The instant obsolescence problem with price-dependent demand

This paper develops ordering policies for a retailer confronted with a product subject to instant obsolescence, as a result of the imminent end to its economic lifetime, usually for technological, economic or change-in-fashion reasons. The retailer's objective function exhibits a profit maximizing rather than a cost minimising optimization objective to better reflect the profit-generating role of the retailer's merchandise. There is also a price-induced demand function to provide the retailer an additional profitability tool to handle the sudden loss of the product's income generating potential. Due to the highly complex nature of the model needed to solve the instant obsolescence problem, three heuristic solutions are proposed. The first exhibits orders of equal size. Such a feature is highly coveted in practice, but produces optimal solutions only under rather restrictive assumptions about the probability distribution of the product's economic lifetime. The second yields approximated solutions, valid for any probability distribution, regardless of whether an optimal solution can be derived. The third includes both features. A numerical example highlights the nature of the various heuristic solutions. This example also brings forward an important supply-chain characteristic, namely without any price incentive when purchasing the item in question, a profit-maximizing retailer may find it rational to discourage sales of the item or even to refuse to stock it at all.