Capacitated service and regional constraints in location-allocation modeling

Planning for the provision of services is complex. Location-allocation modeling has proven to be a vauable approach in siting service facilities. An important consideration in siting facilitites is to ensure an equitable distribution of services. This may be done by requiring the placement of at least one or a few service facilities in certain defined (often political) regions or zones. Although the incorporation of regional requirements does serve to address equity, the location-allocation approach tends to produce siting schemes with highly uneven facility workloads. If the intent of regional constraints is to ensure equity, then facilities with excessive workloads provide relatively poor service and thus do not maintain the intent of the regional placement restrictions. Accordingly, it is necessary to account for capacity limitations at facilities in addition to the use of regionally specified siting requirements. This paper introduces the Capacitated Regionally Constrained p-Median Problem, which incorporates regional requirements in a location-allocation framework, in addition to ensuring that maximum capacity limitations are maintained. Example applications are solved using a Lagrangian-based solution approach.