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Multi-facility Green Weber Problem

Atashıkhoeı, Arsham
Süral, Haldun
Tural, Mustafa Kemal
Multi-facility Green Weber ProblemThe multi-facility Weber problem corresponds to locating a number of facilities on the plane so as to minimize the sum of the weighted Euclidean distances between the customers and the allocated facilities. Its applications can be exemplified by locating warehouses or facilities for a distribution system in which the demands will be delivered directly to the customers. Such distribution systems consume a large amount of fuel and increase the emissions of greenhouse gases.In this scope, the multi-facility green Weber problem (MF-GWP) is a planar location problem that aims to minimize the amount of CO2 emission in a distribution system. The MF-GWP, determines the locations of p facilities on the plane and the speeds of the vehicles while minimizing the total CO2 emission. We formulate the MF-GWP as a mixed integer second order cone programming (MISOCP) problem. Since the MISOCP formulation of the MF-GWP is weak, only small size instances can be solved to optimality in 4 hours. For solving large problem instances, well-known heuristics developed for the multi facility Weber problem such as alternate location-allocation heuristic, transfer follow-up heuristic, and decomposition heuristic are utilized as well as a newly developed local search approach.The computational results represent the difficulties of finding the exact solution of the MF-GWP with the MISOCP formulation even for the small size instances. For larger problem instances, quality of solutions obtained by different settings of computational experiments, depict the performance and benefits of the improvement heuristics proposed in our study.