| Acknowledgements | p. xi |
| Abstract | p. xiii |
| Introduction and Motivation | p. 1 |
| Definition and Formulation of the DOMP | p. 3 |
| Definition of the Problem | p. 3 |
| Modelling Possibilities | p. 5 |
| A Quadratic Formulation of the DOMP | p. 9 |
| Sorting as an Integer Linear Program (ILP) | p. 9 |
| A Formulation of the Location-Allocation Subproblem | p. 11 |
| A Quadratic Integer Programming Formulation of DOMP | p. 13 |
| Conclusions | p. 15 |
| Several Linearisations of the Quadratic Formulation (DOMP) | p. 17 |
| Three Linearisations of (DOMP) | p. 17 |
| A First Linearisation: (LDOMP[subscript 1]) | p. 17 |
| An Alternative Linearisation: (LDOMP[subscript 2]) | p. 22 |
| A Simplified Linearisation: (LDOMP[subscript 3]) | p. 25 |
| Comparison between (LDOMP[subscript 2]) and (LDOMP[subscript 3]) | p. 28 |
| Strengthening the Formulations | p. 30 |
| Improvements for (LDOMP[subscript 1]) | p. 32 |
| Improvements for (LDOMP[subscript 3]) | p. 38 |
| Improvements for (LDOMP[subscript 2]) | p. 45 |
| Comparison between (LDOMP*[subscript 2]) and (LDOMP*[subscript 3]) | p. 50 |
| Comparing Linearisation (LDOMP[subscript 1]) against (LDOMP*[subscript 1]), and Linearisation (LDOMP[subscript 3]) against (LDOMP*[subscript 3]) | p. 52 |
| Comparing (LDOMP*[subscript 1]) against (LDOMP*[subscript 3]) | p. 55 |
| Factorial Experimental Design | p. 55 |
| Analysis of Variance | p. 57 |
| Nonparametric Statistical Methods | p. 61 |
| Conclusions | p. 70 |
| A Specific Branch-and-Bound Method | p. 71 |
| Motivation | p. 71 |
| A Branch-and-Bound Method | p. 74 |
| A Bounding Rule | p. 74 |
| Branching Rules | p. 80 |
| Computational Results | p. 82 |
| Numerical Comparison of the Branching Rules | p. 83 |
| Comparing the B&B Method against the Best Linearisation | p. 84 |
| Comparing the Behaviour of the B&B Method for Different Types of Problems | p. 85 |
| Conclusions | p. 89 |
| Heuristic Procedures | p. 91 |
| An Evolution Program for the DOMP | p. 92 |
| Genetic Algorithms | p. 92 |
| Evolution Program | p. 93 |
| Codification of the Individuals | p. 94 |
| Initial Population | p. 94 |
| Evaluation Function | p. 95 |
| Genetic Operators | p. 95 |
| Selection Criterion | p. 96 |
| Parameter Values | p. 97 |
| A Variable Neighbourhood Search for the DOMP | p. 99 |
| An Implementation of the Modified Fast Interchange Algorithm | p. 100 |
| Initial Solution | p. 101 |
| Move Evaluation | p. 101 |
| Updating First and Second Closest Facilities | p. 101 |
| Modified Fast Interchange Heuristic | p. 103 |
| Variable Neighbourhood Search | p. 104 |
| Computational Results | p. 108 |
| Numerical Experiments with Different Parameter Combinations | p. 108 |
| Additional Tests for Large Problems | p. 112 |
| Large N-Median Problems | p. 113 |
| Large N-Center Problems | p. 115 |
| Large k[subscript 1] + k[subscript 2]-Trimmed Mean Problems | p. 117 |
| Conclusions and Further Research | p. 119 |
| Particular Cases and Related Problems | p. 121 |
| Discrete Partitioned Median Problem | p. 121 |
| DPMP with {[alpha, beta]} = {0, 1} | p. 122 |
| Problem Formulation | p. 122 |
| Linearisation | p. 124 |
| Strengthening the Formulations | p. 127 |
| General DPMP | p. 132 |
| Problem Formulation | p. 132 |
| Linearisation | p. 133 |
| DOMP with [Lambda]-Entries in Non-Decreasing Order | p. 135 |
| Problem Formulation | p. 135 |
| Computational Results | p. 136 |
| Conclusions and Further Research | p. 137 |
| Extension to the Capacitated Case | p. 139 |
| CDOMP with Total Costs | p. 140 |
| CDOMP with Partial Costs | p. 143 |
| Conclusions and Future Research | p. 148 |
| Conclusions and Further Research | p. 149 |
| General DOMP | p. 149 |
| DPMP and DOMP [upward right-pointing arrow] | p. 151 |
| CDOMP | p. 151 |
| Classification of Location Problems | p. 153 |
| Computational Results corresponding to the Linearisations | p. 155 |
| Results of (LDOMP[subscript 1]) and (LDOMP[subscript 3]) | p. 155 |
| Results of (LDOMP*[subscript 1]) and (LDOMP*[subscript 3]) | p. 157 |
| Computational Results corresponding to the Branch-and-Bound Method | p. 165 |
| Results of the B&B Method using the Index-Order Branching Rule | p. 165 |
| Results of the B&B Method with the Max-Regret Branching Rule | p. 174 |
| Computational Results corresponding to the Heuristic Procedures | p. 183 |
| Results of the Evolution Program | p. 183 |
| Results of the Variable Neighbourhood Search | p. 190 |
| Behaviour of Both Heuristic Procedures on Test Problems with M = 100 | p. 197 |
| Computational Results of the Formulation for the DOMP [upward right-pointing arrow] | p. 203 |
| Bibliography | p. 207 |
| List of Main Notations and Abbreviations | p. 213 |
| Index | p. 217 |
| The Author's Scientific Career | p. 221 |
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