Should retailers hold a perishable product having different ages? The case of a homogeneous market and multiplicative demand model

This paper specializes in investigating the common practice of the coexistence of multiple competing perishables, each with different age and price, all of which are associated with the same product. The fundamental postulate investigated by our model is the replacement of the policy of selling a single product-age with a policy of selling multiple product-ages. Coexistence of multiple product-ages on the shelf is associated with shorter cycle lengths as well as with providing consumers with the option of choosing between a fresher product on average and a cheaper product on average. We use a utility corresponding to the factors of price and time. We axiomatically assume the coexistence of multiple product-ages while posing several propositions which present certain difficulties in preferring this policy. With the support of a multiplicative demand with respect to price and time, and by assuming that consumers are homogeneous in their preferences, we analyze a deterministic version of the problem and derive the optimal pricing policy given any cycle length and any duration for which both types coexist on the shelf. We prove that the optimal policy is not to sell multiple product-types at all. By means of a numerical example we show that the operational mode of the coexistence of multiple product-ages reduces the retailer's profit per unit time by at least 15%. Sensitivity analysis of some of the most influential parameters is introduced. The superiority of the single product-age operational mode over the competitor mode sharply decreases as the optimal cycle length is approached.