Environment and Planning B Planning and Design · 1988 · 114 citations · 0 references
ManagementIndustrial EngineeringCapacity PlanningFacilities PlanningFacility LocationAssignment ProblemsFacility SitingP-median ProblemCapacitated P-median ProblemCovering ProblemsGeneralized Assignment ProblemHeuristicsMaximal Covering Location ModelMaximal Covering Location ProblemUncapacitated P-median ProblemUncapacitated Plant Location
Set covering and maximal covering location problems have been extensively studied, but existing models assume uncapacitated facilities, limiting applicability in scenarios where capacity matters. The study aims to use theoretical links to inspire new heuristics for large capacitated covering problems. The authors exploit links to known problems, enabling planners to solve small to moderate real‑world instances with existing methods. The paper formulates capacitated set and maximal covering location problems and demonstrates their theoretical connections to capacitated plant location, p‑median, and generalized assignment problems.
Because of their widespread applicability, the set covering location problem and the maximal covering location problem have received considerable attention in the facility-location literature. There have been many extensions and modifications to these problems as they have been applied to various planning scenarios. A basic underlying assumption of the location-covering models formulated to date is that the facilities being sited are uncapacitated. Although this assumption is valid in many location-planning settings, there certainly exist situations in which this assumption severely limits the application of covering models. Capacitated versions of the set covering location problem and the maximal covering location problem have thus been formulated. In addition, the theoretical links between these models and the capacitated plant location problem, the capacitated p-median problem and, the generalized assignment problem are shown. By exploiting these links, planners can solve small and moderately sized real-world problems with existing solution methods. It is expected that these theoretical links will also give insight into developing new heuristics for large-sized capacitated covering problems.