Reverse maximum flow problem under the weighted Chebyshev distance

¹ Department of Industrial Engineering, Birjand University of Technology, Birjand, Iran.
² Department of Mathematics, Faculty of sciences, Imam Ali University, Tehran, Iran.

^* Corresponding author: kazemi@birjandut.ac.ir

Received: 9 April 2017
Accepted: 30 November 2017

Abstract

Given a network G(V, A, u) with two specific nodes, a source node s and a sink node t, the reverse maximum flow problem is to increase the capacity of some arcs (i, j) as little as possible under bound constraints on the modifications so that the maximum flow value from s to t in the modified network is lower bounded by a prescribed value v⁰. In this paper, we study the reverse maximum flow problem when the capacity modifications are measured by the weighted Chebyshev distance. We present an efficient algorithm to solve the problem in two phases. The first phase applies the binary search technique to find an interval containing the optimal value. The second phase uses the discrete type Newton method to obtain exactly the optimal value. Finally, some computational experiments are conducted to observe the performance of the proposed algorithm.