On a discrete-in-time deterministic inventory model for deteriorating items with time proportional demand

A lot-size inventory system is considered here in which the demand rate is changing linearly with time and the deterioration of units is a constant fraction of the on hand inventory. The planning horizon is finite and known with equal replenishment periods. The model of the system is continuous in units and discrete in time. The problem is to find the optimal number of replenishments which are instantaneous. In the absence of deterioration, the developed model is related to the corresponding model for nondeteriorating items. An example followed by sensitivity analysis is given to illustrate the derived results.