Drayage Operations Research Articles

Adaptive large neighborhood search for drayage routing problems involving longer combination vehicles

Longer combination vehicles (LCVs)—tractor-trailer combinations with two or more trailers—can move more cargo per trip than standard trucks, potentially reducing costs and emissions. Acknowledging this, the drayage industry has recently launched initiatives to increase the adoption of LCVs, aiming to mitigate supply chain issues. This paper aims to support these kinds of initiatives by tackling drayage routing problems involving LCVs and further aspects, such as heterogeneous truck fleets, containers of any size and cargo category, and compatibility constraints based on the containers’ sizes and loads. As solution method, we propose an adaptive large neighborhood search (ALNS) heuristic, whose search operators account for aspects such as truck/container compatibility and load configurations specific to each truck. The proposed ALNS heuristic also incorporates a novel acceptance criterion that seeks to escape local optima while allowing for revisiting the current best solution and avoiding search stagnation. Through a series of benchmark tests against a state-of-the-art exact approach, we show that the proposed ALNS heuristic can consistently find high-quality solutions for a wide range of instances while, in some cases, cutting runtimes from hours or even days to a few minutes. We also show that the proposed acceptance criterion enables improved performance. Finally, we use the proposed ALNS heuristic to derive managerial insights into the savings delivered by different types of LCVs in drayage operations.

Electric truck feasibility for port drayage operations: Port Houston case study

Heavy-duty fleet electrification has the potential to reduce lifecycle operation costs, greenhouse gases, and criteria pollutant emissions. However, there are several obstacles to shifting from diesel fleets to full-electric fleets, such as range constraints and a lack of public charging infrastructure. This study developed an analytical feasibility framework for assessing the transition of an all-diesel heavy-duty fleet to a full-electric or a mixed electric and diesel fleet for drayage trucks operating at and around ports. The proposed framework devised a structured approach and multiple measures for determining the viability of heavy-duty fleet electrification, taking technological, operational, and economic aspects into account. The case study showed that, while battery electric trucks cannot replace entire diesel fleets yet, they are technologically and economically feasible for a portion of drayage operations. This practice will facilitate fleet electrification, particularly heavy-duty, by tackling major roadblocks and providing insight into the numerous unknown possibilities.

A Novel Auction-Based Truck Appointment System for Marine Terminals

Background: Increased maritime trade has led to a surge in drayage operations, causing congestion and environmental issues in port areas. Truck Appointment Systems (TASs) are commonly used to manage truck arrival rates, yet transparency and equity in slot allocation remain problematic, fostering distrust between Licensed Motor Carriers (LMCs) and Marine Terminal Operators (MTOs). Methods: This study proposes a polycentric approach to improve truck scheduling and ensure that those impacted by decisions are involved in the decision-making process. A single-round auction mechanism focused on optimizing the truck hauling process through a pricing policy that promotes sincere bidding is introduced. The proposed approach employs an optimization strategy to achieve equitable coordination in truck synchronization through means of adaptable capacity management. Results: Numerical experiments assessing scenarios of noncollaborative behavior against partial collaboration between MTOs and LMCs demonstrate the effectiveness of the proposed approach in enhancing user satisfaction and terminal conditions for a case study focused on a medium-sized terminal. Collaboration between trucking companies is shown to increase utility per monetary unit spent on slot acquisition. Conclusions: The polycentric strategy offers a solution to TAS limitations by ensuring stakeholder participation with respect to flexibility and transparency by ensuring that those impacted by decisions are involved in the decision-making process.

An Intelligently Controlled Charging Model for Battery Electric Trucks in Drayage Operations

An Intelligently Controlled Charging Model for Battery Electric Trucks in Drayage Operations

An exact algorithm for the multi-trip container drayage problem with truck platooning

Container Drayage Problem (CDP) refers to the optimization problem of routing and scheduling a set of container trucks around a container terminal. Conventionally, a driver is stuck to one container truck and allowed to perform multiple trips (multi-trip) to the terminal within their working time. The recent development of automation technologies enables semi-autonomous trucks to follow the leading human-driven truck as a platoon on the road; therefore, truck platooning can save human labor and reduce the fuel cost of following trucks through aerodynamic drag reduction. In this paper, we study a multi-trip container drayage problem with truck platooning (MT-CDP-TP), where multi-trip, truck platooning, and fuel cost reduction are simultaneously considered in a CDP. Despite the operational benefits brought by the MT-CDP-TP, the problem is challenging to solve due to its NP-hardness when formulated as a multi-trip pickup and delivery problem with load-dependent cost. We propose a Branch-and-Price-and-Cut (BPC) algorithm, with a route-based set partitioning model and tight linear relaxations, to yield the exact solutions. Valid inequalities are generated based on a graph structure, where each node represents a feasible route, and each arc stands for the conflict between two routes. Moreover, we design a tailored pulse propagation algorithm with novel pruning procedures based on the dual information from the master problem and valid inequalities to solve the pricing problem efficiently. Extensive numerical experiments are conducted for performance validation, and the computational results show that the proposed exact algorithm can solve instances with up to 100 task nodes (i.e., 50 customers) and facilitate reducing the labor cost and fuel consumption by a wide margin in container drayage operations.

