Optimal Ordering Quantities for Substitutable Items Under Joint Replenishment with Cost of Substitution

Abstract

In this paper, we study an inventory system of two mutually substitutable items where when an item is out of stock, demand for it is met by the other item and any part of demand not met due to unavailability of the other item is lost. In the event of substitution, there is an additional cost of substitution involved for each unit of the substituted item. The demands are assumed to be deterministic and constant. Items are ordered jointly in each ordering cycle, in order to take advantage of joint replenishment. The problem is formulated and a solution procedure is suggested to determine the optimal ordering quantities that minimize the total inventory cost. The critical value of the substitution rate is defined to help in deciding the optimal value of decision parameters. Extensive numerical experimentation is carried out, which shows that prior knowledge of the critical value of the substitution rate helps to minimize the total inventory cost. Sensitivity analysis is carried out for the improvement in the optimal total cost with substitution as compared to the case without substitution to draw insights into the behaviour of the model.