A Multi-period Profit Maximization Policy for a Stochastic Demand Inventory System with Upward Substitution

This paper deals with a periodic-review substitutable inventory system for a finite and an infinite number of periods. Here an upward substitution structure, a substitution of a more costly item by a less costly one, is assumed, with two products. At the beginning of each period, a stochastic demand comes for the first item only, which is quality-wise better and hence costlier. Whenever an arriving demand finds zero inventory of this product, a fraction of unsatisfied customers goes for its substitutable second item. An optimal ordering policy has been derived for each period. The results are illustrated with numerical examples. A sensitivity analysis has been done to examine how sensitive the optimal solution and the maximum profit are to the values of the discount factor, when there is a large number of periods. Keywords—Multi-period model, inventory, random demand, upward substitution. AMS 2000 Subject Classification—Primary 62L99, 90B05; Secondary 90B50