A discrete equal-capacity p-Median problem
This thesis deals with the analysis of a discrete equal-capacity p-median problem, where the costs are directly proportional to the shipping distance and the amount shipped. A mixed integer programming formulation of the unbalanced, but equal capacitated case is analyzed. First we develop a dynamic...
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ndltd-VTETD-oai-vtechworks.lib.vt.edu-10919-461342021-05-15T05:26:26Z A discrete equal-capacity p-Median problem Marathe, Vikram Industrial and Systems Engineering LD5655.V855 1992.M372 Mathematical optimization This thesis deals with the analysis of a discrete equal-capacity p-median problem, where the costs are directly proportional to the shipping distance and the amount shipped. A mixed integer programming formulation of the unbalanced, but equal capacitated case is analyzed. First we develop a dynamic programming procedure for a p-median problem on a chain graph. In the second part we develop an algorithm to solve a p-median problem on a general network. First a heuristic algorithm is used to obtain an upper bound on the problem. Next, we obtain a lower bound on the problem by solving a Lagrangian relaxation of a reformulated problem via a conjugate subgradient optimization procedure. We obtain Benders’ cuts from the above procedures and proceed to a modified Benders’ approach to solve the continuous relaxation of the original problem. Finally a branch-and-bound algorithm that enumerates over the location decision variable space is used to obtain an integer optimal solution. Computational experience is provided to demonstrate the efficacy of the algorithm. Master of Science 2014-03-14T21:51:03Z 2014-03-14T21:51:03Z 1992 2009-12-05 2009-12-05 2009-12-05 Thesis Text etd-12052009-020104 http://hdl.handle.net/10919/46134 http://scholar.lib.vt.edu/theses/available/etd-12052009-020104/ en OCLC# 26354943 LD5655.V855_1992.M372.pdf viii, 105 leaves BTD application/pdf application/pdf Virginia Tech |
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LD5655.V855 1992.M372 Mathematical optimization |
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LD5655.V855 1992.M372 Mathematical optimization Marathe, Vikram A discrete equal-capacity p-Median problem |
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This thesis deals with the analysis of a discrete equal-capacity p-median problem, where the costs are directly proportional to the shipping distance and the amount shipped. A mixed integer programming formulation of the unbalanced, but equal capacitated case is analyzed. First we develop a dynamic programming procedure for a p-median problem on a chain graph. In the second part we develop an algorithm to solve a p-median problem on a general network. First a heuristic algorithm is used to obtain an upper bound on the problem. Next, we obtain a lower bound on the problem by solving a Lagrangian relaxation of a reformulated problem via a conjugate subgradient optimization procedure. We obtain Benders’ cuts from the above procedures and proceed to a modified Benders’ approach to solve the continuous relaxation of the original problem. Finally a branch-and-bound algorithm that enumerates over the location decision variable space is used to obtain an integer optimal solution. Computational experience is provided to demonstrate the efficacy of the algorithm. === Master of Science |
author2 |
Industrial and Systems Engineering |
author_facet |
Industrial and Systems Engineering Marathe, Vikram |
author |
Marathe, Vikram |
author_sort |
Marathe, Vikram |
title |
A discrete equal-capacity p-Median problem |
title_short |
A discrete equal-capacity p-Median problem |
title_full |
A discrete equal-capacity p-Median problem |
title_fullStr |
A discrete equal-capacity p-Median problem |
title_full_unstemmed |
A discrete equal-capacity p-Median problem |
title_sort |
discrete equal-capacity p-median problem |
publisher |
Virginia Tech |
publishDate |
2014 |
url |
http://hdl.handle.net/10919/46134 http://scholar.lib.vt.edu/theses/available/etd-12052009-020104/ |
work_keys_str_mv |
AT marathevikram adiscreteequalcapacitypmedianproblem AT marathevikram discreteequalcapacitypmedianproblem |
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1719404690940100608 |