Price competition for retailers with profit and revenue targets

Price competition for retailers has been extensively studied in the literature assuming the objective of (expected) profit maximization. In this paper, we make a major contribution by studying price competition for retailers with both profit and revenue targets. Consequently, each retailer maximizes her profit and revenue probability, namely, the probability of achieving the profit and revenue targets simultaneously. More specifically, we analyze a scenario where two competing retailers purchase a perishable product from a common supplier and sell to a common market. Employing the isoelastic demand model, we derive the closed-form solutions of the optimal order quantity, the optimal selling price, and the maximal profit and revenue probability for each retailer. It is shown that when revenue is a relevant performance measure, positive and non-positive salvage values lead to different optima for competing retailers. Moreover, as price elasticity and/or price competition intensity becomes higher, the optimal retail price decreases and the optimal order quantity increases for each retailer.