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.

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...

We present combinatorial interior point methods for the generalized minimum cost flow and the generalized circulation problems based on Wallacher and Zimmermann’s combinatorial interior point method for the minimum cost network flow problem. The algorithms have features of both a combinatorial algorithm and an interior point method. They work towards optimality by iteratively reducing the value...

Given a product design and a repair network for capital goods, a level of repair analysis determines for each component in the product (1) whether it should be discarded or repaired upon failure and (2) at which location in the repair network to do this. In this paper, we show how the problem can be modelled as a minimum cost flow problem with side constraints. Advantages are that (1) solving o...

We introduce a broad class of algorithms for finding a minimum cost flow in a capacitated network. The algorithms are of the primal-dual type. They maintain primat feasibility with respect to capacity constraints, while trying to satisfy the conservation of flow equation at each node by means of a wide variety of procedures based on flow augmentation, price adjustment, and ascent of a dual func...

We present a combinatorial method for the min-cost flow problem and prove that its expected running time is bounded by Õ(m3/2). This matches the best known bounds, which previously have only been achieved by numerical algorithms or for special cases. Our contribution contains three parts that might be interesting in their own right: (1) We provide a construction of an equivalent auxiliary netwo...

The submodular flow problem is extended by considering a nonseparable cost function, which is assumed to enjoy a variant of the exchange property of the base polyhedron of a submodular system. Two optimality criteria are established, one in terms of potentials associated with vertices and the other in terms of negative cycles in an auxiliary graph. These are natural extensions of the well-known...

We present two efficient algorithms for solving the electric power transaction problem. The electric power transaction problem appears when maximizing the social benefit on electric power transactions among some private companies. The problem is a special case of the minimum cost flow problem defined on a network with many leaves, where each leaf corresponds to a (private) company who wants to ...