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The expansion of the transport problem

Author: WangChunLi
Tutor: XuCheng
School: Qingdao University
Course: Applied Mathematics
Keywords: transportation problems inverse problems network with gains the optimal expansion
CLC: F50
Type: Master's thesis
Year: 2008
Downloads: 160
Quote: 0
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Abstract


This article discusses the inverse transportation problems with bounded variables,the inverse transportation problems in network with gains and the optimal expansion of capacitated transportation problems.In the first chapter,we study the inverse transportation problems including upper and lower bound constraints,supposing that the basic feasible solutions are existed.We need to adjust the cost coefficients of a given transportation problem as less as possible so that a known feasible solution becomes the optimal one.Firstly,the according model is offered,then a method is suggested which is based on the optimality conditions for transportation problems,respectively under l1 and l∞measures.Under l1 measure,the primal problem is transformed into a minimum cost circulation problem which has many quick methods to solve;under l∞measure,we find the method to build the new cost coefficients.In the second chapter,we consider the inverse transportation problems in network with gains.Firstly,we give the according model,and then transform the primal problem into a minimum cost circulation problem under l1 measure,according to the study of the inverse transportation problems in the first chapter.The dual problems and inverse problems about transportation are discussed as well as the simplex method for solving transportation problems in network with gains.In the third chapter,we study the optimal expansion of capacitated transportation problems.We address the problem of allocating a given budget to increase the capacities of arcs in a transportation problem to minimize the cost of flow in the network.The capacity expansion costs of arcs are assumed to be linear convex functions.We use properties of the optimum solution to find the optimal conditions after converting this problem into a parametric network flow problem.The resulting algorithm yields an optimum solution of the capacity expansion problem for all budget levels less than or equal to the given budget.

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