Parametric replenishment policies for inventory systems with lost sales and fixed order cost

In this paper we consider a single-item inventory system with lost sales and fixed order cost. We numerically illustrate the lack of a clear structure in optimal replenishment policies for such systems. However, policies with a simple structure are preferred in practical settings. Examples of replenishment policies with a simple parametric description are the (s, S) policy and the (s, nQ) policy. Besides these known policies in literature, we propose a new type of replenishment policy. In our modified (s, S) policy we restrict the order size of the standard (s, S) policy to a maximum. This policy results in near-optimal costs. Furthermore, we derive heuristic procedures to set the inventory control parameters for this new replenishment policy. In our first approach we formulate closed-form expressions based on power approximations, whereas in our second approach we derive an approximation for the steady-state inventory distribution. As a result, the latter approach could be used for inventory systems with different objectives or service level constraints. The numerical experiments illustrate that the heuristic procedures result on average in 2.4 percent and 1.8 percent cost increases, respectively, compared to the optimal replenishment policy. Therefore, we conclude that the heuristic procedures are very effective to set the inventory control parameters.