Optimal ordering quantities for substitutable deteriorating items under joint replenishment with cost of substitution

In this paper we develop an inventory model, to determine the optimal ordering quantities, for a set of two substitutable deteriorating items. In this inventory model the inventory level of both items depleted due to demands and deterioration and when an item is out of stock, its demands are partially fulfilled by the other item and all unsatisfied demand is lost. Each substituted item incurs a cost of substitution and the demands and deterioration is considered to be deterministic and constant. Items are order jointly in each ordering cycle, to take the advantages of joint replenishment. The problem is formulated and a solution procedure is developed to determine the optimal ordering quantities that minimize the total inventory cost. We provide an extensive numerical and sensitivity analysis to illustrate the effect of different parameter on the model. The key observation on the basis of numerical analysis, there is substantial improvement in the optimal total cost of the inventory model with substitution over without substitution.