The periodic review model with independent age-dependent lifetimes

Abstract

A retailer places orders periodically for items that are shipped by a wholesaler. Items that are not sold perish randomly and independently of one another, with the perish probability depending on the age class. We consider a first-in-first-out policy for depleting items. We model this problem as a Markov decision process with stochastic demand, unit holding, outdating and ordering costs, plus unit penalty costs for lost sales. We prove convexity for the penultimate period and show convexity may not hold any earlier. A dynamic program can be solved optimally for small instances. We introduce both a one-stage-lookahead heuristic and a heuristic which is a combination of two existing standard approaches, the newsvendor and periodic review models. For simulated data, we compare these heuristics to the optimal solution for small problem instances and to further lookahead policies for larger problem instances. We show that the two new heuristics achieve results close to optimal. Our numerical study, which includes real data from a large European retail chain, highlights that products perishing independently from each other strongly affect model behavior compared to existing approaches from the literature.