Assignment and scheduling trucks in cross-docking system with energy consumption consideration and trucks queuing
Introduction
Today, along with increasing competition among companies in different industries, it is vital to adopt appropriate policies for having an efficient supply chain to accelerate the delivery of products to customers. Hence, one of the strategies to improve supply chain performance is the product distribution strategy. Cross-dock is one of the product distribution strategies that serves as an intermediate node between suppliers and customers in a distribution network (Mousavi et al., 2014; Joo and Kim, 2013). As a supply chain strategy, cross-docking seeks to eliminate or reduce the costs of storage and retrieval operations compared to traditional distribution centers. One of the advantages of cross-dock is to reduce inventory, and improve customer satisfaction as well as better control of distribution operations (Yu and Egbelu, 2008; Vahdani et al., 2010, 2012). In this system, in order to expedite the delivery of products to customers, when an inbound truck enters a cross-dock, it is assigned to an inbound door. Then, the shipment of the inbound truck is unloaded. Then, in order to deliver the products to customers, the shipments are split up and loaded onto the outbound trucks after the integration and consolidation processes (Wang et al., 2018). At the decision level, cross-dock problems are classified in three different levels: strategic, tactical and operational levels (Larbi et al., 2011). The strategic level includes network design problems and the location of cross-dock facilities. The tactical level includes static dock assignment problems and deliveries in a cross-dock. Finally, the operational level includes the scheduling and sequencing of operations for the transfer of products in the cross-dock and the assignment of trucks to the doors (Abad et al., 2018).
In the problems addressed in the literature on cross-dock problems, truck scheduling problems and sequencing of trucks in the assignment of cross-dock doors are rarely taken simultaneously. Moreover, in most studies on the assignment of trucks to cross-dock doors, time considerations have not been taken into account. While one of the most important issues to minimize the time spent on doing activities in cross-docks and thereby reduce inventory costs is to consider time-based considerations in how trucks are assigned to cross-dock doors (Ye et al., 2018). Another very important consideration in real-world issues is the existence of several doors for loading and unloading loads from inbound and outbound trucks. Also, due to the high volume of shipment handling in cross-docks, sometimes in some cases, flexible doors with the ability to serve both types of inbound and outbound trucks are used to accelerate the unloading and loading of cargoes and to better coordinate cross-dock processes which can reduce the completion time of the operation and accelerate the circulation of products at the cross-dock level (Bienert et al., 2017). Obviously, taking into account the considerations of the existence of flexible and multiple doors in sequencing and scheduling of trucks and how to assign these trucks to these doors can be one of the most important and practical issues at the level of operational planning in cross-docks that has not so far been considered in the literature.
Another problem with warehouse management exiting in the traditional warehouses and more advanced systems like cross-docks is the shortage of equipment for the transportation of materials and products, such as forklifts and pallet jack (Ferrara et al., 2014). It should be noted that given the higher costs of forklifts than pallet jack, this issue is much more relevant to forklifts. In all studies on cross-docks, considerations regarding the availability of forklifts and how they are assigned to cross-docks have not been considered. If we strive to examine this issue in a realistic way, it can be seen that the shortage of equipment for servicing the outbound trucks will cause queues of outbound trucks and the trucks queuing ‘for assignment to door delayed deliveries to customers and impose costs on the system (Saeed and Larsen, 2016). Therefore, consideration of the queuing expectations of trucks in truck scheduling is necessary, but is rarely dealt with in the literature. It should be noted that given the need for considering time windows for loading and unloading processes in cross-docks, taking into account the considerations related to the mentioned problem is much more important.
On the other hand, regardless of the type of forklift used in the storage system, which can include electric, diesel or other types, one of the most important problems for the planning of the use of forklifts is their fuel consumption saving, so that the total fuel consumed by this transport equipment can be minimized (Al-Shaebi et al., 2017). Therefore, given the cases mentioned, such as lack of equipment, the lack of timely access to the assigned activities can lead to many costs for the system. Therefore, optimizing the fuel consumption of forklifts along with both scheduling and sequencing of trucks as well as how they are assigned to the doors can functionally increase the system functionality and more practical application provided to run in the cross-dock system (Ene et al., 2016).
