Inspection Policy for Inventory System with Deteriorating Products

Typical inventory models usually focus on screening out the deteriorating items, not much attention is paid to the situation that a proportion of deteriorated items are sold to consumers together with serviceable items during a replenishment cycle. This paper first presents a model to formulate the process of such kind of mixed sales. A simple closed-form solution is obtained for maximizing the net profit per unit time under the assumption of small deterioration rate. The effect of shortage back-ordering is then considered and closed-form solutions of optimal ordering quantity and replenishment time are obtained under similar assumption. We further study the effect of inspection policies on optimal decisions for a deteriorating inventory system. A dynamic programming approach is proposed for solving the optimal policy. Numerical examples are then provided to demonstrate our conclusions and results.