Revenue Management of Perishable Products under Competition

We study a multi-period no-replenishment model of competition between retailers who sell an identical good. A single myopic consumer visits only one of two retailers in each period and purchases the good if the posted price is below his valuation. Otherwise, in the ensuing period he switches to the competing retailer.

We find that, as compared to the corresponding single store monopoly model, under our duopoly competition: (i) prices decline exponentially rather than linearly, (ii) the initial price converges to 0.543, rather than 1, (iii) the system profit loss may be up to 29.6% of the monopolistic profit, and (iv) a monopolist may lose up to 64.8% of his monopolistic profit.

We further investigate the behavior of the model when the valuation of the good has a power distribution, and when there are N consumers in the market who are either identical or similar and the system is either capacitated or uncapacitated (in the sense that each retailer can satisfy the entire demand in the market).

Our model is then extended to allow for non-symmetric retailers and a more general store visit pattern. Specifically, consumers may return to the same retailer with probability P. The probability P, which may differ from store to store, could either depend on the experience of the consumer at the store, or, alternatively, it could be affected by market structure characteristics.

We find that prices decline exponentially as long as P is not too close to one, consumers’ surplus is maximized when they zigzag between the retailers, and that while changing a monopoly setting to a duopoly dramatically affects prices, further intensifying competition by introducing other retailers to the market only marginally affects prices.