Min Cost Multicommodity Network Flows A Linear Case For The Convergence And Reoptimization Of Multiple Single Commodity Network Flows
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Min Cost Multicommodity Network Flows A Linear Case For The Convergence And Reoptimization Of Multiple Single Commodity Network Flows
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Author :
language : en
Publisher:
Release Date : 2004
Min Cost Multicommodity Network Flows A Linear Case For The Convergence And Reoptimization Of Multiple Single Commodity Network Flows written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Network Flow problems are prevalent in Operations Research, Computer Science, Industrial Engineering and Management Science. They constitute a class of problems that are frequently faced by real world applications, including transportation, telecommunications, production planning, etc. While many problems can be modeled as Network Flows, these problems can quickly become unwieldy in size and difficult to solve. One particularly large instance is the Min-Cost Multicommodity Network Flow problem. Due to the time-sensitive nature of the industry, faster algorithms are always desired: recent advances in decomposition methods may provide a remedy. One area of improvement is the cost reoptimization of the min-cost single commodity network flow subproblems that arise from the decomposition. Since similar single commodity network flow problems are solved, information from the previous solution provides a "warm-start" of the current solution. While certain single commodity network flow algorithms may be faster "from scratch," the goal is to reduce the overall time of computation. Reoptimization is the key to this endeavor. Three single commodity network flow algorithms, namely, cost scaling, network simplex and relaxation, will be examined. They are known to reoptimize well. The overall goal is to analyze the effectiveness of this approach within one particular class of network problems.
Minimum Cost Multi Commodity Network Flows
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Author :
language : en
Publisher:
Release Date : 1969
Minimum Cost Multi Commodity Network Flows written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
Multicommodity Network Flows
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Author : B. Rothschild
language : en
Publisher:
Release Date : 1969
Multicommodity Network Flows written by B. Rothschild and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
The purpose of this article is to survey the current literature on multicommodity network flows. The study of multicommodity flows is concerned with generalizing the results which are known for single commodity flows in networks. These results fall into three broad categories: optimization, computation and structure. The optimization category includes the question of maximizing flow or minimizing cost in a network. The computation question involves finding algorithms for efficiently computing flows. And the structural results relate the flows to structural properties of the network (e.g., the Max-flow Min-cut Theorem). Because of the added complexity of having many commodities, the results for multicommodity flows sometimes require methods different from those used for analogous single commodity results. As in the one-commodity case, the question of finding a maximal multicommodity flow can be stated as a linear programming problem. In general for n-commodity flow there is the question of feasibility. That is, not only do we wish to know how much flow can be achieved, but more specifically how much of each kind of commodity. (Author).
Multicommodity And Generalized Flow Algorithms
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Author : Jeffrey David Oldham
language : en
Publisher:
Release Date : 1999
Multicommodity And Generalized Flow Algorithms written by Jeffrey David Oldham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Algorithms categories.
Abstract: "We present several simple, practical, and fast algorithms for linear programs, concentrating on network flow problems. Since the late 1980s, researchers developed different combinatorial approximation algorithms for fractional packing problems, obtaining the fastest theoretical running times to solve multicommodity minimum-cost and concurrent flow problems. A direct implementation of these multicommodity flow algorithms was several orders of magnitude slower than solving these problems using a commercial linear programming solver. Through experimentation, we determined which theoretically equivalent constructs are experimentally efficient. Guided by theory, we designed and implemented practical improvements while maintaining the same worst-case complexity bounds. The resulting algorithms solve problems orders of magnitude faster than commercial linear programming solvers and problems an order of magnitude larger. We also present simple, combinatorial algorithms for generalized flow problems. These problems generalize ordinary network flow problems by specifying a flow multiplier [mu](a) for each arc a. Using multipliers permit a flow problem to model transforming one type into another, e.g., currency exchange, and modification of the amount of flow, e.g., water evaporation from canals or accrual of interest in bank accounts. First, we show the generalized shortest paths problem can be solved using existing network flow ideas, i.e., by combining the Bellman-Ford-Moore shortest path framework and Megiddo's parametric search. Second, we combine this algorithm with fractional packing frameworks to yield the first polynomial-time combinatorial approximation algorithms for the generalized versions of the nonnegative-cost minimum-cost flow, concurrent flow, multicommodity maximum flow, and multicommodity nonnegative-cost minimum-cost flow problems. These algorithms show that generalized concurrent flow and multicommodity maximum flow have strongly polynomial approximation algorithms."
Multicommodity Supply And Transportation Networks With Resource Constraints
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Author : Richard D. Wollmer
language : en
Publisher:
Release Date : 1970
Multicommodity Supply And Transportation Networks With Resource Constraints written by Richard D. Wollmer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Freight and freightage categories.
