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An Algorithm and Its Error Bound of Reduced Facility Location Problem with a Case Study of Chiang Mai Waste Management System
In this research, we study facility location problem to locate the service points with minimum total cost in the system. The total costs in the system consist of setup cost and the total transportation cost which is the summation of delivery costs to the service points (or pick up costs from the customers). In general the number of customers in this problem is large with uncertain demands. Hence, a large-scale stochastic problem is involved in this study. We proposed a way to manage the data, an algorithm to reduce the size of the problem and how to relax the problem to a deterministic problem. An error bound for the reduced problem is also given. An illustrate example on Chiang Mai waste management system is solved by our proposed method and compared with the optimum solution to show the error bound. This system consists of candidate places to construct waste power (or disposal) plants (or storages) with different setup costs and capacities. Types of waste in this study include household, agricultural and industrial wastes. The number of waste sources as well as the candidates to construct the plants is considerably large with uncertain waste quantities. The numerical results in the case study show that the size of the problem can be reduced to 47.30% of the original problem with 10.33% different from the optimal solution.