Optimal and simple approximate solutions to a production-inventory system with stochastic and deterministic demand

Abstract We consider a continuous review production-inventory system where demand is a mixture of a deterministic component and a random component which follows a compound Poisson process. Demand is satisfied by a production facility which may be in production or idle. While in production, the facility produces at a constant rate. A two-number (s, S) policy is used to control production. When inventory reaches level S, production is turned off and when inventory drops below level s, production is turned on. A level crossing approach is used to derive the steady-state distribution of inventory level from which the exact total expected cost function, consisting of setup, inventory holding and backorder costs, is determined. The optimal (s, S) policy can be found through a search of the expected cost function. We propose approximations that give simple closed-form solutions with near-optimal performance.