Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems

Abstract

We consider periodic review perishable inventory systems with a fixed product lifetime. Unsatisfied demand can be either lost or backlogged. The objective is to minimize the long-run average holding, penalty, and outdating cost. The optimal policy for these systems is notoriously complex and computationally intractable because of the curse of dimensionality. Hence, various heuristic replenishment policies are proposed in the literature, including the base-stock policy, which raises the total inventory level to a constant in each review period. Whereas various studies show near-optimal numerical performances of base-stock policies in the classic system with zero replenishment lead time and a first-in-first-out issuance policy, the results on their theoretical performances are very limited. In this paper, we first focus on this classic system and show that a simple base-stock policy is asymptotically optimal when any one of the product lifetime, demand population size, unit penalty cost, and unit outdating cost becomes large; moreover, its optimality gap converges to zero exponentially fast in the first two parameters. We then study two important extensions. For a system under a last-in-first-out or even an arbitrary issuance policy, we prove that a simple base-stock policy is asymptotically optimal with large product lifetime, large unit penalty costs, and large unit outdating costs, and for a backlogging system with positive lead times, we prove that our results continue to hold with large product lifetime, large demand population sizes, and large unit outdating costs. Finally, we provide a numerical study to demonstrate the performances of base-stock policies in these systems. This paper was accepted by Victor Martinez de Albéniz, operations management.

Optimal Base-Stock Inventory-Management Policies of Cement Retailers under Supply-Side Disruptions

“…Also, they combined the fixed and known lead time with some unknown demand distribution parameters to develop a learning algorithm with a linearly dependent regret bound. In a sporadic examination of perishable inventory procedures with a specified yield lifetime, Bu et al [43] included a base-stock policy and partial backlogging. They showed that an easy base-stock model was asymptotically optimal for enlarging any one out-of-yield lifetime, order population extent, unit liability cost, and unit outdating expense.…”

“…Wang et al[48] base-stock NA truncated and convoluted demand NA Present study base-stock supply-side selling price dependent partial Figure1. A comparative analysis of the existing literature on inventory models[9,11,16,18,26,31,32,39,41,43].…”

Data‐driven platelet inventory management under uncertainty in the remaining shelf life of units

“…Given these challenges, many studies have proposed heuristic and approximately optimal policies. These approximate policies include base stock or TIS (total‐inventory‐to‐S) policies that bring up the total inventory level to a fixed value (Bu et al., 2022; Cooper, 2001; Nahmias, 1976; Nandakumar & Morton, 1993); NIS (new‐inventory‐to‐S) policies that order a pre‐determined quantity of fresh units in each period (Brodheim et al., 1975; Deniz et al., 2010); and $$(s,S)$$‐type policies (Nahmias, 1978) when fixed ordering costs are considered.…”