(s, S) Optimality in Joint Inventory-Pricing Control: An Alternate Approach

We study a stationary, single-stage inventory system, under periodic review, with fixed ordering costs and multiple sales levers (such as pricing, advertising, etc.). We show the optimality of (s, S)-type policies in these settings under both the backordering and lost-sales assumptions. Our analysis is constructive and is based on a condition that we identify as being key to proving the (s, S) structure. This condition is entirely based on the single-period profit function and the demand model. Our optimality results complement the existing results in this area.