Optimal Ordering Policies For A Perishable And Substitutable Product: A Markov Decision Model

In this paper we consider a generalized version of the newsboy problem and assume that the product (e,g., donuts, vegetables, fashionwear) perishes in two periods, and one-period-old items and fresh (new) items may be substituted if one of them is out of stock. We show that the one-period expected profit expression is a concave function of the order quantity of new items. We model this problem in the stochastic control theory framework and find optimal stationary policies after transforming the control problem to a Markov decision problem. We provide several numerical examples and discuss the sensitivity of the optimal policy to changes in the problem parameters.