Efficient algorithms for the capacitated concentrator location problem
Computers and Operations Research
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
A Bionomic Approach to the Capacitated p-Median Problem
Journal of Heuristics
A column generation approach to capacitated p-median problems
Computers and Operations Research
Constructive Genetic Algorithm for Clustering Problems
Evolutionary Computation
The Lagrangian Relaxation Method for Solving Integer Programming Problems
Management Science
An effective heuristic for large-scale capacitated facility location problems
Journal of Heuristics
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This paper studies a new variant of capacitated clustering problem (VCCP). In the VCCP, p facilities which procure a raw material from a set of suppliers are to be located among n potential sites (np) such that the total cost of assigning suppliers to the facilities and opening such facilities is minimized. Each supplier has a limited supply volume and each facility has a minimum supply requirement that must be satisfied by assigning enough suppliers to the facility. Each supplier can be assigned to at most one facility. When a supplier is assigned to a facility, the former will supply its all available volume to the latter. In order to solve the VCCP, a Lagrangian relaxation approach (LR) with two phases of dual optimization, the subgradient deflection in the first phase and the standard subgradient method in the second phase, is proposed. In the approach, the assignment constraints are relaxed. The resulting Lagrangian relaxed problem can be decomposed into a set of independent knapsack problems, which can be solved to optimality efficiently. At each Lagrangian iteration, a feasible solution is constructed from that of the Lagrangian relaxed problem by applying a greedy algorithm. Finally, the best feasible solution found so far is improved by a simple tabu search algorithm. Numerical tests on random instances show that the proposed LR can produce a tight lower bound and a high quality feasible solution for all instances with up to 4000 suppliers, 200 potential sites, and 100 plants to locate.