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

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 the negative effects of obsolescence.