This paper is concerned with the following problem in network synthesis. Suppose that we are given a network with real-valued capacities on each arc. There is a cost associated with each arc which is proportional to the magnitude of the arc capacity. We wish to determine new arc capacities such...

This paper generalizes the selection problem discussed by J. M. Rhys [Rhys, J. M. W. 1970. Shared fixed cost and network flows. Management Sci. 17 (3, November).], J. D. Murchland [Murchland, J. D. 1968. Rhys's combinatorial station selection problem. London Graduate School of Business Studies,...

The determination of an optimal strategy for reinforcing arcs and nodes in a multi-commodity network is discussed. This strategy will maximize the effort required by an attacker to render the network useless. Under certain assumptions this problem is shown to be equivalent to the problem of...

Some new properties associated with the special class of integer programs known as weighted set covering problems are derived. While it is well known that an optimal integer solution to the set covering problem is a basic feasible solution to the corresponding linear program, we show that there...