A Joint Economic Production Lot Size Model for a Deteriorating Item with Decreasing Warehouse Rental Overtime

Abstract

In real life, the capacity of any distributor’s warehouse is limited. Excess stock must be held in a rented warehouse whenever the capacity of the distributor’s own warehouse is insufficient. Furthermore, we also choose to store in the rented warehouse if it has better facilities and/or a lower cost. In this paper, we consider a single-producer–single-distributor inventory model with deteriorating items in a two-warehouse environment. The rented warehouse normally has better facilities for preservation as compared with one’s own warehouse. Besides, there is an incentive offered by a rented warehouse that allows the rental fee to decrease over time. The incentive mechanism can be proved to perform better than the one without incentive. The object of this study is to develop an optimal joint economic lot size (JELS) policy from the perspectives of the producer and the distributor. Moreover, a criterion to consider the length of time of rented warehouse usage is proposed. Simulated Annealing (SA) method has been developed to find the global optimum for a complex cost surface through stochastic search process. A computer program in C-language has been developed for this purpose and is implemented to derive the optimum decision for the decision maker. Numerical examples and sensitivity analyses are given to illustrate the results.