The minimum cost multiple-source unsplittable flow problem is studied in this paper. A simple necessary condition to get a solution is proposed. It deals with capacities and demands and can be seen as a generalization of the well-known semi-metric condition for continuous multicommdity flows. A cutting plane algorithm is derived using a superadditive approach. The inequalities considered here a...

Let G = (V, E) be a digraph (i.e., a directed graph) with n vertices and m edges, and w : E → IR be a weight function on the edges. A directed cycle is closed walkC = (v0, v1, . . . , vt), where vt = v0 and (vi → vi+1) ∈ E, for i = 0, . . . , t − 1. The average cost of a directed cycle is AvgCost(C) = ω(C)/t = (∑e∈C ω(e)) /t. For each k = 0, 1, . . ., and v ∈ V , let dk(v) denote the minimum le...

An inverse optimization problems is defined as follows: Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost vector, and xO be a given feasible solution. We want to perturb the cost vector c to d so that x is an optimal solution of P with respect to the cost vector d , and lid clip is minimum, where 11.llp denotes some selected Lp norm. In this pape...

In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the Edmonds-Karp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n nodes and m arcs and runs in O(n log n (m + n log n)) time. Using a standard transformation, thjis ...

We present a Cost Decomposition approach for the linear Multicommodity Min-Cost Flow problem, where the mutual capacity constraints are dualized and the resulting Lagrangean Dual is solved with a dual-ascent algorithm belonging to the class of Bundle methods. Although decomposition approaches to block-structured Linear Programs have been reported not to be competitive with general-purpose softw...

The dynamic version of the minimum cost multicommodity flow problem that generalizes the static minimum cost multicommodity flow problem is formulated and studied. This dynamic problem is considered on directed networks with a set of commodities, time-varying capacities, fixed transit times on arcs, and a given time horizon. We assume that cost functions, defined on edges, are nonlinear and dep...