A Probabilistic Analysis of the K-Location Problem

SYNOPTIC ABSTRACTThe “K-location problem” involves the location of K facilities to maximize the profit from supplying a commodity tom clients. The profit from supplying customer i using a facility at j is cij > 0, and there is no limit on the number of clients that can be served by a particular facility. This problem has a number of applications. In this paper we show that if the cij's are independent and identically distributed random variables from a certain class of distributions then the relative error of a randomly generated solution to the K-location problem converges to zero in probability as problem size grows. Thus, in certain random environments the K-location problem becomes trivial to solve asymptotically. In addition we identify conditions under which a set of solution values is approximately normally distributed.