A non-cooperative game model for managing a multiple-aged expiring inventory under consumers' heterogeneity to price and time

The considered inventory system includes the coexistence of old and new types belonging to an identical product. A non-cooperative game approach between the retailer and the market, where the retailer aims to increase her profit, is developed. The market, on the other hand, may seek different objectives. In particular, the objectives of price minimization, freshness maximization, and maximization of the quantity on shelf are analyzed. The main objectives are to develop a model of a multiple-aged inventory system and to specify the conditions under which multiple types on the shelf are not beneficial to either the retailer or the market. Using an analytic optimization approach, the optimal response functions of the two players are derived, while with the aid of numerical iterations, the non-cooperative game Nash equilibrium is obtained. The main theoretical result indicates that selling an inventory that simultaneously holds multiple ages is not optimal; that is, both the retailer and consumers lose out from such a situation. This conclusion is general enough to be valid for a market that is heterogeneous with respect to both price sensitivity and sensitivity to the remaining time until expiration. A numerical example and a sensitivity analysis of the key parameters support the conclusions and highlight their importance.