Optimal ordering quantities for substitutable deteriorating items under joint replenishment

In this paper, we study an inventory system for two substitutable deteriorating items where when an item is out of stock, the 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. The level of inventory of both items deplete due to combined effect of demand fulfilment and deterioration. The rates of demand and deterioration are assumed to be deterministic and constant. Items are ordered jointly in each ordering cycle so as to take advantage 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. An extensive numerical analysis is carried out to illustrate the parameters of the model. The results indicate that there is substantial improvement in the optimal total cost of the inventory system with substitution over the case without substitution.