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Demand Allocation in Systems with Multiple Inventory Locations and Multiple Demand Sources

Graduate Program in Industrial Engineering, Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455
Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong
Department of Management Science, School of Business, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China
Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada
saif{at}umn.edu
yanzhili{at}cityu.edu.hk
xudongsheng{at}gmail.com
elhedhli{at}engmail.uwaterloo.ca

We consider the problem of allocating demand that originates from multiple sources among multiple inventory locations. Demand from each source arrives dynamically according to an independent Poisson process. The cost of fulfilling each order depends on both the source of the order and its fulfillment location. Inventory at all locations is replenished from a shared production facility with a finite production capacity and stochastic production times. Consequently, supply lead times are load dependent and affected by congestion at the production facility. Our objective is to determine an optimal demand allocation and optimal inventory levels at each location so that the sum of transportation, inventory, and backorder costs is minimized. We formulate the problem as a nonlinear optimization problem and characterize the structure of the optimal allocation policy. We show that the optimal demand allocations are always discrete, with demand from each source always fulfilled entirely from a single inventory location. We use this discreteness property to reformulate the problems as a mixed-integer linear program and provide an exact solution procedure. We show that this discreteness property extends to systems with other forms of supply processes. However, we also show that supply systems exist for which the property does not hold. Using numerical results, we examine the impact of different parameters and provide some managerial insights.

Key Words: production-inventory systems; optimal demand allocation; make-to-stock queues; facility location
History: Received: October 17, 2005; accepted: December 21, 2006.