3.2.1. FPP Parameters

In the fleet placement problem (FPP), there are two types of parameters, inputs and instance parameters. Input parameters are the number of fleet stations, maximum walking distance, and station radius as shown in Table 1. Instance parameters are related to the problem graph instance, which are the set of street nodes, buildings, population, and distance between street nodes and buildings as summarized in Table 2. Stations are put on the street node in *S* = {*<sup>s</sup>*1,*s*2,...,*sn*} and have a unique size *r* (see Figure 2). Users are assumed to start the trip from their residence (referred to as building) in B = {b\_1, b\_2, ..., b\_m} where each residence or building has a different number of users defined as *P* = {*p*1, *p*2,..., *pm*}. Each street node covers a set of buildings, which depends on the defined walking distance *w* and a set of distance *D* = {*d*11, *d*12,..., *dij*} where *dij* denotes walking distance between node *si* and building *bj* where a distance function *d*(*si*, *bj*) = *dij*. A station *si* covers a building *bj iff* that station locates at most *w* − *r* meters from the building.

**Table 1.** FPP input parameters.




#### 3.2.2. FPP Variables

The variable of FPP consists of three variables. The first variable is the set of the state of buildings *C* where *ci j* represents the fact that building *bj* is or is not covered by a station *si*. If the building *bj* is covered then *cij* = 1 and *cij* = 0 otherwise. A building is covered when the center point of a station (at least) is located within walking distance smaller than *w* − *r*. The second variable is a set of state street nodes (*S*), where *s i* represents the state of node *si* (*si* ∈ *S*). A node is active if it is the center point of a station. If *si* is active then *s i* = 1 and *s i* = 0 if *si* is inactive. It is important to note that a station can be active even if it does not cover any buildings. In this version, the station is able to accommodate only one vehicle at a time. Finally, the maximum global walking distance (*z*) denotes maximum walking distance from every selected stations to their covered buildings (hence, covered population) as shown in Table 3.

#### **Table 3.** FPP variables.

