We present strongly polynomial time algorithms for the minimum cost flow problem and for the weighted bipartite matching problem, also known as the assignment problem. 1 The minimum cost flow problem A flow network with prices, demands and capacities N = (G, a, b, c) is composed of a directed graph G = (V, E), a cost function a : E → R, a demand function b : V → R, and a capacity function c : E...

In this paper, we introduce the truncated primal-infeasible dual-feasible interior point algorithm for linear programming and describe an implementation of this algorithm for solving the minimum cost network flow problem. In each iteration, the linear system that determines the search direction is computed inexactly, and the norm of the resulting residual vector is used in the stopping criteria...

In the present paper we extend the out-of-kilter method for the ordinary minimum-cost flow problem to the submodular flow problem considered by Edmonds and Giles. From the algorithmic point of view, there is no essential difference between a submodular flow problem described by a submodular function on a crossing family and one described by a submodular function on a distributive lattice, if we...

Given an instance of the minimum cost flow problem, a version of the corresponding inverse problem, called the capacity inverse problem, is to modify the upper and lower bounds on arc flows as little as possible so that a given feasible flow x becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. Here, we consider the capacity inver...

In this paper, we consider an integer convex optimization problem where the objective function is the sum of separable convex functions (that is, of the form Σ(i,j)∈Q ij ij F (w ) + Σi∈P i i B ( ) μ ), the constraints are similar to those arising in the dual of a minimum cost flow problem (that is, of the form μi μj ≤ wij, (i, j) ∈ Q), with lower and upper bounds on variables. Let n = |P|, m = ...

administrative regulations for water flow decrease distribution efficiency and effect the economical operation of irrigation networks. complications in distribution systems and the decrease in availability of water require study of the hydraulic performance of existing flow control structures. control systems designed by neyrpic (zayandeh rud network) and usbr (doroodzan network) were investiga...

In this paper the method for the minimum cost flow determining in fuzzy dynamic network with nonzero lower flow bounds is proposed. Considered method takes into account fuzzy nature of networks’ parameters and deals with fuzzy arc flow bounds, fuzzy transmission costs. Fuzzy arc flow bounds, costs and transit times can vary depending on the flow departure time. The method allows introducing the...

968 A Fuzzy Residual Network Approach to Minimum Cost Flow Problem with Fuzzy Parameters M. Bagherian Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran. [email protected] . ABSTRACT The Minimum Cost Flow (MCF) problem has been defined as to determine a least cost shipment of a commodity through a network in order to satisfy demands at ce...

This article considers the problems of maximum flow and minimum cost flow determining in fuzzy network. Parameters of fuzzy network are fuzzy arc capacities and transmission costs of one flow unit represented as fuzzy triangular numbers. Conventional rules of operating with fuzzy triangular numbers lead to a strong “blurring” of their borders, resulting in loss of selfdescriptiveness of calcula...