A mixed integer linear programming model and a basic variable neighbourhood search algorithm for the repatriation scheduling problem

Commercial flights nearly halted due to the COVID-19 pandemic in the second quarter of 2020. Consequently, several countries have had to schedule repatriation flights to return their citizens stranded in other countries. Flight routes and schedules are known in normal circumstances, and passengers buy seats on these flights; however, the reverse steps happen in repatriation. Passengers express their need to travel, and flights are scheduled to satisfy their requests. The problem behind this flight schedule can be called the repatriation scheduling problem (RSP), in which we need to repatriate citizens from different countries. The objective of the RSP is to return the most vulnerable citizens first. The capacity of available airplanes and quarantine locations limit the number of repatriated citizens. To address this problem, we have developed a mixed-integer linear program (MILP) to model the RSP. Moreover, we suggest a basic variable neighbourhood search (BVNS) algorithm to solve the problem. We test the BVNS algorithm by creating and solving a set of 108 RSP instances and then comparing the BVNS solutions with the exact ones. Despite allocating only 20 s to run the BVNS algorithm compared to eight hours for a commercial exact solver’s branch and bound algorithm, the BVNS algorithm could find better results than the lower bounds for 62 instances and similar values for 17 instances.