Ergodic inventory control with diffusion demand and general ordering costs

• Published in: Operations research letters Vol. 49; no. 4; pp. 578 - 585
• Main Authors: Wei, Bo, Yao, Dacheng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2021
• Subjects: [formula omitted] policy; Diffusion process; General ordering costs; Impulse control; Stochastic inventory model; General ordering costs; Diffusion process; (s,S) policy; Stochastic inventory model; Impulse control
• ISSN: 0167-6377; 1872-7468
• DOI: 10.1016/j.orl.2021.06.007

•Consider ergodic inventory control with diffusion demand.•Ordering cost function is not even necessarily continuous and monotone.•An (s, S) policy is optimal.•Provide a lower bound approach with a comparison theorem. In this work, we consider a continuous-time inventory system where the demand process follows an inventory-dependent diffusion process. The ordering cost of each order depends on the order quantity and is given by a general function, which is not even necessarily continuous and monotone. By applying a lower bound approach together with a comparison theorem, we show the global optimality of an (s,S) policy for this ergodic inventory control problem.