A Decision Support System for Computing Optimal (R, S) Policy Parameters

Retail replenishment is a high-value activity. According to the US Commerce Department, $1.1 trillion in inventory supports $3.2 trillion in annual US retail sales [...]. Improving distribution centre efficiency of just a few percentage points through advanced automation and real-time replenishment may deliver significant savings and require less capital to be tied up in inventory. An interesting class of production/inventory control problems is the one that considers the single-location, single-product case under non-stationary stochastic demand, fixed production/ordering cost and per-unit holding cost. Exact and efficient approaches for computing optimal production/replenishment decisions are a key factor for achieving profitability in retail business. One of the possible policies that can be adopted to manage stocks is the replenishment cycle policy [6]. In this policy the inventory review times are set under a here-and-now strategy at the beginning of the planning horizon. These decisions are not affected by the actual demand realized in each period. On the other hand, for each inventory review we observe the actual demand realized in former periods to compute the actual order quantity. This provides an effective means of damping planning instability (deviations in planned orders, also known as nervousness) and coping with demand uncertainty. We developed Constraint Programming (CP) [1] models augmented with dedicated cost-based filtering [2] strategies in order to improve efficiency. Our approach is now the state-of-the-art technique for computing optimal replenishment cycle policy parameters [7, 4]. An extension considering a stochastic delivery lag is under development [5]. These techniques have been embedded in a Decision Support System (DSS) (Fig. 1) developed in Java on the top of Choco [3], an open source CP solver. Our DSS can run both as a web or desktop application. Our system receives the following inputs: a planning horizon of N periods and a demand dt for each period t ∈ {1, . . . , N}, which is a normally distributed random variable with probability density function gt(dt). We assume that demands in different periods are independent. A fixed delivery cost a is considered for each order and also a linear holding cost