| Issues on the interfaces between operations management and marketing research have attracted much attention recently. The developments integrating marketing decisions into inventory management are not only of academic interest, but also of practical importance. With uncertain demand, this research studies the joint determination of inventory and sales lever decisions such as price, incentives to salesforce, and short-term promotions, or a combination of them.; We consider a single-item, periodic-review system with the objective of maximizing the long-run average profit over an infinite planning horizon. Demand in a period is a non-negative, discrete random variable with its distribution dependent on the sales lever chosen for the period. A replenishment order can be placed at the beginning of a period incurring both fixed and variable ordering costs. The sales lever is determined jointly, and its execution may incur possible cost, for example, promotion cost. For such a model, we take particular interest in a so-called (s, S, z) policy, which operates as follows: whenever the inventory level falls to or below s, an order is placed to bring it up to S; when the inventory level is above s, no order is issued; the choice of sales lever z depends on the inventory level.; Assuming that unmet demand is fully backlogged, a newsvendor-type profit function which is defined as the resulting expected one-period profit with sales lever being optimized for every inventory level, fails to be unimodal. By assuming the newsvendor-type profit function to have a finite number of local maxima, we develop an efficient algorithm for finding the optimal ( s, S, z) policy with the long-run average profit derived by the renewal theory. We further identify the conditions under which the (s, S, z) policy is globally optimal.; Assuming that all unmet demand is fully lost, we begin our study by confining the sales lever to be price only, that is, z = p , and ignoring the cost for executing the sales lever. Given a stationary (s, S, p) policy, we find that the profit function for the lost-sales case exhibits the same structure as the one for the backlogging case. We further show that the relaxed assumption on the news-vendor type profit function can also be satisfied by a broad class of demand function. We can therefore extend the optimizing algorithm and the optimality analysis developed earlier to the lost-sales case. We further demonstrate that the results can be extended to the general sales lever decisions.; We finally conduct an extensive numerical study for both the backlogging and lost-sales cases. We compare the benefits of the dynamic sales lever strategy with those of the semi-dynamic as well as the static sales lever strategy, and find that the profit gains are significant. By sensitivity analysis, we bring out the impact of cost parameters on the optimal solutions. |
