  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. Determining optimal
ordering quantities is a challenging task due to the short maximum shelf-life
of platelets (3-5 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 non-convex 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 to the historical hospital performance and other
benchmarks. The ADP policy can be computed online in a few minutes and results
in more than 50% lower expiry and shortage rates compared to the historical
performance. In addition, it performs better or as well as an exact policy that
ignores uncertainty in shelf-life and becomes hard to compute for larger
instance of the problem.
