Berth assignment for liner carrier clusters under a cooperative environment

Abstract The berth allocation problem (BAP) has been extensively studied in the literature, which seeks to determine berths and times for upcoming ships. The previous studies do not distinguish berths and ships among different liner carriers. By taking into account the increasing use of dedicated berths in practice, this paper proposes a special BAP where berths and ships could be distinguished among different liner carriers. For our BAP under a cooperative environment, we propose a mixed-integer programming model. Based on an assignment model with binary variables, our BAP can be reduced to the liner carrier clustering problem. To generate stable liner carrier clusters used in our assignment model, queueing theory and core theory are applied. A three-stage optimization method is proposed to solve our BAP. Namely, stage I proposes a queueing theory approach for various liner carrier clusters, and based on core theory stage II determines the stability of different liner carrier clusters. Based on the results obtained in stages I and II, stage III solves the liner carrier clustering problem. Numerical experiments are carried out to demonstrate the effectiveness of the proposed method.