Comparison of two mathematical formulations for the offline routing of personal rapid transit system vehicles

Optimal Fleet Sizing of Personal Rapid Transit System

“…A nal conclusion obtained from our study and contrary to the case of minimization of total traveled distance for PRT [9], FB performs better than the MTZ formulation for the case of the minimization of the eet size.…”

“…Kara [8] studied to compare two mathematical formulations for distance constrained vehicle routing problem (DCVRP). Fatnassi et al [9] proposed to compare two valid mathematical formulations for the PRT case to minimize total traveled distance. Blazewichz et al [10] proposed to study mathematical models for single-machine, parallel-machine and job shop scheduling problems.…”

“…But in our search, only two papers focused on mathematical formulations for routing problems. The exceptions are the papers presented by Kara [8] and Fatnassi et al [9]. They developed an integer linear programming model for DCVRP in order to minimize the total traveled distance.…”

“…They ensure that the electric energy consumed by the selected roads don't exceed the battery capacity. Finally, Constraints (9) indicates that x ij are binaries variables and (10) z i are real positive variables.…”

Dealing with the Empty Vehicle Movements in Personal Rapid Transit System with Batteries Constraints in a Dynamic Context

“…Several studies related to PRT have focused on the feasibility and design of such a system [3][4][5][6] and, until recently, had sought to tackle operating issues in PRT, such as waiting times for passengers [7,8], dynamic routing [9][10][11], agentbased simulation [12], network design [13], fleet sizing [14], and energy consumption in both static [15][16][17][18] and dynamic context [19]. For more details on the PRT literature, the reader is referred to [1,20].…”