On the minimum solution of the inventory system for deteriorating items with shortages and time-varying demand

Abstract

We study the inventory model for deteriorating items with shortages and time-varying demand. In 1991, Goswani and Chaudhuri published a paper in the Journal of the Operational Research Society for the inventory model for deteriorating items with shortages and a lineal trend in demand. In 1995, in the same journal, Hariga pointed out and corrected the errors of Goswani and Chaudhuri. To a more sound mathematical formulation. we provided some improvement for the results of Hariga. The purpose of this paper is fourfold. First, when the reorder number is fixed, we prove the fraction of no-shortage is constant. Second, when the reorder number is fixed. we show that the total cost function has minimum solution. Third, we verify that the algorithm of Hariga has a finite step computation. Fourth, we offer some refined works in the numerical examples.