Container Drayage Research Articles

The container drayage problem for heterogeneous trucks with multiple loads: A revisit

In this study, we revisit the container drayage problem for heterogeneous trucks with multiple loads in view of its practical significance. We first propose a tailored mixed-integer linear programming (MILP) model explicitly to reflect the reality of container drayage operations. To solve medium-scale problems more effectively, two relaxed MILP models are built to provide a solution that is close to optimal with less computational time. These two relaxed models are proven to work as intended and provide optimal solutions under certain conditions. Moreover, an effective hybrid heuristic method incorporating the cheapest feasible insertion mechanism and the variable neighborhood search scheme is designed to solve large-scale problems. Extensive numerical experiments demonstrate the scalability of the heuristic method in real-world applications.

Local container drayage problem with truck platooning mode

This study examines the local container drayage problem under a semi-autonomous platooning mode. The benefits of this mode include labor cost saving via the semi-autonomous truck fleet and fuel cost saving via air drag reduction. The problem of routing drivers and trucks according to the characteristics of platooning is mathematically modeled. The lower bound is analyzed through comparison with the traditional mode. A tabu search heuristic is developed to solve the problem. Numerical experiments are conducted to assess the performance of the algorithm, quantify the benefits of the platooning mode, and analyze the effects of some key model parameters.

A bi-objective model for robust local container drayage problem

Local Container Drayage Problem (LCDP) refers to the optimization of the process of planning and scheduling container trucks between a terminal and customers to offer door-to-door service to customers in a local area. The time required for (un)packing containers at customers’ sites are often relatively long and uncertain due to the current (un)packing work level and unexpected deviations in operational situations, which has a significant influence on the planning and scheduling of the container transportation process. This paper examines the LCDP with Separable tractors and trailers, and additionally with consideration of (un)packing time Uncertainties (LCDPSU). A proactive strategy is employed to tackle the uncertainty by proposing a “model robust” bi-objective optimization model to balance the tradeoff between operational cost, which includes traveling cost and tractor deployment setup cost, and robustness, which is represented as an exponential expression of the time buffer between two stages of each individual task. The deterministic version of our problem is proved to be NP hard, and an Ant Colony Optimization (ACO) scheme is therefore proposed to search for feasible solutions in which the Zoutendijk feasible direction algorithm is embedded in order to tackle the nonlinearity brought in by the robustness of the model. Numerical experiments are conducted to validate the efficiencies and effectivenesses of the proposed models and methods, and managerial implications are drawn from the numerical results.

The Multi-period Multi-trip Container Drayage Problem with Release and Due Dates

The Container Drayage Problem (CDP) aims at routing a fleet of trucks, based at a common terminal, to serve customers while minimizing the total travel distance. Each trip starts from and ends at the terminal, and handles a subset of customers. Each customer requires either that a container is picked up or delivered. We introduce a more realistic variant, i.e., the Multi-trip Multi-period CDP with Release and Due Dates (MM-CDP-RDD), in which the planning horizon is composed of several periods (days). On each day, each truck may perform more than one trip respecting the Release and Due Dates (RDD) associated with customer services, corresponding to the first and the last day on which the service can be carried out, respectively. Drivers’ contracts impose limitations on the maximum driving time allowed on each day, on two consecutive days and on the whole weekly planning horizon. To model the MM-CDP-RDD, we propose both an Arc-based Integer Linear Programming (ILP) formulation and a Trip-based ILP formulation that receives as input all the feasible non-dominated trips. To efficiently address medium/large-sized instances of the problem, we also design six Combinatorial Benders’ Cuts approaches. All the methods are compared on a rich set of instances generated for this new problem.

Container drayage modelling with graph theory-based road connectivity assessment for sustainable freight transportation in new development area

