A single-product network design model with lead time and safety stock considerations

Abstract

Most existing network design and facility location models have focused on the trade-off between the fixed costs of locating facilities and variable transportation costs between facilities and customers. However, operational performance measures such as service levels and lead times are what motivates customers to bring business to a company and should be considered in the design of a distribution network. While some previous work has considered lead times and safety stocks separately, they are closely related in practice, since safety stocks are often set relative to the distribution of demand over the lead time. In this paper we consider a two-stage supply chain with a production facility that replenishes a single product at retailers. The objective is to locate Distribution Centers (DCs) in the network such that the sum of the location and inventory (pipeline and safety stock) costs is minimized. The replenishment lead time at the DCs depends on the volume of flow through the DC. We require the DCs to carry enough safety stock to maintain the prescribed service levels at the retailers they serve. The explicit modeling of the relationship between the flows in the network, lead times and safety stocks allows us to capture the trade-off between them. We develop a Lagrangian heuristic to obtain near-optimal solutions with reasonable computational requirements for large problem instances.