Interactive Computer Graphical Approaches to some Maximin and Minimax Location Problems

Abstract

This study describes algorithms for the solution of several single facility location problems with maximin or minimax objective functions. Interactive computer graphical algorithms are presented for maximizing the minimum rectilinear travel distance and for minimizing the maximum rectilinear travel distance to a number of point demands when there exist several right-angled polygonal barriers to travel. For the special case of unweighted rectilinear distances with barriers, a purely numerical algorithm for the maximin location problem is described. An interactive computer graphical algorithm for maximizing the minimum Euclidean, rectilinear, or general 1p distance to a number of polygonal areas is described. A modified version of this algorithm for location problems with the objective of minimizing the maximum cost when the costs are non-linear monotonically decreasing functions of distance is presented. Extension of this algorithm to problems involving the minimization of the maximum cost when the costs are functions of both distance and direction is discussed using asymmetric distances.