Directed hypergraphs have been introduced quite recently in connection with different application areas, such as propositional satisfiability, deductive data bases and Leontief substitution systems. In [Jeroslow, Martin, Rardin&Wang, 1989], the uncapacitated min-cost flow problem on hypergraphs is considered, and its properties are studied. Here we address the capacitated case, and show how the...

In the present paper, we apply the network simplex algorithm for solving the minimum cost flow problem, to the maximum flow problem. Then we prove that the cycling phenomenon which causes the infinite loop in the algorithm, does not occur in the network simplex algorithm associated with the maximum flow problem.

We consider the quickest flow problem in dynamic networks with a single source s and a single sink t: given a flow F , find the minimum time needed to send F from s to t, and the corresponding optimal flow over time. We introduce new mathematical formulations and derive optimality conditions for the quickest flow problem. Based on the optimality conditions, we develop a new cost-scaling algorit...

Let N be a single-source single-sink ow network with n nodes, m arcs, and positive arc costs. We present a pseudo-polynomial algorithm that computes a maximum ow of minimum cost for N in time O(3=4 m p log n), where is the cost of the ow. This improves upon previously known methods for networks where the minimum cost of the ow is small. We also show an application of our ow algorithm to a well-...

We consider the quickest flow problem in dynamic networks with a single source s and a single sink t: given an amount of flow F , find the minimum time needed to send it from s to t, and the corresponding optimal flow over time. We introduce new mathematical formulations and derive optimality conditions for the quickest flow problem. Based on the optimality conditions, we develop a new costscal...

In this paper, theory and algorithms for solving the multiple objective minimum cost flow problem are reviewed. For both the continuous and integer case exact and approximation algorithms are presented. In addition, a section on compromise solutions summarizes corresponding results. The reference list consists of all papers known to the authors which deal with the multiple objective minimum cos...

Given a generalized network and a generalized feasible flow f, we consider a problem finding a modified edge cost d such that f is minimum cost with respect to d and the maximum deviation between the original edge cost and d is minimum. This paper shows the relationship between this problem and minimum mean circuit problems and analyze a binary search algorithm for this problem.

The problem to find a valid integer flow with flow multipliers on nodes or arcs is long known to be NP-complete [10]. We show that the problem is still hard when restricted to instances with a limited number of integral multipliers. To find an integer minimum cost maximal pseudoflow, respecting only the node balance constraints of the inner nodes, is also still a difficult task. Further, we dem...

To the best of our knowledge very few methods have been proposed in previous studies for comparing intuitionistic fuzzy (IF) numbers. In this paper, the limitations and the shortcomings of all these existing methods are pointed out. In order to overcome these limitations and shortcomings a new ranking approach—by modifying an existing ranking approach—is proposed for comparing IF numbers. Thus,...

MINIMUM COST FLOW PROBLEM WITH ARBITRARY COSTS A. Sedeño-Noda, C. González-Martín, S. Alonso Departamento de Estadística, Investigación Operativa y Computación (DEIOC) Universidad de La Laguna, 38271 La Laguna, Tenerife (Spain). Abstract We address the undirected minimum cost flow problem with arbitrary arcs costs. The optimal solutions for this problem is characterized proving that the flow of...