This paper addresses the problem of key resource scheduling of container terminals for energy-efficient operation. A combination of key resource scheduling and energy-efficient operation in container terminals is firstly described. An energy-efficient evaluation model of the key resource scheduling is then proposed. The objective set, decision variable set, and constraint set of key resource scheduling of a container terminal for energy-efficient operation are established in this paper. At the same time, their mapping relationship is carefully analyzed and the system structure of the key resource scheduling for energy-efficient operation of a container terminal is finally proposed.

The key resources in a container terminal usually include a berth, quay cranes, a storage yard, and yard cranes, as shown in Figure

Key resources of a container terminal.

“Energy efficiency" is also regularly called “efficient energy use" at an international level, and, together with a renewable energy policy, these are considered to be the two pillars of future sustainable energy policies [

Container terminals act as an important hub for global economic and trade activities and are facing increasing environmental pressure [

Within the industry, model programming problems have been studied by many scholars. Wang proposed a novel hybrid-link-based model that nests existing origin-link-based and destination-link-based models as special cases [

The scheduling problems of key resources in container terminals have gradually become a hot topic in academia and industry [

Although current researchers have made certain progress in key resource scheduling of container terminals, an energy-efficient and integrated scheduling method has not been effectively proposed. Therefore, there is no complete integration of key resources scheduling systems nor any efficiency study including the objective set, the decision-making variable set, and the constraint set which defines the mapping relationship between them. In this paper, an integrated key resource scheduling system will be designed and the mapping relationship of the objective set, the decision-making variable set, and the constraint set will be defined.

In Section

Energy-efficient scheduling of various types of core resources is the key to energy-efficient operation of a container terminal. A container terminal includes four types of key resources: a berth, quay cranes, a storage yard, and yard cranes. Obviously the berth and storage yard are spatial resources, and the quay cranes and yard cranes are equipment resources. In contrast with general resource scheduling problems, the efficient scheduling of resources needs to consider not only the efficiency of the allocations but also the evaluation index of the energy consumption.

In this paper, efficient operation of the container terminal requires efficient scheduling of the four key resources: the berth, the quay cranes, the storage yard, and the yard cranes. The scheduling of each of these four types of key resources depends on each other. The scheduling results of one type of resource may provide the initial conditions for the scheduling of another type of resource. At the same time, the results of scheduling the second resource type may have an impact on scheduling of other resources.

In this section, the parameters are defined as follows:

CT: the time delay of the ship leaving the port.

Primarily, the scheduling of a berth requires decisions to be made on the berthing location and the berthing time of ships. There are many factors that can impact the results, including the ship specifications, the ship arrival time, the loading and unloading quantity required for each ship, the currently moored ships, and the length of each shoreline ship on the berth. In this efficiency evaluation model, the objectives used for making a decision are to ensure that a ship is at port for the shortest possible time while maintaining the lowest possible energy consumption for the ship at port and the shortest horizontal transport distance. The calculation models for energy consumption and efficiency evaluation for berth scheduling can be illustrated as follows.

The scheduling of quay cranes depends mainly on the time when each quay crane starts service and the distribution of each quay crane. There are many factors that need to be considered, including the number of quay cranes, the current position of each quay crane, the current state of each quay crane, the shipping carts, the efficiency of each quay crane, and the energy consumption of each quay crane per unit of time. In this paper, the objectives that are used for decision-making are based on obtaining the shortest service time of ships and the minimum energy consumption of quay cranes during loading and unloading operations.

Generally, the scheduling of a yard includes scheduling blocks and bays. There are some additional factors that have an impact on the scheduling of a yard, such as the loading and unloading of the ship, the division of blocks, the location of blocks, the position of the berthing ship, and the availability of the blocks in the container terminal. The objectives used for decision-making are mainly based on achieving the shortest horizontal transportation distance, the highest economic balance of the blocks, the shortest moving distance of the yard cranes, and the minimum energy consumption for the horizontal transportation.

