A myopic policy for the gradual obsolescence problem with price-dependent demand

Abstract

The purpose of this paper is to develop a retailer's profit-maximizing myopic inventory policy for an item recognized as subject to gradual obsolescence. Demand is assumed to be a decreasing function of both the retailer's sale price and of time, up to a certain stochastic time point when obsolescence occurs and, as a result, the demand suddenly drops to zero. For each ordering cycle, the decision variables are the retailer's selling price and the order size. A stop-ordering rule is developed on the basis of finding the time point beyond which it is profitable to stop ordering, even if there is still some demand for the item. In addition, the sudden obsolescence problem is shown to be a limiting and non-trivial case of its gradual counterpart. The numerical example illustrates the main features of the model, including the importance of the vendor dropping the price charged to retailers, so as to provide the needed incentives for the retailers to drop the price charged to their own customers and thereby palliate as much as possible to negative effects of obsolescence. Scope and purpose This paper develops a myopic policy to evaluate a retailer's decision process, when an item is recognized as subject to gradual obsolescence. The model considers demand to be a decreasing function of both the retailer's sale price and of time, up to a certain stochastic time point when obsolescence occurs and, as a result, the demand suddenly drops to zero. The retailer's profit-maximizing policy consists of an optimal selling price and an order size for each ordering cycle, as well as the time point beyond which it is profitable to stop ordering, even if there is still some demand for the item. This is in contrast to alternate formulations, where the stopping rule is based upon minimizing the cost of obsolescence, rather than evaluating the profitability of the item in question. Finally, the numerical example illustrates the need for vendor/retailer collaboration in the development of the pricing policies. Otherwise, the retailer has no incentive to keep prices low and thus counteract the normal decreases in demand that occur as time passes by and the probability of obsolescence increases.