## A decomposition algorithm for public central facilities location |

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### Contents

A Decomposition Algorithm for Public Central | 13 |

Extensions of the Decomposition Algorithm | 27 |

Computational Results | 31 |

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### Common terms and phrases

approximate artificial variables artificial vectors associated with node basic basis inverse Central Facilities Location clinics closest open center computation convex combination convex set Cornell University cost of demolition coupling constraints current basis decision-maker Decomposition Algorithm demolition cost dual variables associated extreme point solutions favorable vector feasible solution fixed-charge problem gible global optimum heuristic ineligible nodes infeasibility initial solution integer property j-th position j-th subproblem j=l i=l linear programming location methods Maranzana mathematical structure matrix Minimize n-component column vector n-component vector node ineligibility noise constraint number of centers objective function objective value obtained open facility operator optimal solution partitioning population at node potential sites problem 1.1 Public Central Facilities required nodes ReVelle 13 ReVelle formulation ReVelle's formulation satisfies 2.1b simplex method solu solution is optimal solution VII solved Ten-Node Location Problem thesis tion total regional utility total shipping cost transportation cost user population user-distance user-miles travelled warehouse