Discrete Location Problems

177 Pages·2016·2.34 MB·English

2016-11
Sune Lauth Gadegaard
PhD Dissertation
Discrete Location Problems –
Theory, Algorithms, and Extensions to
Multiple Objectives
DEPARTMENT OF ECONOMICS AND BUSINESS ECONOMICS
AARHUS BSS (cid:2) AARHUS UNIVERSITY (cid:2) DENMARK
Discrete Location Problems
– Theory, algorithms, and extensions to
multiple objectives
A PhD dissertation
by
Sune Lauth Gadegaard
Aarhus BSS, Aarhus University
Department of Economics and Business Economics.
April 2016

Discrete Location Problems
– Theory, algorithms, and extensions to
multiple objectives
Dissertation advisors
– Lars Relund Nielsen (main)
– Andreas Klose
– Kim Allan Andersen
Sune Lauth Gadegaard
Department of Economics and Business Economics
School of Business and Social Sciences
Aarhus University
Fuglesangs Allé 4
Building 2622
DK-8210
Denmark
[email protected]
http://pure.au.dk/portal/en/[email protected]
Copyright (cid:13)c 2013-2016 Sune Lauth Gadegaard
Rules of usage: None except the standard copyright rules. If any of the work, that being
theory, computational results or figures, is used or reproduced in any way, cite the work and
the author(s) in appropriate manners.
Layout and typography is chosen and implemented by the author
Font: Latin modern. 12pt scaled to 95 percent
Produced with pdfLATEX and the memoir–class
All figures have been made using TikZ

To Irene who has the decency not to realize she is way out of my league
and to Selma – You are my sunshine

Table of contents
Resumé (abstract in Danish) v
Abstract vii
Acknowledgments ix
Notation xi
1 Introduction 1
1.1 Facility location problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 A historic overview of facility location . . . . . . . . . . . . . . . . . 2
1.1.2 Characterizing facility location by topology and objective . . . . . . 6
1.2 Bi–objective facility location . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Contribution and outline of the dissertation . . . . . . . . . . . . . . . . . . . 9
2 An improved cut–and–solve algorithm for the single–source capacitated
facility location problem 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Solution methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 Phase 1 – Cutting planes . . . . . . . . . . . . . . . . . . . . . . . . . 18
Lifted cover inequalities . . . . . . . . . . . . . . . . . . . . . . . . . 21
Fenchel cutting planes . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.2 Phase 2 – Local branching . . . . . . . . . . . . . . . . . . . . . . . . 25
Initial feasible solution . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Refining the locational decision . . . . . . . . . . . . . . . . . . . . . 26
Refining the allocation decision . . . . . . . . . . . . . . . . . . . . . 26
Heuristic stop criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.3 Phase 3 – Cut–and–solve . . . . . . . . . . . . . . . . . . . . . . . . . 27