For yard scheduling, there are two factors that influence the moving distance of a yard crane: the concentration of bays in a block and the continuity of the block in the bay. Therefore, calculation of the moving distance of a yard crane can be broken down into two steps. The first step is the calculation of the distance between distributed bays and the second step is calculation of the continuity assigned to the bay in the container terminal. In (

The continuity of the sending containers can be evaluated based on the continuity assigned to the bay. The parallelism between the sending containers is mainly determined based on whether the distribution of blocks in the same port is scattered or not, as shown in

The scheduling of yard cranes requires decision-making on the task group needing service, the start time of that service, and the number of containers to be loaded and unloaded for that service. There are many factors impacting this scheduling, including the block and bay of the task group, the handling efficiency of the yard crane, the current position of the yard crane, and the number of yard cranes. The objectives for decision-making are mainly based on achieving the minimum delay in completing a task group, the minimum number of transitions of yard cranes, and the minimum energy consumption of yard cranes during both moving and handling.

In practice, the scheduling of core resources in a container terminal consists of a series of decision-making processes. Decision-making is required for scheduling of the berth, quay cranes, storage yard, and yard cranes. Since the berthing position of ships is required to make decisions on when to implement the scheduling of quay cranes, the loading and unloading time of ships must be considered for quay crane scheduling, which is decided by the berth scheduling. Therefore, integration is required between the scheduling problems for quay cranes and berths. In this paper, they are considered to be a unified problem for the purposes of decision-making and optimization. The decision objectives for the core resource allocation in traditional container terminals are mainly based on time (

The parameters are defined as follows:

BQ: the decision-making variable set for integrated scheduling of the berth and quay cranes.

BL: the decision-making variable set for yard scheduling.

YC: the decision-making variable set for yard crane scheduling.

TC: the time constraint set.

SC: the space constraint set.

EC: the equipment constraint set.

The optimized objective set for efficient scheduling of key resources in a container terminal consists of time (

Mapping relationship between the objective set and the decision-making problem set for key resource energy-efficient scheduling of a container terminal.

The scheduling of key resources in a container terminal consists of multiple optimization decision-making problems, including the integrated scheduling of the berth and quay cranes, yard scheduling, and yard crane scheduling. The decision variables of each decision-making problem are shown in Figure

Decision variable set for key resource energy-efficient scheduling of the container terminal.

The decision-making problems of the application can be regarded as being composed of many decision-making subquestions. For this purpose, each decision problem is regarded as a vector. The decision-making variable vector for integrated scheduling of the berth and quay cranes can be indicated by

In the energy-efficient scheduling decision-making model of key resources in a container terminal, the constraint set is quite complicated. The optimization decision-making model of the constraint set usually includes time constraints, space constraints, and equipment constraints. For example, the berthing time of a ship must be greater than or equal to the arrival time of the ship. Then the berthing location of a ship must be within the quay side line. Additionally, the number of assigned quay cranes must be less than or equal to the total number of quay cranes in the wharf. Therefore, the constraint set of the scheduling model can be expressed as

As previously discussed, in the efficient decision-making scheduling model of key resources, a mapping relationship exists between the decision-making variable set, the constraint set, and the objective set. In this model, the calculation model for the objective functions and the constraint conditions is comprised of decision-making variables and constants. Equation (

The mapping relationship between the decision-making variable set, the constraint set, and the objective set in the efficient decision-making scheduling model of key resources in the container terminal is shown in Figure

Mapping relationship between the objective set, constraint set, and decision variable set for key resource energy-efficient scheduling of a container terminal.

This paper has firstly described the combination of key resources scheduling and energy-efficient operation in a container terminal. An energy-efficient evaluation model for key resource scheduling has then been proposed. The objective set, decision variable set, and constraint set of key resource scheduling of container terminals for energy-efficient operation are then established in this paper. At the same time, their mapping relationship is carefully analyzed and the system structure of the key resource scheduling for energy-efficient operation in a container terminal is finally proposed.

In future studies, we will establish an efficient operation process analysis framework for container terminals, and subdivision of the evaluation objective will be studied on this basis. In addition, an evaluation index system for an efficient operation process will be established which will include carbon load properties.

The authors declare that they have no competing interests.

This work was supported by funding from Shanghai Science and Technology Committee (16DZ2349900, 16DZ1201402, 16DZ2340400, 16040501500, 15590501700, 14DZ2280200, and 14170501500), National Natural Science Foundation of China (61540045 and 71602114), Shanghai Municipal Education Commission (14CG48), and Shanghai Talent Development Fund.