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Facility and covering location models are key elements in many decision aidtools in logistics, supply chain design, telecommunications, publicinfrastructure planning, and many other industrial and public sectors. In manyapplications, it is likely that customers are not dichotomously covered byfacilities, but gradually covered according to, e.g., the distance to the openfacilities. Moreover, customers are not served by a single facility, but by acollection of them, which jointly serve them. In this paper we study therecently introduced multiple gradual cover location problem (MGCLP). The MGCLPaddresses both of the issues described above.  We provide four different mixed-integer programming formulations for theMGCLP, all of them exploiting the submodularity of the objective function anddeveloped a branch-and-cut framework based one these formulations. Theframework is further enhanced by starting and primal heuristics andinitialization procedures.  The computational results show that our approach allows to effectivelyaddress different sets of instances. We provide optimal solution values for 13instances from literature, where the optimal solution was not known, andadditionally provide improved solution values for seven instances. Many ofthese instances can be solved within a minute. We also analyze the dependenceof the solution-structure on instance-characteristics.

An exact solution framework for the multiple gradual cover location problem