Optimal Minimax Path of a Single Service Unit on a Network to Nonservice Destinations

In this paper we consider the problem of finding an optimal path of a single service unit that travels toward a “nonservice” destination. Two types of objective functions are examined. One objective function is the minimization of the maximum distance (or weighted distance) between the moving service unit and any demand (node) of the network. The second objective function is the minimization of the total time period that the distance (or weighted distance) between the moving service unit and any node exceeds a response time threshold λ. For these two objective functions, we present algorithms which can be calculated, respectively, in 0(n³) and 0(n³logn) elementary operations.