Platelet Inventory Management with Approximate Dynamic Programming

We study a stochastic perishable inventory control problem with endogenous (decision-dependent) uncertainty in shelf life of units. Our primary motivation is determining ordering policies for blood platelets. Hospitals typically order their required platelets from a central supplier, and as such, the shelf life of units at the time of delivery can be subject to significant variability. Determining optimal ordering quantities is a challenging task because of the short maximum shelf life of platelets (three to five days after testing) and high uncertainty in daily demand. We formulate the problem as an infinite-horizon discounted Markov decision process (MDP). The model captures salient features observed in our data from a network of Canadian hospitals and allows for fixed ordering costs. We show that with uncertainty in shelf life, the value function of the MDP is nonconvex and key structural properties valid under deterministic shelf life no longer hold. Hence, we propose an approximate dynamic programming (ADP) algorithm to find approximate policies. We approximate the value function using a linear combination of basis functions and tune the parameters using a simulation-based policy iteration algorithm. We evaluate the performance of the proposed policy using extensive numerical experiments in parameter regimes relevant to the platelet inventory management problem. We further leverage the ADP algorithm to evaluate the impact of ignoring shelf-life uncertainty. Finally, we evaluate the out-of-sample performance of the ADP algorithm in a case study using real data and compare it with the historical hospital performance and other benchmarks. After tuning the parameters, the ADP policy can be computed online in a few seconds and results in more than 50% lower expiration and shortage rates compared with the historical rates. In addition, it performs better or as well as other benchmarks, including an exact policy that ignores uncertainty in shelf life and becomes hard to compute for larger instances of the problem.