Supply network model with base-stock control and service requirements

We develop a supply network model that takes as input the bill of materials, the (nominal) lead times, the demand and cost data, and the required customer service levels. In return, the model generates the base-stock level at each store - the stocking location for a part or an end-product, so as to minimize the overall inventory capital throughout the network and to guarantee the customer service requirements. The key ingredient of the model is a detailed, albeit approximate, analysis of the actual lead times at each store and the associated demand over such lead times, along with a characterization of the operation at each store via an inventory-queue model. The gradients are derived in explicit forms, and a conjugate gradient routine is used to search for the optimal solution. Several numerical examples are presented to validate the model and to illustrate its various features.