Joint Location-Inventory Planning with Risk Pooling

by

Leyla Ozsen
Industrial Engineering and Management Sciences
Northwestern University

In this talk, we present two integrated location-inventory models with inventory capacity constraints at the distribution centers. In both models, we consider a two-echelon logistics system consisting of a single plant and multiple retailers, each with uncertain demand. Distribution centers serve as the direct intermediary between the plant and the retailers to achieve risk-pooling benefits. Safety stock is retained at the distribution centers to buffer against stock outs during the lead time. The models are capable of evaluating the tradeoff between having more distribution centers versus ordering more frequently through the definition of capacity. The first model forces the retailers to be assigned to a single distribution center, whereas the second model allows the demands of a retailer to be served by more than one distribution center. The models are formulated as non-linear mixed-integer programs. Model and solution properties are outlined. A Lagrangian Relaxation solution algorithm is proposed. We discuss the sensitivity of the results to changes in the inventory and transportation cost weights. We conclude that the value of allowing the retailers to be multi-sourced increases as the transportation costs increase.