A three-stage decomposition method for the joint vehicle dispatching and storage allocation problem in automated container terminals
Introduction
Automated container terminals (ACTs) are more efficient and reliable than traditional container terminals and can significantly reduce the operational costs associated with terminal human resources and equipment. As such, ACTs have attracted the increasing attention of scholars and terminal operators. ACTs mainly use three types of equipment: automated quay cranes (AQCs), a type of large dockside gantry crane for loading and unloading containers from container ships; automated yard cranes (AYCs), a type of smaller gantry crane located at the yard for loading and unloading containers from trucks; and automated vehicles, a type of truck to carry the containers between the yard and dockside (Liu, Jula, & Ioannou, 2002). About the horizontal transportations of ACTs, considering the efficiency, investment and environmental protection factors, the most common automated vehicles in ACTs are automated guided vehicles (AGVs) and automated lifting vehicles (ALVs). An AGV receives/delivers a container between quayside and storage yard with the help of QC/YC. While ALVs are capable of lifting/lower a container from/to the ground by themselves (Le, Yassine, & Moussi, 2012). Since the different characteristics of AGVs and ALVs, the interactive modes with the AQCs and AYCs and the time windows are all completely different.
Fig. 1 shows a typical layout of an ACT, where three types of machines cooperate closely to complete the unloading and loading of containers from and onto ships moored at the berth. During the unloading process, an AQC unloads a container from a vessel onto a vehicle (e.g., ALV or AGV). Then, the vehicle delivers the container to a storage area in the yard. Finally, an AYC collects the container from the vehicle and stacks it in an assigned slot (Luo & Wu, 2015). The loading process is the same as the unloading process, but in the reverse order.
To ensure high equipment use, a series of optimization problems have been proposed, including AQC scheduling, AYC scheduling, vehicle dispatching and routing, and storage allocation. More about different port operational problems are addressed in reviews by Carlo et al., 2014a, Carlo et al., 2014b. For a container terminal operator, the operational time of a moored vessel is a key performance index to evaluate the efficiency of the container terminal; this time is decided by the loading and unloading operations of the AQC. The vehicle dispatching problem relates to assigning vehicles for loading and unloading tasks, guaranteeing AQC operations at a minimum cost. Optimizing vehicle dispatches can shorten the total travel distance and reduce the number of vehicles used to complete the loading/unloading tasks. Several papers have discussed the vehicle dispatching problem. The strategies of vehicle pooling and double cycling are adopted to minimize the operational cost of vehicles (Lee et al., 2010, Nguyen and Kim, 2010, Nguyen and Kim, 2013). They mentioned that vehicle pooling can shorten the travel time of each vehicle’s trip while double cycling technique has been used especially for reducing the total empty trips of handling equipment so that the operational productivity can be improved.
The storage allocation problem investigates space allocation (i.e., blocks) to store unloaded containers, and determines the destination of the dispatched vehicles. Therefore, some researchers suggest that overall efficiency benefits by integrating vehicles in routing and storage allocation (Bish et al., 2001, Bish, 2003, Lee et al., 2009, Luo and Wu, 2015, Luo et al., 2016). The current literature has not fully compared AGVs and ALVs with respect to ATCs, integrating the vehicles, yard cranes, and storage locations. Existing papers do not consider the capacities of blocks and AYCs, or the time windows associated with loading and unloading containers. In addition, it is necessary to improve the efficiency of the algorithms proposed in previous research.
This paper focuses on the joint vehicle dispatching and storage allocation problem (JVD–SAP) in ACTs, which includes assigning automated vehicles to containers, the handling sequence associated with placing containers onto vehicles and the allocation of storage spaces to store unloaded containers. This study makes the following contributions:
- (1)
The first contribution of this manuscript to the literature is that a more realistic joint vehicle dispatching and storage allocation problem is proposed in this manuscript, because some practical factors, such as the storage capacity of blocks and reasonable time window, are taken into account. It’s noted that the existing related studies usually ignored those practical factors, which may create biased decisions. The vehicles are classified into two types: AGVs and ALVs, and two mixed integer programming (MIP) models are proposed for AGVs and ALVs, respectively. In addition, the operational differences between AGVs and ALVs are analyzed in detail, which are seldom studied in previous researches.
