Technical Note - Approximation Algorithms for Perishable Inventory Systems with Setup Costs

We develop the first approximation algorithm for periodic-review perishable inventory systems with setup costs. The ordering lead time is zero. The model allows for correlated demand processes which generalize the well-known approaches to model dynamic demand forecast updates. The structure of optimal policies for this fundamental class of problems is not known in the literature. Thus, finding provably near-optimal control policies has been an open challenge. We develop a randomized proportional-balancing policy (RPB) that can be efficiently implemented in an online manner, and show that it admits a worst-case performance guarantee between 3 and 4. The main challenge in our analysis is to compare the setup costs between RPB and the optimal policy in the presence of inventory perishability, which departs significantly from the previous works of Chao et al. (2015b,a). The numerical results show that the average performance of RPB is good (within 1% of optimality under i.i.d. demands and within 7% under correlated demands).