Joint Pricing and Inventory Control with Fixed and Convex/Concave Variable Production Costs

Abstract

This study considers a periodic‐review joint pricing and inventory control problem for a single product, where production incurs a fixed cost plus a convex or concave variable cost. Our objective is to maximize the expected discounted profit over the entire planning horizon. We fully characterize the optimal policy for the single‐period problem. As the optimal policy for the multi‐period problem is too complicated to be implemented in practice, we develop well‐structured heuristic policies, and establish worst‐case performance bounds on the profit gap between the heuristic policies and the optimal policies. Numerical studies show that our heuristic policies perform extremely well. To further reveal the structural properties of the optimal policies, we also introduce two new concepts named κ‐convexity and sym‐ κ‐convexity, provide the associated preservation results, and then characterize the optimal policies.