2-Approximation Algorithms for Perishable Inventory Control When FIFO Is an Optimal Issuing Policy

TL;DR

This paper introduces efficient approximation algorithms for perishable inventory control under FIFO policies, providing worst-case guarantees and demonstrating superior performance through numerical analysis.

Contribution

It proposes the marginal-cost dual-balancing and truncated-balancing policies, with proven 2-approximation guarantees when FIFO is optimal, and offers conditions for FIFO optimality.

Findings

Algorithms achieve at most twice the cost of optimal policies.

Numerical results show algorithms outperform worst-case bounds.

Truncated-balancing policy significantly improves over balancing policy.

Abstract

We consider a periodic-review, fixed-lifetime perishable inventory control problem where demand is a general stochastic process. The optimal solution for this problem is intractable due to "curse of dimensionality". In this paper, we first present a computationally efficient algorithm that we call the marginal-cost dual-balancing policy for perishable inventory control problem. We then prove that a myopic policy under the so-called marginal-cost accounting scheme provides a lower bound on the optimal ordering quantity. By combining the specific lower bound we derive and any upper bound on the optimal ordering quantity with the marginal-cost dual-balancing policy, we present a more general class of algorithms that we call the truncated-balancing policy. We prove that when first-in-first-out (FIFO) is an optimal issuing policy, both of our proposed algorithms admit a worst-case performance guarantee of two, i.e. the expected total cost of our policy is at most twice that of an optimal ordering policy. We further present sufficient conditions that ensure the optimality of FIFO issuing policy. Finally, we conduct numerical analyses based on real data and show that both of our algorithms perform much better than the worst-case performance guarantee, and the truncated-balancing policy has a significant performance improvement over the balancing policy.