2-Approximation Policies for Perishable Inventory Systems when FIFO Is an Optimal Issuing Policy

Motivated by a platelet inventory management problem, we study periodic-review, fixed-lifetime perishable inventory systems where demand is a general stochastic process. The optimal solution for this problem is computationally intractable due to the “curse of dimensionality”. In this paper, we first present an approximation policy that we call the marginal-cost dual-balancing policy for perishable inventory systems. We prove that when first-in-first-out (FIFO) is an optimal issuing policy, our proposed policy admits a constant worst-case performance bound of two, a tighter performance bound compared to the existing results presented in the perishable inventory literature. We then extend the literature on the optimality of the FIFO issuing policy and present new sufficient conditions to ensure the optimality of FIFO. Further, we present a tight example to show that the performance bound of two of the balancing policy can be achieved asymptotically when the unit shortage penalty goes to infinity (in which case the balancing policy tends to under-order). Motivated by this result, we anticipate that the balancing policy as well as other existing balancing-type policies presented in the literature may perform poorly when the unit shortage penalty becomes large (these policies all tend to under-order), and we present a new policy that we call the truncated-balancing policy to overcome this shortcoming. By combining our worst-case analysis ideas for the balancing policy with a structural property called L-natural-convexity, we prove that the truncated-balancing policy also has a worst-case performance guarantee of two when FIFO is an optimal issuing policy. Finally, we conduct extensive numerical analyses and show that the truncated-balancing policy has a significant performance improvement over the existing policies when the unit shortage penalty becomes (reasonably) large