Application of a multi-objective multi traveling salesperson problem with time windows

The pilgrimage to Mecca, which is called Hajj, is the largest annual pedestrian crowd management problem in the world. During the Hajj, the pilgrims are accommodated in camps. For safety reasons, exact times and directions are given to the pilgrims who are moving between holy sites. Despite the importance of complying with those schedules, violations can often be conjectured. Directing a small workforce between the camps to monitor the pilgrims’ compliance with the schedule is an important matter, which will be dealt with in this paper. A type of multi-objective multiple traveling salesperson optimization problem with time windows is introduced to generate the tours for the employees monitoring the flow of pilgrims at the campsite. Four objectives are being pursued: As many pilgrims as possible (1), should be visited with a preferably small workforce (2), the tours of the employees should be short (3) and employees should have short waiting times between visits (4). A goal programming, an enumeration, Augmecon2 and an interactive approach are developed. The topic of supported and non-supported efficient solutions is addressed by determining all efficient solutions with the enumeration approach. The suitability of the approaches is analyzed in a computational study, while using an actual data set of the Hajj season in 2015. For this application, the interactive approach has been identified as the most suitable approach to support the generation of an offer for the project.