In this study, we consider a stochastic inventory system in which the objective of the manufacturer is to maximize the long-run average profit by dynamically offering the selling price and switching the production on or off. The demand process is non-homogeneous Poisson with a price-dependent arrival rate. System costs consist of switching costs, inventory holding and backlogging costs. We show that an    $(s,S,{\mathbf p})$   policy is optimal. Moreover, we characterize the structural properties of the optimal profit function and pricing strategy, and show that the optimal price is a quasiconcave function of the inventory level when the production is off and is a quasiconvex function when the production is on.
['Ping Cao', 'Jingui Xie']
Optimal Control of an Inventory System With Joint Production and Pricing Decisions