Among the studies in the literature, the study of Bodnar et al. (2015) is most closely related to this paper. In this study, scheduling of trucks in a multi-door cross-dock is considered with respect to time window constraints. Moreover, some of the doors are flexible in order to be able to serve the outbound and inbound trucks. In addition, in the cross-dock, a temporary storage area is considered for short-term storage of products. In this paper, in addition to the considerations mentioned in the above research, several novelties are considered, which are as follows: the allocation of trucks to doors, sequencing of inbound and outbound trucks, considering both truck waiting queues for door assignment and energy consumption of forklifts in the cross-dock.
Given both the above mentioned cases and the review of the literature, it can be seen that no study has yet been made of scheduling and sequencing of trucks, the assignment of trucks and forklifts to cross-docks, in which a cross-dock has multiple doors as well as flexible doors. In addition, in none of the studies conducted on the issue, optimizing the use of forklifts as transportation equipment in cross-docks has not been considered. On the other hand, the issues mentioned in any of the studies in the subject literature have not been considered simultaneously with the issue of the waiting queue for outbound trucks to be assigned to outbound doors. Therefore, in this research, a bi-objective scheduling model is proposed for scheduling trucks and their optimal sequencing in the assignment of cross-dock doors, along with the assignment of trucks to the doors of the cross-dock. Moreover, a queuing system is considered to minimize the waiting times for trucks in the queue for assignment to doors. The first objective function of the proposed model is to minimize the cost of holding products in a cross-dock, the cost of delaying trucks in delivering shipments to customers, and the cost of waiting for trucks in the queue. The second objective function is to minimize the energy consumption of the carrier in the cross-dock. In order to solve the problem, two meta-heuristic algorithms, including a multi objective imperialist competitive algorithm (MOICA) and a multi objective grey wolf optimizer (MOGWO) are presented. Therefore, the novelties of this paper, in comparison with the other studies in the subject literature, are summarized below:
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Presenting a novel scheme for the synchronization of activities related to operational level decisions in a cross dock and energy consumption.
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Presenting a novel mathematical model to integrate scheduling and sequencing decisions of trucks, including assigning them to doors in a multi-door cross-dock with a complex door service capability.
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Optimizing the energy consumption of transport equipment inside a cross-dock.
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Proposing a M/M/1 queuing model for modeling the trucks queuing to allocate them to the doors of a cross-dock
The rest of this paper is organized as follows. A brief review of the literature is presented in Section 2. The problem definition and mathematical model are presented in Section 3. The suggested solutions are provided in Section 4. Computational results are shown in Section 5. Finally, Section 6 concludes the paper.
Section snippets
Literature review
Given a varied number of previous studies on the types of cross-dock problems, a short review on classification related to operational level problems in a cross-dock is just presented in this section for highlighting the problem under study. In addition, for more information, the literature review studies by Van Belle et al. (2012) and Ladier and Alpan (2016) can be mentioned.
Li et al. (2004) proposed an optimization model for scheduling a cross-dock operation with the aim of minimizing storage
Problem definition
In this study, the truck sequencing, scheduling and assignment problems in a multi-door cross-dock are considered with regard to time window constraints. In this way, trucks are not available at the beginning of the planning horizon, and trucks’ arrival and departure times are different. As a result, trucks will be assigned to the doors after entering the cross-dock on the basis of their entrance sequence. Therefore, on the one hand due to the different departure and arrival times of trucks and
Solution approaches
The model proposed in this study is considered as a part of the Np-hard problems; therefore, its solution in medium and large sizes takes long time using commercial software (Zandieh et al., 2009). Therefore, in this study, two meta-heuristic algorithms, namely MOMICA and MGWO were used to solve a multi-objective model. Moreover, in order to display the appropriate performance of the presented algorithms, two other multi-objective meta-heuristic algorithms, including the non-dominated sorting
Computational experiments
To display the correctness of the proposed model and meta-heuristic algorithms, twenty problems are considered. Input parameter values are presented in Table 2. Furthermore, to demonstrate the accuracy of the proposed model, the results of the first problem obtained by GAMS software are graphically illustrated in Fig. 9. It should be noted that, since the presented optimization model is multi-objective, the LP metric technique is applied to change it into a single-objective.
The components of
Conclusion
In the present study, a bi-objective mathematical model was proposed to determine both scheduling and sequencing of the inbound and outbound trucks in a multi-door cross-dock, including inbound, outbound and flexible doors. In addition, the proposed model described the assignment of inbound and outbound trucks and forklifts, which were internal carriers for the cross-dock. Moreover, due to the nature of the operational processes of the cross-docks at different time periods, the above decisions
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