Effect of Deterioration and Partial Substitution on Optimal Inventory Decisions for Complementary and Substitutable Items with Cost of Substitution under Joint Replenishment

This paper addresses the effect of deterioration and partial substitution on optimal inventory decisions for an inventory model of two substitutable items, where one item is composed with two complementary components. In practical, substitution frequently occurs in situation of stock-out. Here, the level of inventory depletes due to combined effect of deterioration and demand, and in situation of stock-out, the unmet demand of one item is partially substituted by another item. The demand and deterioration are taken to be deterministic and constant. In the proposed model, we formulate the problem in two possible cases: partial substitution and no substitution. Further, pseudo-convexity for total cost functions is derived to ensure unique optimal solution and the solution procedure is outlined to find optimum value of order quantities such that the total cost is minimized. Numerical example and sensitivity analysis are provided to demonstrate the effect of different input parameters on optimal solution.