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Transportation Problem (transportation + problem)

Distribution by Scientific Domains

Mathematics and Statistics	44%
Engineering	22%

Selected Abstracts

A Combined Cluster and Interaction Model: The Hierarchical Assignment Problem

GEOGRAPHICAL ANALYSIS, Issue 3 2005
Mark W. Horner
This article presents a new spatial modeling approach that deals with interactions between individual geographic entities. The developed model represents a generalization of the transportation problem and the classical assignment problem and is termed the hierarchical assignment problem (HAP). The HAP optimizes the spatial flow pattern between individual origin and destination locations, given that some grouping, or aggregation of individual origins and destinations is permitted to occur. The level of aggregation is user specified, and the aggregation step is endogenous to the model itself. This allows for the direct accounting of aggregation costs in pursuit of optimal problem solutions. The HAP is formulated and solved with several sample data sets using commercial optimization software. Trials illustrate how HAP solutions respond to changes in levels of aggregation, as well as reveal the diverse network designs and allocation schemes obtainable with the HAP. Connections between the HAP and the literature on the p-median problem, cluster analysis, and hub-and-spoke networks are discussed and suggestions for future research are made. [source]

A solution approach for log truck scheduling based on composite pricing and branch and bound

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 5 2003
Myrna Palmgren
Abstract The logging truck scheduling problem is one of the most complex routing problems where both pick-up and delivery operations are included. It consists in finding one feasible route for each vehicle in order to satisfy the demands of the customers and in such a way that the total transport cost is minimized. We use a mathematical formulation of the log truck scheduling problem where each column represents a feasible route. We generate a large pool of columns based on solving a transportation problem. Then we apply a composite pricing algorithm, which mainly consists of pricing the pool of columns and maintain an active set of these, for solving the LP relaxed model. A branch and price approach is used to obtain integer solutions in which we apply composite pricing to generate new columns. Numerical results from case studies at Swedish forestry companies are presented. [source]

An Explicit Solution of a Generalized Optimum Requirement Spanning Tree Problem With a Property Related to Monge

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 3 2001
Tsutomu Anazawa
The paper considers a generalization of the optimum requirement spanning tree problem (ORST problem) first studied by Hu in 1974. Originally, ORST was regarded as a communication network of tree type with the minimum average cost, and it is obtained by the well-known Gomory,Hu algorithm when the degrees of vertices are not restricted. The ORST problem is generalized by (i) generalizing the objective function and (ii) imposing maximum degree constraints. The generalized ORST problem includes some practical problems, one of which is proposed in this paper, but is not efficiently solvable in general. However, I show that a particular tree (which is obtained by a sort of greedy algorithm but is explicitly definable) is a solution of the generalized problem when a certain practical condition is satisfied. The condition is closely related to the Monge property, which is originally discussed in the Hitchcock transportation problem, and is known to make some NP-hard problems efficiently solvable. [source]

Solving generalized transportation problems via pure transportation problems

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 7 2002
Elsie Sterbin Gottlieb
Abstract This paper investigates certain issues of coefficient sensitivity in generalized network problems when such problems have small gains or losses. In these instances, it might be computationally advantageous to temporarily ignore these gains or losses and solve the resultant "pure" network problem. Subsequently, the optimal solution to the pure problem could be used to derive the optimal solution to the original generalized network problem. In this paper we focus on generalized transportation problems and consider the following question: Given an optimal solution to the pure transportation problem, under what conditions will the optimal solution to the original generalized transportation problem have the same basic variables? We study special cases of the generalized transportation problem in terms of convexity with respect to a basis. For the special case when all gains or losses are identical, we show that convexity holds. We use this result to determine conditions on the magnitude of the gains or losses such that the optimal solutions to both the generalized transportation problem and the associated pure transportation problem have the same basic variables. For more general cases, we establish sufficient conditions for convexity and feasibility. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 666,685, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10034 [source]

A branch-and-cut algorithm for the single-commodity, uncapacitated, fixed-charge network flow problem,

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2003
Francisco Ortega
Abstract We present a branch-and-cut algorithm to solve the single-commodity, uncapacitated, fixed-charge network flow problem, which includes the Steiner tree problem, uncapacitated lot-sizing problems, and the fixed-charge transportation problem as special cases. The cuts used are simple dicut inequalities and their variants. A crucial problem when separating these inequalities is to find the right cut set on which to generate the inequalities. The prototype branch-and-cut system, bc,nd, includes a separation heuristic for the dicut inequalities and problem-specific primal heuristics, branching, and pruning rules. Computational results show that bc,nd is competitive compared to a variety of special purpose algorithms for problems with explicit flow costs. We also examine how general purpose MIP systems perform on such problems when provided with formulations that have been tightened a priori with dicut inequalities. © 2003 Wiley Periodicals, Inc. [source]

Meta-Optimization Using Cellular Automata with Application to the Combined Trip Distribution and Assignment System Optimal Problem

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 6 2001
Wael M. ElDessouki
In this paper, meta-optimization and cellular automata have been introduced as a modeling environment for solving large-scale and complex transportation problems. A constrained system optimum combined trip distribution and assignment problem was selected to demonstrate the applicability of the cellular automata approach over classical mixed integer formulation. A mathematical formulation for the selected problem has been developed and a methodology for applying cellular automata has been presented. A numerical example network was used to illustrate the potential for using cellular automata as a modeling environment for solving optimization problems. [source]

Optimal transportation meshfree approximation schemes for fluid and plastic flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010
B. Li
Abstract We develop an optimal transportation meshfree (OTM) method for simulating general solid and fluid flows, including fluid,structure interaction. The method combines concepts from optimal transportation theory with material-point sampling and max-ent meshfree interpolation. The proposed OTM method generalizes the Benamou,Brenier differential formulation of optimal mass transportation problems to problems including arbitrary geometries and constitutive behavior. The OTM method enforces mass transport and essential boundary conditions exactly and is free from tension instabilities. The OTM method exactly conserves linear and angular momentum and its convergence characteristics are verified in standard benchmark problems. We illustrate the range and scope of the method by means of two examples of application: the bouncing of a gas-filled balloon off a rigid wall; and the classical Taylor-anvil benchmark test extended to the hypervelocity range. Copyright © 2010 John Wiley & Sons, Ltd. [source]