## $$(s, S)$$ optimality in joint inventory-pricing control: An alternate approach.(English)Zbl 1167.90332

Summary: 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.

### MSC:

 90B05 Inventory, storage, reservoirs 90C39 Dynamic programming
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