Densely populated cities, suffered from land scarcity, are often encountered the need of exploring new development areas. This initiative in developed cities usually includes reconsolidating container depots and proposing multi-storey cargo centre as part of urban development roadmap. Changes on road network and connectivity between ports and container depots affect the efficiency of container drayage operations. A novel container drayage optimization model incorporating the road network and connectivity metrics is developed to minimise the total traveling distance, truck fuel cost, container rental cost and container movements among multiple consignees and shippers. The model is adopted in assessing the container logistics low between the ports and the Hung Shui Kiu New Development Area (HSKNDA) in Hong Kong, one of the most densely populated cities in the world. In assessing the impact of HSKNDA towards container drayage operations in the environment of congested urban area, the road logistics connectivity is evaluated with graph theory-based network metrics using ArcGIS. Road network files are analysed using ArcMap and the road connectivity are evaluated on its completeness, circuitry and complexity using road connectivity metrics and ArcMap. The road connectivity of the circumstances before and after HSKNDA are evaluated and the results revealed that the alpha, beta and gamma indexes changed slightly but the node number, link number and link length are decreased, benefiting container truck movements. The results have been adopted in optimising the container drayage problem in HSKNDA, the operating cost has been reduced in four simulated scenarios when compared to the results obtained by the traditional approach. The proposed approach integrates the GIS and optimisation modelling to improve the effectiveness and reduce operating cost in container drayage process, contributing to the research with the development of the integrated novel container drayage model as a smart urban logistics for sustainable freight transportation and the evaluation of the road connectivity on the new development area. It provides optimal solutions for ship liners and logistics firms in restructuring the physical logistics network, enhancing liner operations efficiency, mitigating carbon emission, and enabling a higher quality of living in the city.

The one container drayage problem with soft time windows

Intermodal freight transport consists of using different modes of transport without changing the load unit. This results in a significant reduction in the time that goods spend at intermodal terminals, where transshipment takes place. Drayage refers to the transport of freight on trucks among intermodal terminals, depots, customers and suppliers. In spite of the fact that drayage only represents between 5 and 10 percent of total distance, it may amount up to more than 30 percent of the total costs. The aim of this work is to study drayage operations. First, an extensive literature review is undertaken. Since the intermodal transport chain can become more efficient by means of a proper organisation of the drayage movements, the optimization of the daily drayage problem has been identified as one of the main ways of reducing the drayage cost and improving intermodal operations. On this problem, the lack of a common benchmark has hindered reaching further conclusions from all the research carried out. Therefore, this paper proposes a common framework and presents a generalized formulation of the problem, which allows modeling most drayage policies, with the limitation of only considering one-container problems. Results show that flexible tasks in the repositioning of empty containers as well as soft time windows can reduce the operating costs and facilitate the management of drayage companies. This work may help consider adequate policies regarding drayage operations in intermodal terminals.

A generalised model for container drayage operations with heterogeneous fleet, multi-container sizes and two modes of operation

We propose a generalized model of drayage operations that incorporates the coupling and precedence principles, allows for live and separation operation modes, relaxes the assumptions about fleet composition and truck size, and operates in a realistic network. The results of the experiments reveal that the model efficiently and effectively allocates container transport requests and can find close to optimal solution in reasonable time for small and medium size problems. The results also suggest the existence of a threshold strongly related to the ratio of the fleet capacity over the number of requests where the fleet is utilised most effectively.

Multi-Trailer Drop-and-Pull Container Drayage Problem

This paper presents a so-called multi-trailer drop-and-pull container drayage (MTDPCD) problem. The MTDPCD problem allows a tractor to carry multiple trailers and a tractor can leave the customer while the container is being packed / unpacked. This mode has been applied in real life and shown its great potential to improve transportation efficiency but not been reported in literature. We model the MTDPCD problem based on node decomposition as a nonlinear program and then linearize it. A backtracking adaptive threshold accepting algorithm is proposed to solve the problem. A named 3-vector procedure is designed to calculate the number of trailers and to check feasibility of solutions. A decoding algorithm including three stages is presented to adjust starting times of trucks given sequences of drayage orders. Experiments based on randomly generated instances validate the aforementioned methodology and indicate that pulling 2 trailers can save about 30% of operating costs than pulling 1 trailer.

A generic model for the local container drayage problem using the emerging truck platooning operation mode

The local container drayage problem (LCDP) plays an important role in the waterborne transportation for global trade. Truck platooning is an emerging and promising container transportation mode in which a platoon is formed by a leading truck followed by a set of trucks using semi-automated technologies. This paper focuses on the truck platooning operation mode (TPOM) in which only the leading truck is human-driven. We also focus on attempts to exploit the advantages of the new operation mode, such as the ability to use multiple trucks simultaneously with only one driver. Moreover, one customer can be serviced by two different drivers through coordination, and one container can be shared among customers without returning to the depot. All of these advantages improve the LCDP operational performance. A mathematical model is proposed to capture these advantages and related features pertaining to this new operation mode. The model is compared, theoretically and numerically, with three well-studied LCDP models reported in the literature, and we prove that our model is a generalization of the previous three models. For even small-scale problems, CPLEX has difficulty achieving satisfactory solutions due to the NP-hardness and complicated structure of the problem. Therefore, a heuristic method that incorporates the learning mechanism based on the ant colony algorithm is proposed to overcome the problem. Extensive numerical experiments were conducted to validate the model and proposed methods, and the experimental results show that the benefits of the new operation mode can be achieved by increasing the platoon length and/or well coordinating the sharing of containers among customers.

