Impact of cost of substitution and joint replenishment on inventory decisions for joint substitutable and complementary items under asymmetrical substitution

In this paper, impact of cost of substitution and joint replenishment on inventory decisions for joint substitutable and complementary items under asymmetrical substitution has been studied. The phenomenon of substitution is considered in a stock-out situation and when items become out of stock due to demand then unfulfilled demand is asymmetrically substituted by another item. We formulate the inventory model mathematically and derived optimal ordering quantities, optimal total costs and extreme value of substitution rate for all possible cases. Moreover, pseudo-convexity of the total inventory cost function is obtained and the solution procedure is provided. Numerical example and sensitivity analysis have been presented to validate the effectiveness of the inventory model and substantial improvement in total optimal inventory cost with substitution with respect to optimal total inventory cost without substitution is seen.