Solving an integrated mathematical model for crew pairing and rostering problems by an ant colony optimisation algorithm

The crew pairing problem (CPP) and the crew rostering problem (CRP) are two sub-problems of a crew scheduling problem (CSP). Solving these problems based on a sequential approach may not yield the optimum solution. Therefore, the present study aims to consider the integrated CPP and CRP and present a new mathematical formulation. Due to its NP-hardness complexity, a meta-heuristic algorithm based on ant colony optimisation (ACO) is designed and used to solve the integrated problem and sequential approach (CRP followed by CPP) in some test problems extracted from a data set. The solutions provided by ACO for the integrated problem show 21.64% cost reduction in a reasonable time increase in comparison with those obtained by the sequential approach. Also, the ACO algorithm can provide solutions with a 2.96% average gap to the optimal solutions (by the exact method) for small-sized problems. Also, the proposed integrated approach leads to solutions with the best/optimal number of crew members to be assigned. The findings indicate that the proposed ACO has an efficient performance in solving the integrated problem. [Received: 20 May 2020; Accepted: 8 April 2021]