Global Optimization Approach for the Capacitated Euclidean Location-Allocation Problem

In this chapter, we present a procedure that seeks the global minimum for the capacitated Euclidean location-allocation problem which is defined as follows. Given the fixed location of m existing facilities or customers on a continuous plane and their associated demands, we wish to determine the location of n new facilities or sources with known capacities, and the allocation of its supply, in order to satisfy the demand requirements of customers at a minimum total cost. The decisions are where to locate the n sources and how much shipment to send from each source to each customer. The costs are directly proportional to the quantities shipped and the Euclidean distance over which this shipment occurs. For convenience, we assume that the total supply is equal to the total demand. This problem can be mathematically stated as follows.