with Random Product Yield and Downward Substitutability, IEETransactions, Vol. 32, No. 9, pp. 785-795, 2000.
 Y. Bassok, R. Anupindi and R. Akella, Single-period Multi-product Inventory Models with Substitution, Operations Research, Vol. 47, No. 4, pp. 632-642, 1999 (DOI: 10.1287/opre.47.4.632).
 A. Hsu and Y. Bassok, Random Yield and Random Demand in a Production System with Downward Substitution, Operations Research, Vol. 47, No. 2, pp. 277-290, 1999.
 R. Leachman, Preliminary Design and Development of a Corporate-level Production System for the Semiconductor Industry, Working Paper ORC 86-11, Operations Research Center, University of California, Berkeley, CA, 1987.
 H. Wagner and T.W. Whitin, Dynamic Version of the Economic Lot Size Model, Management Science, Vol. 5, pp. 89-96, 1958.
 I. Civelek, A.Scheller-Wolf and I. Karaesmen, Blood Inventory Management with Protection Levels and Substitution, INFORMS MSOM 2009 Conference Proceedings, June 29-30, 2009, MIT, Cambridge, MA, 2009.
 R. Haijema, J. van der Wal and N.M. van Dijk, Blood Platelet Production: A Multi-type Perishable Inventory Problem, Research Memorandum, FEE, University of Amsterdam, 2005.
 G. Stuer, K.Vanmechelen and J. Broeckhove, A Commodity Market Algorithm for Pricing Substitutable Grid Resources, Future Generation Computer Systems, Vol. 23, No. 5, pp. 688-701, 2007.
 K.Y. K. Ng and M.N. Lam, Standardisation of Substitutable Electrical Item, The Journal of the Operational Research Society, Vol. 49, No. 9, pp. 992-997, 1998.
 D.A. Sumner and J.M. Alston, Substitutability for Farm Commodities: The Demand for US Tobacco in Cigarette Manufacturing, American Journal of Agricultural Economics, Vol. 69, No. 2, pp. 258-265, 1987.
 B. A. Pasternack and Z. Drezner, Optimal Inventory Policies for Substitutable Commodities with Stochastic Demand, Naval Research Logistics, Vol. 38, No. 2, pp. 221-240, 2006.
 M. Parlar and S.K. Goyal, Optimal Ordering Decisions for Two Substitutable Products with Stochastic Demands, Opsearch, Vol. 21, No. 1, pp. 1-15, 1984.
 S.P. Mukherjee and S. Roychowdhury, A Random Demand Inventory Model for Substitutable Commodities, IAPQR Transactions, Vol. 15, No. 2, pp. 55-67, 1990.
 A.W. Roberts and D.E. Varberg, Convex Functions, Academic Press, New York and London, 1973.
 M.H. De Groot, Optimal Statistical Decisions, McGraw-Hill Inc., USA, 1970.