Waste Reduction of Perishable Products through Markdowns at Expiry Dates

We study the question whether giving discounts for perishable products on their expiry dates can simultaneously reduce waste and increase profit. In this paper, we consider a seller of a single perishable product who daily replenishes inventory up to a certain order-up-to level, and who serves customers whose purchase probabilities both depend on price and on the remaining shelf life of the product. We model the inventory dynamics as a Markov process and show that the system admits a unique stationary distribution. This distribution does not lead to informative expressions concerning the optimal discount or magnitude of waste reduction, and the absence of any structural properties make numerical optimization computationally challenging. We therefore consider a scaling limit in which both the customers' arrival rate and the order-up-to level grow at the same rate. We prove that the scaled system converges to a deterministic dynamical system and that the latter has a globally attracting fixed point. As a result, the scaled inventory levels converge to non-random values, which allows us to derive explicit expressions for expected waste and profit in this asymptotic regime. In a multinomial logit demand setting we show that optimizing expected profit by both optimizing regular prices and discounts reduces waste compared to only optimizing regular prices and not giving discounts. If the order-up-to level is also a decision variable, waste will be zero (in the scaling limit) and profit cannot be further improved by giving discounts. Our results imply that sellers of perishable products can use simple pricing rules to simultaneously reduce waste and increase profit.