- (2)
The second contribution of this manuscript is the innovation of our solution method. According to the characteristic of the JVD-SAP and structure of the proposed models, this study develops a three-stage decomposition approach which can efficiently solve the proposed models. In stage 1 and 2, heuristic algorithms based on particle swarm optimization and greedy search are used to determine storage allocation and task assignment decisions. And then, the problem can be decomposed into several small-scale traveling salesman problems with time windows (TSPTWs) which can be solved directly in stage 3 by commercial solver, such as CPLEX. The solution results in stage 3 are then feedback to stage 1 until a termination criterion is fulfilled.
- (3)
In Stage 2, conflict tasks are identified and not allowed to be assigned to the same vehicle to avoid generating infeasible solutions. Compared to AGV, conflict task pairs for ALVs are harder to be identified because the time windows for ALVs are flexible. So, a new concept, named as “Degree of Conflict (DoC)”, is proposed to measure the possibility of conflict between two tasks. The DoCs can help the PSO-based greedy search to find feasible task assignments more efficiently, which is the contribution of this manuscript as well.
The rest of the paper is organized as follows. Section 2 reviews relevant literature. Section 3 describes the problem and proposes two formulations for AGVs and ALVs. The PSO-based greedy search method is proposed in Section 4. Section 5 reports the numerical experiments and analysis of results. Section 6 presents the conclusions.
Section snippets
Literature review
This section reviews the literature that has explored the problem addressed in this study. Studies can be divided into three categories: vehicle dispatching and routing problems, storage allocation problems, and JVD–SAPs. As for the other optimization problems in ports, such as berth allocation and equipment scheduling, readers are suggested to refer to Stahlbock and Voß (2008).
Problem description
The proposed JVD–SAP problem in this paper includes the assignment of automated vehicles to containers, the handling sequence to move the containers to the vehicle, and the storage space allocations to store unloaded containers.
Given the QC schedule, vehicles must deliver a set of loading and unloading containers between the water side and storage yard. For the loading container, the destination—i.e., the berth of the operating vessel, is predetermined. While for discharging container, the
Solution approach
The JVD–SAPs are well-known NP-hard problems (Lee et al., 2009). For small-scale cases, both M_ALV and M_AGV can be solved using a commercial solver, such as CPLEX. However, for real-world cases with large scales, the software cannot yield a good solution in a reasonable time and may not arrive at a feasible solution. Accordingly, PSO-based greedy search heuristic method is designed in this paper to obtain near-optimal solutions within reasonable time.
Computational experiments
This section reports on the different experiments used to evaluate the computational performance of the proposed solution algorithm. First, we use the commercial solver within CPLEX 12.5 to solve test cases at a small scale. Then, the optimal solutions are compared to the near-optimal solutions obtained using the method proposed in Section 4. As the problem size increases, it becomes difficult to obtain optimal solutions within a reasonable time (set as 3 h here). The proposed three-stage
Conclusions and future research
This study addresses a real time JVD–SAP in ACTs, to investigate the operational control of AGVs and ALVs. Two MILP models are developed, by considering the storage yard’s capacity. A three-stage decomposition method is proposed to solve the models. Numerical experiments with different problem scales are conducted to verify the proposed approach. The proposed method is very effective, due to the decomposition strategy and the new DoC concept. The results of the numerical experiments also show
Acknowledgement
This research is supported by the National Natural Science Foundation of China [Nos. 71771143, 71771180 and 71774109], Human Arts & Social Science Foundation of Ministry of Education of China (No. 16YJC630112), Shanghai Pujiang Program [No. 15PJ1402800], and the Scientific Research Foundation for the Returned Overseas Chinese Scholars (No. 49 batch).
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