A novel mathematical model and a large neighborhood search algorithm for container drayage operations with multi-resource constraints

Multi-resource constraints in container drayage operations exist widely in real-life scenarios but have been seldom reported in literature. This study mainly addresses a container drayage problem with a limited number of empty containers at depots, with the goal of minimizing both the number of trucks in operation and the total working time of trucks. The problem is firstly formulated as a bi-objective mathematical model based on a so-called determined-activities-on-vertex graph. Three schemes are proposed to handle the developed mathematical model as: (a) a nonlinear constraint is linearized; (b) a parameter that is a large enough constant in the model is analyzed and tuned deeply; and (c) the bi-objective model is converted into a single-objective model. Furthermore, a large neighborhood search algorithm is designed to solve the problem. The two solution methods are validated and evaluated based on randomly generated instances as well as instances from literature. Numerical experimental results indicate that the methods can provide optimal or near-optimal solutions for medium- and large-scale instances in a short running time.

Range-based truck-state transition modeling method for foldable container drayage services

Manufacturing technologies of foldable containers have almost matured. The use of foldable containers might save transportation costs; however, incorporating them into drayage services also creates great challenges. The foldable container drayage (FCD) problem is formulated as a sequence-dependent multiple traveling salesman problem with time windows using a range-based truck state transition method. An improved reactive tabu search algorithm is designed and validated to solve the FCD problem. The methodology is evaluated extensively on the basis of randomly generated instances. Compared to the use of standard containers, the use of four-in-one foldable containers can save approximately 10% on transportation costs.

An exact algorithm for the container drayage problem under a separation mode

In this paper, we consider the container drayage problem under a separation mode in which a container can be separated from the truck during (un-)loading operation, and some emptied containers should return to the depot for maintenance. The problem is equivalently transformed into a variant of the asymmetric vehicle routing problem with time windows (a-VRPTW) based on a determined-activities-on-vertex (DAOV) graph. We present an arc-flow formulation and propose a branch-and-price-and-cut algorithm to exactly solve it. Computational results on a set of randomly generated instances show that the proposed algorithm outperforms CPLEX in terms of efficiency and effectiveness and the separation mode is advantageous over the stay-with mode.

An efficient mixed integer programming model for pairing containers in inland transportation based on the assignment of orders

The inland transportation takes a significant portion of the total cost that arises from intermodal transportation. In addition, there are many parties (shipping lines, haulage companies, customers) who share this operation as well as many restrictions that increase the complexity of this problem and make it NP-hard. Therefore, it is important to create an efficient strategy to manage this process in a way to ensure all parties are satisfied. This paper investigates the pairing of containers/orders in drayage transportation from the perspective of delivering paired containers on 40-ft truck and/or individual containers on 20-ft truck, between a single port and a list of customer locations. An assignment mixed integer linear programming model is formulated, which solves the problem of how to combine orders in delivery to save the total transportation cost when orders with both single and multiple destinations exist. In opposition to the traditional models relying on the vehicle routing problem with simultaneous pickups and deliveries and time windows formulation, this model falls into the assignment problem category which is more efficient to solve on large size instances. Another merit for the proposed model is that it can be implemented on different variants of the container drayage problem: import only, import–inland and import–inland–export. Results show that in all cases the pairing of containers yields less cost compared to the individual delivery and decreases empty tours. The proposed model can be solved to optimality efficiently (within half hour) for over 300 orders.

Synchronizing Trucks and Trailers in a Multiresource Problem with Variable Neighborhood Search

A real-world container drayage problem in which containers are transported between an intermodal terminal, a container terminal, and customer locations is considered. The problem was modeled as a multi-resource routing problem (MRRP) that included trucks, trailers, and containers. Given a fleet of trucks and trailers, the goal is to use these resources most efficiently to complete a number of given orders. Orders consisted of several tasks with time windows, such as picking up a container at the terminal, delivering it to a customer, and bringing the processed container back. A challenging aspect of this problem is the management of trailers, which are required to transport the containers. Here, the compatibility between container types and trailer types must be considered. Thus, the decision of which trailer should be attached to which truck depends on the containers that must be transported, the day of availability of trailers, and the toll costs of the truck and trailer combination on the highways. This paper presents an efficient way to model this problem and proposes a metaheuristic approach based on a variable neighborhood search. It uses a compact solution representation and tailored neighborhood structures to reduce the search space. Classical MRRP neighborhood structures, as well as problem-specific ones, were used in combination and contributed to the overall success. The results show that the given real-world problem can be solved efficiently, and it can be shown that with proper planning, the utilization of resources can be increased.

