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.