An exact solution framework for the multiple gradual cover location problem

TL;DR

This paper introduces an exact solution framework for the multiple gradual cover location problem, utilizing mixed-integer programming and branch-and-cut methods to efficiently solve complex location and coverage problems.

Contribution

It develops four new MIP formulations exploiting submodularity and enhances solution efficiency with heuristics, solving previously unresolved instances and analyzing solution structures.

Findings

Successfully solved 13 previously unsolved instances.

Improved solutions for seven existing instances.

Most instances solved within a minute.

Abstract

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