Optimal inventory policies for finite horizon deterministic inventory models for non-instantaneous deteriorating items and permissible-delay in payment

Abstract

This paper is concerned with the search for the optimal inventory policy for a finite horizon inventory model with time-varying demand, non-instantaneous deteriorating items, and permissible delay in payment. The optimal inventory policy consists of the determination of the number and timing of replenishment schedules that minimise some total inventory costs. The search for such policy is formulated as a mixed integer nonlinear programming problem (MINLP). It turns out that the non-instantaneous deterioration phenomenon coupled with permissible delay in payment introduce non-smoothness in the objective function of the MINLP. This leads to failure of direct applications of known solution methods to the MINLP. To circumvent this problem, a methodology is proposed for solving fully the MINLP problem. It is shown, through careful mathematical analysis, that earlier results on similar problems can be adapted to solve this problem. Conditions under which the solution of the MINLP is unique are identified. Moreover, convexity with respect to the number of replenishment orders is established. This makes the search for the optimal inventory policy handy. Numerical experiments are also conducted to test the applicability, to identify the key elements and to provide managerial insights to the model.