The paper presents a method for treating multicommodity network flows in which limited resources are shared among several arcs instead of only one. The study extends the previous solution methds for networks with individual arc capacity constraints to cover joint constraints. This formulation can handle one or more joint capacity constraints in a multicommodity network; with some adjustment in the objective function, it can maximize a linear combination of commodity flows and find a feasible routing to meet flow requirements.
Modeling And Analysis Of Multicommodity Network Flows Via Goal Programming
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Author : Matthew A. Scott
language : en
Publisher:
Release Date : 2002-03-01
Modeling And Analysis Of Multicommodity Network Flows Via Goal Programming written by Matthew A. Scott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-01 with Commodity control categories.
In this work goal programming is used to solve a minimum cost multicommodity network flow problem with multiple goals. A single telecommunication network with multiple commodities (e.g., voice, video, data, etc.) flowing over it is analyzed. This network consists of: linear objective function, linear cost arcs, fixed capacities, specific origin-destination pairs for each commodity. A multicommodity network flow problem with goals can be successfully modeled using linear goal programming techniques. When properly modeled, network flow techniques may be employed to exploit the pure network structure of a multicommodity network flow problem with goals. Lagrangian relaxation captures the essence of the pure network flow problem as a master problem and sub-problems (McGinnis and Rao, 1977). A subgradient algorithm may optimize the Lagrangian function, or the Lagrangian relaxation could be decomposed into subproblems per commodity; each subproblem being a single commodity network flow problem. Parallel to the decomposition of the Lagrangian relaxation, Dantzig-Wolfe decomposition may be implemented to the linear program. Post-optimality analyses provide a variety of options to analyze the robustness of the optimal solution. The options of post-optimality analysis consist of sensitivity analysis and parametric analysis. This mix of modeling options and analyses provide a powerful method to produce insight into the modeling of a multicommodity network flow problem with multiple objectives.
Multi Stage Multi Commodity Network Flows
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Author : William Torrillo Torres
language : en
Publisher:
Release Date : 1971
Multi Stage Multi Commodity Network Flows written by William Torrillo Torres and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
Multiattribute Multicommodity Flows In Transportation Networks
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Author : Douglas Allen Popken
language : en
Publisher:
Release Date : 1988
Multiattribute Multicommodity Flows In Transportation Networks written by Douglas Allen Popken and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Network analysis (Planning) categories.
Previously developed minimum cost multicommodity network flow models do not simultaneously consider the weights, volumes, and inventory holding costs of the commodities. ignoring one or more of these attributes may prevent detection of potential savings; however, simultaneously accounting for all three attributes leads to a problem considerably more difficult to solve. This thesis examines a multiattribute multicommodity flow formulation of a transportation network with transshipment terminals, which seeks to minimize total vehicle and inventory related costs. First, a decomposition strategy transforms the model formulation, P, into an equivalent formulation, P'. In P', the vehicle flow variables may be found as function of the commodity flow variables; furthermore, the vehicle capacity constraints need not be explicitly considered. The decomposition, however, creates a situation whereby a commodity's incremental cost function on a given arc may contain concave and/or convex portions. This feature implies the presence of numerous local optima, over which an exhaustive search for a global optimum is computationally infeasible. Computational results from a series of test problems measure solution quality and algorithm efficiency. (SDW).
Minimum Cost Capacity Installation For Multicommodity Network Flows
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Author : Daniel Bienstock
language : en
Publisher:
Release Date : 1995
Minimum Cost Capacity Installation For Multicommodity Network Flows written by Daniel Bienstock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Commodity control categories.
The Dantzig Wolfe Decomposition Principle And Minimum Cost Multicommodity Network Flows
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Author : Richard D. Wollmer
language : en
Publisher:
Release Date : 1969
The Dantzig Wolfe Decomposition Principle And Minimum Cost Multicommodity Network Flows written by Richard D. Wollmer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Economics categories.
J.A. Tomlin published a paper on meeting required multicommodity network flows at minimum cost. He formulated this problem in both node-arc and arc-chain form. The node-arc linear program was attacked by the Dantzig-Wolfe decomposition principle by expressing the derived master program as convex combinations of the extreme points of the derived subprograms. In this note, it is shown that this problem is really a special case of the problem where one is attempting to meet minimum cost multicommodity flows without flow requirements on the individual commodities. Tomlin's algorithm is than modified to solve this more general problem. When this is done, the subprograms are homogeneous and the master program is a nonnegative combination of their independent solutions. (Author).