On the exact solution of large-scale simple plane location problems

The simple plant location problem deals with the selection of facility sites from a set of possible locations with the intention of serving a given set of customers from the chosen locations. The objective is to minimize the sum of the fixed charges for establishing the facilities and the transportation costs corresponding to the supply of the demands. The paper shows how to modify a primal-dual version of Erlenkotter’s exact algorithm to get an improved procedure. Computational experience with large-scale problems indicates that, compared with Erlenkotter’s code, an implementation of the modified algorithm is faster by more than one order of magnitude. For real-life problems with 1500 potential facility sites the increase of computational speed may even exceed the factor of 100.