Constraint (5) ensures that ifyi ¼

Constraint (5) ensures that ifyi ¼ 1, then demand areaAiis fully covered by at least one facility. Constraint (6) implies that ifvi ¼ 1, then demand areaAiis partially covered by at least θ facilities. Finally, constraint (7) ensures that a demand area may be either fully covered or partially covered, but not both. The partial coverage demand coefficient α may be equal to the population ofAi or the profit achieved by fully covering of this demand area. The valuedijand the setsNðiÞand WðiÞare now determined using the capabilities of geographic information systems (GIS) rather than by a single calculation. A similar GIS function can determine the percentage of coverage in the case of partial coverage 0 � α � 1. MCLP-SO with α ¼0 is reduced to an MCLP-Model, which can be viewed as a modified version of the MCLP (shown in Model 2), in which demand is represented by the demand polygons themselves and where GIS functions are used to determine the level of coverage achieved. MCLP-SO with α ¼ 1 represents the scenario in which demand is represented by demand polygons, and partial coverage is possible, and is considered equivalent to full coverage. It can be viewed as the equivalent of the model proposed by Murray and Wei (2013) for the location set covering problem (LSCP). 3.3. Mathematical model and balance