Generalized mixed integer and VNS heuristic approach to solving the multisize containers drayage problem

AbstractThis paper addresses the problem of vehicle routing in drayage operations, where vehicles can carry containers of different sizes. The multisize container drayage problem with time windows is modeled as a multiple matching problem and formulated as a mixed integer linear program (MILP) model. The proposed MILP model determines optimal pickup and delivery routes of vehicles and is applicable to any type of vehicles capable of simultaneously transporting any arbitrary number of 20‐ and 40‐ft containers. To solve larger sized problems, we proposed a variable neighborhood search (VNS) heuristic. Both MILP and VNS approaches have been tested on numerous test instances and their performances are reported.

Spatial analysis for an intermodal terminal to support agricultural logistics

Purpose – The purpose of this study is to address an importance of an intermodal terminal regarding container drayage trips, which have a major concern for agricultural product exporters in the Upper Great Plains. Thus, this study aims to develop a geospatial model considering travel distance and total logistics costs for determining an alternative intermodal terminal location. Design/methodology/approach – This paper develops a spatial model integrating integer linear programming to determine an intermodal facility location that minimizes total logistics costs. This research considers travel distance and total logistics costs including highway, rail and transshipment costs. Findings – The results shows that a Dilworth, Minnesota, terminal reduces vehicle miles of travel on both the highways and rail networks and decreases system-wide total logistics costs compared to the do-nothing scenario while decreasing urban congestion costs in metropolitan areas. Research limitations/implications – The major contribution of the study is that it provides an integrated tool of spatial and economic analyses to support regional decision-making. The paper will be of interest to regional planners and to those in the private business sectors including farmers and manufacturers. The future study should address demand forecasting on the containerized freight in the region. Originality/value – The novel approach of this paper is to use a link blocking constraint, considering the directions of the freight flow in a p-hub intermodal problem.

A Combinatorial Benders’ Cuts Algorithm for the Local Container Drayage Problem

This paper examines the local container drayage problem under a special operation mode in which tractors and trailers can be separated; that is, tractors can be assigned to a new task at another location while trailers with containers are waiting for packing or unpacking. Meanwhile, the strategy of sharing empty containers between different customers is also considered to improve the efficiency and lower the operation cost. The problem is formulated as a vehicle routing and scheduling problem with temporal constraints. We adopt combinatorial benders’ cuts algorithm to solve this problem. Numerical experiments are performed on a group of randomly generated instances to test the performance of the proposed algorithm.

Local container drayage problem with tractor and trailer operating in separable mode

In recent years, the Local Container Drayage Problem (LCDP) has received lots of studies in research as part of container transportation. This paper examines the LCDP under a special operation mode in which tractors and trailers can be separated, i.e., tractors can be assigned to a new task at another location while trailers are waiting for packing or unpacking. The problem is formulated as a vehicle routing and scheduling problem with temporal constraints. The resulting formulation can be used to solve small-scale problems. For large-scale problems, we develop a max–min Ant colony optimization algorithm to reduce the computation time. Numerical experiments with randomly generated instances are performed to demonstrate the performance of the algorithm.

A tabu search heuristic for the local container drayage problem under a new operation mode

This paper examines the Local Container Drayage Problem (LCDP) under an operation mode in which a tractor can be detached from its companion trailer and assigned to a new task. We have incorporated a set of temporal constraints into the classical VRP to realize this operation by utilizing the idle time available to tractors and coordinating the empty containers moving between customers. A tabu search algorithm is proposed. Some numerical experiments are conducted to assess the performance of the proposed algorithm, quantify the benefit of the new operation mode, and identify the conditions under which the mode is effective.

Container drayage problem with flexible orders and its near real-time solution strategies

This article studies a container drayage problem with flexible orders defined by using requiring and releasing attributes as a unified formulation of various order types. A determined-activities-on-vertex (DAOV) graph introduces a temporary vertex set to formulate different truck statuses. The problem is formulated as a mixed-integer nonlinear programming model based on the DAOV graph. Four strategies including a window partition based (WPB) strategy are presented and evaluated extensively to solve the problem. Results indicate that the WPB method could solve the problem effectively and efficiently. Furthermore, this method is robust considering the operating time biases compared to other algorithms.