3.2.3. FPP Objectives

In the fleet placement problem, the objectives are to maximise the users coverage of a station and to minimise the maximum global walking distance between users and fleet stations. With these two objectives, the optimization model is formulated as follows:


C denotes a constraint. Constraint 1 denotes that the number of stations cannot exceed the provided number *f* of fleet stations. Constraint 2, 3, and 4 restrict the model to consider any building *bj* to be covered by one station and to be calculated only once for user coverage. The building *bj* is covered *iff* there is at least one active station in its proximity (the proximity is defined by *w* − *r*). Constraint 5 finds the maximum walking distance of the active station *si* from all buildings *bj* that it covers. Constraint 6 impose the global walking distance to always be positive. Constraints 7 and 8 indicate that there are only two states for street nodes (active: 0, inactive: 1) and buildings (not covered: 0, covered: 1). Finally, constraints 9 and 10 denote the domains of indices *i* and *j* accordingly.
