An accelerated Benders decomposition algorithm for the integrated storage space assignment, berth allocation, and yard crane deployment problem

In this paper, storage space assignment problem, berth allocation problem, and yard crane deployment problem are integrated with due attention to traffic congestion in the passing lines of storage yards. The paper provides a mixed-integer programming model for the integrated problem with the objective of minimizing the movement and operating costs of yard cranes, the cost of moving container flow between the storage yard and berths, and the delay cost of vessels. The planning horizon is considered to be one day and the berth layout is assumed to be discrete. Since the integrated storage space assignment and yard crane deployment problem is NP-hard and so is berth allocation problem, the integration of these three problems will be at least equally complex. Thus, an Accelerated Benders Decomposition Algorithm is also developed for solving the integrated problem. This is done by introducing a combinatorial Benders cut to the classical Benders decomposition algorithm to improve its performance and also adding 8 valid inequalities derived from the problem properties and assumptions to the algorithm formulation to accelerate the solution process. The proposed mathematical model and solution approach are evaluated by generating instances of different sizes for the problem and assessing the solution results. The results show the good performance of the proposed accelerated Benders decomposition algorithm. Taking the integrated approach to the modeling of the three problems rather than the non-integrated approach improved the cost of terminal operations by 11.15% on average.