Location and Design of Urban Facilities considering Competitors’ Responses: A Case Study of Putuo District, Shanghai

Table 1

Notations.

Symbols	Description
	The set of demand point, indexed by and .
	The set of existing facility, indexed by and .
	Location of the ith demand point
	Purchasing power of the ith demand point
	Location of the jth existing facility
	Location of the new facility
	Quality level of the new facility
	Old and new quality level of the jth existing facility, respectively
,	Upgrade cost for unit quality level of the new and jth existing facility, respectively
	Quality weight of the ith demand point
	Distance weight of the ith demand point
	Minimal distance between demand point and facility
	Distance between the ith demand point and the jth existing facility
	Distance between the ith demand point and the new facility
	Quality level range for all facilities
	Nonnegative and nondecreasing damping factor in attractive function
	Attraction that the ith demand point has for the jth facility
	Attraction that the ith demand point has for the new facility
	Income from the sale of unit goods