Absolute and Vertex Restricted p-Center Problems

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Table of contents

1 Introduction 
2 Notation and Denitions 
3 Literature Review 
3.1 Absolute and Vertex Restricted p-Center Problems
3.2 Capacitated p-Center Problem
3.3 Contribution of the Thesis Work
4 The Vertex Restricted p-Center Problem 
4.1 Mathematical Formulations Existing in the Literature
4.2 Proposed Formulations
4.3 Relaxation and Heuristic Bounds
4.3.1 LP Relaxations
4.3.2 Semi Relaxations
4.3.3 Attaining Quick Lower and Upper Bounds
4.4 Double Bound Algorithms
4.5 Computational Experiments
4.5.1 Unweighted Problems
4.5.2 Weighted Problems
4.6 Conclusion
5 Absolute p-Center Problem 
5.1 Generation of the Intersection Points
5.2 Improved Lower and Upper Bounds
5.3 Computational Experiments
6 Single Allocation Capacitated p-Center Problem 
6.1 Proposed Formulations
6.2 Successive p-Center-Allocation Algorithm
6.3 Computational Experiments
6.4 Conclusion
7 A Branch and Cut Algorithm for Solving the Multiple Allocation Capacitated p-Center Problem 
7.1 Proposed Formulations
7.2 A Branch and Cut Algorithm
7.3 Computational Experiments
8 Conclusions and Future Research Directions 
8.1 Preliminary Results of a Benders Decomposition Algorithm for Solving the p-Center Problem
8.2 Contribution Summary
8.3 Future Research Directions