Hybrid Cell Selection-based Heuristic for capacitated multi-facility Weber problem with continuous fixed costs

Location-allocation problem (LAP) has attracted much attention in facility location field. The LAP in continuous plane is well-known as Weber problem. This paper assessed this problem by considering capacity constraints and fixed costs as each facility has different setup cost and capacity limit to serve customers. Previous studies considered profitable areas by dividing continuous space into a discrete number of equal cells to identify optimal locations from a smaller set of promising locations. Unfortunately, it may lead to avoid choosing good locations because unprofitable areas are still considered while locating the facilities. Hence, this allows a significant increment in the transportation costs. Thus, this paper intelligently selected profitable area through a hybridization of enhanced Cell Selection-based Heuristic (CSBH) and Furthest Distance Rule (FDR) to minimize total transportation and fixed costs. The CSBH divides customer distribution into smaller set of promising locations and intelligently selected profitable area to increase possibility of finding better locations, while FDR aims to forbid the new locations of the facilities to be close to the previously selected locations. Numerical experiments tested on well-known benchmark datasets showed that the results of hybrid heuristic outperformed single CSBH and FDR, while producing competitive results when compared with previously published results, apart from significantly improving total transportation cost. The new hybrid heuristic is simple yet effective in solving LAP.