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Advances in Operations Research
Volume 2012, Article ID 768929, 16 pages
Research Article

Optimal Policies for a Finite-Horizon Production Inventory Model

Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 26 October 2011; Revised 29 February 2012; Accepted 17 March 2012

Academic Editor: Imed Kacem

Copyright © 2012 Lakdere Benkherouf and Dalal Boushehri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the problem of finding the optimal production schedule for an inventory model with time-varying demand and deteriorating items over a finite planning horizon. This problem is formulated as a mixed-integer nonlinear program with one integer variable. The optimal schedule is shown to exist uniquely under some technical conditions. It is also shown that the objective function of the nonlinear obtained from fixing the integrality constraint is convex as a function of the integer variable. This in turn leads to a simple procedure for finding the optimal production plan.