Narrow Results

This paper focuses on the berth allocation problem, which is to determine where and when the vessels to be loaded and unloaded at a terminal within a given planning horizon, with consideration of uncertain factors, mainly including the arrival and operation time of the calling vessels. Based on the concept of service level which is commonly used in the inventory system, a decision model is constructed to minimize the cost of baseline schedule, which includes delay cost and nonoptimal berthing location cost. According to the specific characteristics of the model, the upper and lower bounds are found. And due to the NP-hardness of the constructed model, an adaptive differential evolution is employed to solve the problem. Finally, extensive numerical experiments are conducted to test the performance of the proposed models and solution approaches.

This paper examines the simultaneous allocation of berths and quay cranes under discrete berth situation in container terminals. The berths of discrete type have been broadly applied in realistic production especially for the terminals whose berths are not aligned in a straight line. The typical features of such berths including wharf length constraints, water depth constraints, and berth-bound quay cranes have been considered in this paper. In contrast to the previous work which only deployed the number of quay cranes besides the assignment of berths, this paper assigns berths and quay cranes simultaneously. In addition, to better fit the realistic production, some practical features related to quay cranes including the interference between quay cranes, the berth-dependent productivity of quay cranes, and limited adjustments of the assigned quay cranes during operations have also been considered in this paper. An integer programming model is formulated for this problem, and a sub-gradient-based Lagrangian relaxation algorithm is proposed. A simple but efficient greedy insertion heuristics is developed to solve the decomposed primal problems to optimality. Based on actual data, numerical experiments are conducted to test the performance of the proposed algorithm.

This study investigates an integrated model for the continuous berth allocation and quay crane scheduling problem by considering quay crane coverage range, ship fuel consumption, and transshipment costs. A nonlinear mixed-integer programming model is proposed. Some nonlinear parts in this model are linearized by approximation approaches. While the objective function aims to minimize waiting costs, it also seeks to minimize fuel consumption costs from the current port to the next port and housekeeping costs generated by transshipment between vessels. A local branching-based solution algorithm is designed to solve the proposed model. Computational experiments are conducted to validate the effectiveness of the proposed scientific programming model and efficiency of the algorithm.

Berth scheduling is the process of determining the time and position at which each arriving ship will berth. This paper attempts to minimize the serving time to ships, after introducing a proposed mathematical model, considers the berth allocation problem in form of mixed integer nonlinear programming. Then, to credit the proposed model, the results of Imai et al.'s model have been used. The results indicate that because the number of nonlinear variables in the proposed model is less than prior model, so by using the proposed model, we can obtain the results of model in less time rather than prior model.