Confronting the challenges provided by jumbo container vessels, managers of world-class seaports must take into consideration water depths-related constraints when making the vessel berthing decisions. That is, when the water depths satisfy the requirement of jumbo vessels’ drafts, these vessels are allowed to sail through the navigation channel. In this paper, we study a tactical berth allocation problem under the consideration of time-varying water depths. For the resolution, we propose an integer programming model, a set partitioning formulation and an improved differential evolutionary algorithm. Computational experiments demonstrate that the set partitioning formulation outperforms the integer programming model and can be applied to solve small- and medium-sized problems. The improved differential evolutionary algorithm is recommended for large-sized problems.

With the development of seaborne logistics, the international trade of goods transported in refrigerated containers is growing fast. Refrigerated containers, also known as reefers, are used in transportation of temperature sensitive cargo, such as perishable fruits. This trend brings new challenges to terminal managers, that is, how to efficiently arrange mechanics to plug and unplug power for the reefers (i.e., tasks) at yards. This work investigates the reefer mechanics scheduling problem at container ports. To minimize the sum of the total tardiness of all tasks and the total working distance of all mechanics, we formulate a mathematical model. For the resolution of this problem, we propose a DE algorithm which is combined with efficient heuristics, local search strategies, and parameter adaption scheme. The proposed algorithm is tested and validated through numerical experiments. Computational results demonstrate the effectiveness and efficiency of the proposed algorithm.

This paper addresses the drop-and-pickup container drayage problem with empty container constraints. In this problem, a truck is allowed to drop off the container at the customer and then leave. After the container has been packed/unpacked, the truck returns to pick it up. The problem is further complicated by the fact that empty containers at the depot are often limited in number. This container drayage problem is of great practical importance but seldom investigated. In this paper, we first formulate the problem as a directed graph and then mathematically model it as a mixed-integer linear program (MILP) with the objective of minimizing total travel costs. To solve the MILP effectively, we devise a branch and price algorithm that incorporates several performance enhancement strategies, including three versions of the bi-directional label setting algorithm, preprocessing of time windows and a heuristic for high-quality upper bounds. The experimental results indicate that (1) the proposed algorithm significantly outperforms CPLEX in terms of efficiency and effectiveness, (2) an average cost saving of 9.95∼12.25% can be achieved from the drop-and-pickup mode and (3) the benefit of drop-and-pickup mode increases when the customer density and the fixed cost increase.

In this paper, we investigate the resource-constrained order acceptance and scheduling on unrelated parallel machines that arise in make-to-order systems. The objective of this problem is to simultaneously select a subset of orders to be processed and schedule the accepted orders on unrelated machines in such a way that the resources are not overutilized at any time. We first propose two formulations for the problem: mixed integer linear programming formulation and set partitioning. In view of the complexity of the problem, we then develop a column generation approach based on the set partitioning formulation. In the proposed column generation approach, a differential evolution algorithm is designed to solve subproblems efficiently. Extensive numerical experiments on different-sized instances are conducted, and the results demonstrate that the proposed column generation algorithm reports optimal or near-optimal solutions that are evidently better than the solutions obtained by solving the mixed integer linear programming formulation.

As an effective solution to the first- and last-mile logistics of door-to-door intermodal container transportation, inland container transportation involves transporting containers by truck between terminals, depots, and customers within a local area. This paper is the first to focus specifically on the inland container transportation problem with limited depot capacity, where the storage of empty containers is constrained by physical space limitations. To reflect a more realistic scenario, we also consider the initial stock levels of empty containers at the depot. The objective of this problem is to schedule trucks to fulfill inland container transportation orders such that the overall cost is minimum and the depot is neither out of stock or over stocked at any time. A novel graphical representation is introduced to model the constraints of empty containers and depot capacity in a linear form. This problem is then mathematically modeled as a mixed-integer linear programming formulation. To avoid discretizing the time horizon and effectively achieve the optimal solution, we design a tailored branch-and-price-and-cut algorithm where violated empty container constraints for critical times are dynamically integrated into the restricted master problem. The efficiency of the proposed algorithm is enhanced through the implementation of several techniques, such as a heuristic label-setting method, decremental state-space relaxation, and the utilization of high-quality upper bounds. Extensive computational studies are performed to assess the performance of the proposed algorithm and justify the introduction of enhancement strategies. Sensitivity analysis is additionally conducted to investigate the implications of significant influential factors, offering meaningful managerial guidance for decision-makers.

This paper investigates the inland container transportation problem with a focus on multi-size containers, fuel consumption, and carbon emissions. To reflect a more realistic situation, the depot’s initial inventory of empty containers is also taken into consideration. To linearly model the constraints imposed by the multiple container sizes and the limited number of empty containers, a novel graphical representation is presented for the problem. Based on the graphical representation, a mixed-integer programming model is presented to minimize the total transportation cost, which includes fixed, fuel, and carbon emission costs. To efficiently solve the model, a tailored branch-and-price algorithm is designed, which is enhanced by improvement schemes including a heuristic label-setting algorithm, decremental state-space relaxation, and the introduction of a high-quality upper bound. Results from a series of computational experiments on randomly generated instances demonstrate that (1) the proposed branch-and-price algorithm demonstrates a superior performance compared to the tabu search algorithm and the genetic algorithm; (2) each additional empty container in the depot reduces the total transportation cost by less than 1%, with a diminishing marginal effect; (3) the rational configuration of different types of trucks improves scheduling flexibility and reduces fuel and carbon emission costs as well as the overall transportation cost; and (4) extending customer time windows also contributes to lower the total transportation cost. These findings not only deepen the theoretical understanding of inland container transportation optimization but also provide valuable insights for logistics companies and policymakers to improve efficiency and implement more sustainable operational practices. Additionally, our research paves the way for future investigations into the integration of dynamic factors and emerging technologies in this field.