An approximate optimal ordering policy with multiple deliveries and disposals for short-life time products

Abstract

In a convenience store, new items like lunch boxes and dairy products are delivered several times in one day. In addition, old unsold items must be disposed because of their expiration dates. The order is made once in a day, and the retailer has to decide the number of items ordered based on the current remaining items in the store and the demand distribution. This paper considers an optimal ordering problem with short lifetime products, where each order is made once in one day whereas delivery of ordered products and disposal of out-of-date products are twice in one day. The objective is to find the optimal numbers of items which are delivered twice in the next day, which minimize the total expected discounted cost over an infinite horizon. The model is formulated as a Markov decision process. To overcome curse of dimensionality, the appropriate set of basic functions are investigated to approximate the optimal value function of the Markov decision process. The derived approximate optimal ordering policy for the large-size problems is an unbalanced ordering policy under which more items are ordered in one delivery of one day than in another delivery of the same day even when the demand distribution is time-independent. In addition, it is shown through numerical examples that as the probability is larger that an old item is selected by a customer when both old and new items are in the store, the sub-optimal policy is more unbalanced and gains more profit.

Keywords

• order
• inventory
• markov decision process
• linear programming
• basic function