Related papers: A Note on the Quickest Minimum Cost Transshipment …
The Quickest Transshipment Problem is to route flow as quickly as possible from sources with supplies to sinks with demands in a network with capacities and transit times on the arcs. It is of fundamental importance for numerous…
In this paper we show that every maximum minimum-cost flow over time problem has an optimal solution with a repeated structure if the given time horizon is large enough.
Network flows over time are a fascinating generalization of classical (static) network flows, introducing an element of time. They naturally model problems where travel and transmission are not instantaneous and flow may vary over time. Not…
We present a specialized network simplex algorithm for the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total…
We investigate the complexity and approximability of the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value…
This paper deals with robust optimization applied to network flows. Two robust variants of the minimum-cost integer flow problem are considered. Thereby, uncertainty in problem formulation is limited to arc unit costs and expressed by a…
This paper presents a heuristic algorithm to solve Minimum Convex-Cost Network Flow Problems (MC-CNFP). This solution algorithm is constructed on the concepts of Network Simplex Method (NSM) for minimum cost network flow problem, Convex…
In this article we consider a certain sub class of Integer Equal Flow problem, which are known NP hard [8]. Currently there exist no direct solutions for the same. It is a common problem in various inventory management systems. Here we…
Robust network flows are a concept for dealing with uncertainty and unforeseen failures in the network infrastructure. They and their dual counterpart, network flow interdiction, have received steady attention within the operations research…
Flows and colorings are disparate concepts in graph algorithms -- the former is tractable while the latter is intractable. Tutte introduced the concept of nowhere-zero flows to unify these two concepts. Jaeger showed that nowhere-zero flows…
The minimum cost flow problem is one of the most studied network optimization problems and appears in numerous applications. Some efficient algorithms exist for this problem, which are freely available in the form of libraries or software…
We describe a simple deterministic near-linear time approximation scheme for uncapacitated minimum cost flow in undirected graphs with real edge weights, a problem also known as transshipment. Specifically, our algorithm takes as input a…
We give a short overview of advantages and drawbacks of the classical formulation of minimum cost network flow problems and solution techniques, to motivate a reformulation of classical static minimum cost network flow problems as optimal…
When planning transportation whose operation requires non-consumable resources, the peak demand for allocated resources is often of higher interest than the duration of resource usage. For instance, it is more cost-effective to deliver…
We explore here surprising links between the time-cost-tradeoff problem and the minimum cost flow problem that lead to fast, strongly polynomial, algorithms for both problems. One of the main results is a new algorithm for the unit capacity…
Algorithms for computing fractional solutions to the quickest transshipment problem have been significantly improved since Hoppe and Tardos first solved the problem in strongly polynomial time. For integral solutions, runtime improvements…
We suggest a global perspective on dynamic network flow problems that takes advantage of the similarities to port-Hamiltonian dynamics. Dynamic minimum cost flow problems are formulated as open-loop optimal control problems for general…
Dynamic network flows, sometimes called flows over time, extend the notion of network flows to include a transit time for each edge. While Ford and Fulkerson showed that certain dynamic flow problems can be solved via a reduction to static…
Millions of flows are routed concurrently through a modern data-center. These networks are often built as Clos topologies, and flow demands are constrained only by the link capacities at the ingress and egress points. The minimum congestion…
Transshipment, also known under the names of earth mover's distance, uncapacitated min-cost flow, or Wasserstein's metric, is an important and well-studied problem that asks to find a flow of minimum cost that routes a general demand…