Joint berth allocation and ship loader scheduling under the rotary loading mode in coal export terminals

Abstract

Due to nonmatching between the efficiency of ship deballasting and terminal loading, operations in modern coal export terminals (CETs) are frequently interrupted and significantly restricted by ship deballasting delays. This paper addresses a novel integrated problem of berth allocation and ship loader scheduling arising in CETs with new features, including the symmetrical berth layout-based rotary loading mode (SBLRLM) and deballasting restrictions. A mixed-integer programming (MIP) model is proposed to make joint decisions to minimize the total tardiness of all ships. By exploring the problem's decomposable structure, an exact method that relies on logic-based Benders decomposition (LBBD) is proposed to obtain optimal solutions. According to the problem features, the monolithic MIP formulation is decomposed into a new MIP (master problem) and a constraint programming (subproblem). Combinatorial valid inequalities are developed to enhance the master problem model and obtain a tighter lower bound. A Benders cut strengthening heuristic is developed to generate feasibility and optimality cuts to ensure efficient algorithm convergence. To evaluate the proposed method, computational experiments are conducted on a set of test instances generated based on real data collected from a major CET in northern China. The results indicate that the LBBD algorithm can optimally solve large-scale problem instances within a reasonable amount of time. The plan generated by the LBBD algorithm achieves a 51.9% reduction in ship tardiness, on average, compared to that of practical scheduling methods. By using the proposed method, the superiority of the SBLRLM in reducing deballasting delays becomes more significant as the problem scale increases. In addition, considering different working intensities, the results could also help port operators make decisions about the number of berths in the SBLRLM.