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This article presents a matheuristic algorithm for the single-sourcecapacitated facility location problem (SSCFLP) and its variants: SSCFLP with Kfacilities (SSCKFLP), SSCFLP with contiguous service areas (CFLSAP), and SSCFLPwith K facilities and contiguous service areas (CKFLSAP). The algorithm startsfrom an initial solution, and iteratively improves the solution by exactlysolving large neighborhood-based sub-problems. The performance of the algorithmis tested on 5 sets of SSCFLP benchmark instances. Among the 272 instances, 191optimal solutions are found, and 35 best-known solutions are updated. For thelargest set of instances with 300-1000 facilities and 300-1500 customers(Avella and Boccia 2009), the proposed algorithm outperforms existing methodsin terms of the solution quality and the computational time. Furthermore, basedon two geographic areas, two sets of instances are generated to test thealgorithm for solving SSCFLP and its variants. The solutions found by theproposed algorithm approximate optimal solutions or the lower bounds withaverage gaps of 0.07% for SSCFLP, 0.22% for CFLSAP, 0.04% for SSCKFLP, and0.13% for CKFLSAP.

A matheuristic algorithm for the single-source capacitated facility location problem and its variants