A network design model with lead time and safety stock considerations

The operational performance of a firm, as embodied in service levels and lead times, are the only aspects of the supply chain that the customer sees from day to day, and which motivate the customer to bring business to that firm. The main contribution of this research is the explicit modeling of the non-linear relationships between the flows in the network, lead times, and safety stocks which allows us to capture the trade-off between risk-pooling benefits and congestion costs. We consider a two-stage supply chain with a production facility that replenishes a single product at a given set of retailers. The objective is to locate distribution centers such that the sum of location and inventory (pipeline and safety stock) costs is minimized. We develop a Lagrangian heuristic to obtain near-optimal solutions in reasonable CPU times for large problems. We then develop genetic algorithms for the model and compare their performance to that of the Lagrangian heuristic. A novel chromosome representation that combines binary vectors with random keys is shown to give a good solution quality. Finally, we develop a multiproduct network design model to capture the effects of demand profiles. We develop a Lagrangian heuristic and a genetic algorithm to approximately solve the model