570 / 2024-04-25 22:56:54

Inventory Control with a General Wholesale Cost Framework

wholesale cost,periodic-review inventory system,optimal policy,Q-increasing,(K,c)-bounded

This paper studies the optimal policies for stochastic periodic-review inventory systems with general wholesale costs, where both fixed costs and unit costs decrease with increasing order quantity. This framework covers three commonplace contracts by suppliers: free shipping quantity (FSQ) contract, all-units discount (AUD) contract, and minimum order quantity (MOQ) contract. Unmet demand can be either backordered or lost. We characterize the single-period optimal policy. We introduce two technical properties called Q-increasing and (K,c)-bounded, which enables us to characterize the structure of the finite-horizon optimal policies. For infinite-horizon case, we prove that the optimal policies under discounted cost criteria and average cost criteria both maintain the same structure of the finite-horizon case. Finally, we demonstrate the application of the framework on specific inventory models.