Combined Sales Effort and Inventory Control under Demand Uncertainty

We study the joint inventory and sales effort management problems of a retailer in a broad context and investigate the optimal policies for a single item, periodic-review system. In each period, the demand is uncertain depending on the sales effort level exerted by the retailer, which incurs an associated cost. The retailer's objective is to find a joint optimal inventory replenishment and sales effort policy to maximize the discounted profit over a finite horizon. We first consider a basic setting with zero setup cost and no batch ordering, under which the base stock list sales effort policy is optimal. Two extensions are then investigated: (1) the case with nonzero setup cost, under which we show that (s, S, e) policy is optimal; and (2) the case with batch ordering, under which we prove the optimality of the (r, Nq, e) policy. Finally, we conduct numerical studies to provide additional managerial insights.