Impact of Second-Tier Container Port Facilities on Drayage Operation

Background: An increasing number of container and chassis staging, “dray-off”, drop yard, and depot facilities are being established outside of North American marine container terminals. The increased use of these “second-tier” facilities implies that there must be some capacity, delivery time, service, or reliability benefit that offset the additional cost and complexity. Methods: This paper builds on the previously developed integrated drayage scheduling model to determine the impact of second-tier port facilities on drayage operation. It modifies the previously developed model by incorporating the following features: (1) trucks do not have to wait at customers’ locations during the import unloading and export loading operations; (2) drayage operations can include a drop yard (i.e., second-tier facility) for picking up or/and dropping off loaded containers outside the marine container terminal; and (3) a customer is allowed to request any of the following jobs: pick up an empty container, pick up a loaded container, drop off an empty container, and drop off a loaded container. Results: The results indicated that by moving the location of import pickup and export delivery from inside the marine container terminal to a location outside the terminal, the efficiency of drayage operation could increase. Additionally, when import pickup and export delivery take place inside the marine container terminal, the most efficient location for the chassis yard and empty container depot is inside the terminal. However, when the location of import pickup and/or export delivery are outside the terminal, the most efficient location for the chassis yard and empty container depot is also outside the terminal. Conclusions: The modeling results suggest that in addition to adding reserved capacity for marine terminals or as buffers to reconcile the preferred delivery times of importers, the second-tier facilities could also yield operational savings. However, the potential drayage efficiencies depend heavily on shorter queuing and turn time at these less-complex facilities compared to marine container terminals. Lastly, the modeling results suggest that the observed evolution of North American marine container terminals from self-contained entities into multi-tier systems is likely to continue to add additional capacities to accommodate container trade growth. This finding has important implications for regions and communities concerned over the impact of growing container ports.

Container port drayage operations and management: Past and future

Although long-haul intermodal container transportation combines multiple transportation modes including shipping, the most critical aspect of enabling door-to-door service is container port drayage operation. Container port drayage connects customers and container ports and provides an effective solution to the first/last-mile problem faced by the container logistics industry. Therefore, container port drayage has a significant impact not only on the economic advantages of the long-haul intermodal container transportation chain, but also the management, environment and social benefits of the stakeholders involved. In this paper, we comprehensively review the existing literature on container port drayage studies from different methodological angles (e.g., model development and algorithm design) and technological angles (e.g., autonomous truck and blockchain). Moreover, with the shifting of industrial focus from traditional operations and management of container port drayage towards e-commerce platforms, we identify potential issues for future research directions.

A two-stage hybrid heuristic solution for the container drayage problem with trailer reposition

Container drayage operations with tractor-trailer distinction and trailer reposition exist widely in real-world logistics yet have seldom been reported in the literature. This paper studies a container drayage problem with trailer reposition (CDPTR), in which trailers might be provided at pickup locations and kept at delivery locations. A two-stage solution framework is adopted to solve the problem. The first stage generates tractor schedules to maximize profit, and the second stage aims to ensure sufficient trailers at each trailer depot during the container drayage operation. A hybrid large neighborhood search and tabu search (LNS-TS) heuristic is developed to solve the problem. We construct 72 instances with different characteristics, for example, time window duration, initial trailer resource and distribution, and the number of requests. Results show that our solutions outperform the solutions obtained from the solver. A detailed analysis of the results also reveals several insights for container drayage operators.

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.

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.

On the integration of container availability constraints into daily drayage operations arising in France: Modelling and optimization

The paper discusses a containers’ drayage by trucks, which is motivated by a real-life application arising in the intermodal freight transportation. This problem considers not only classical assumptions of the intermodal transportation, but also introduces the availability of containers as a new concept. For this purpose, we first describe the industrial context and provide the mathematical optimization model which combines a set of known and new constraints. We then propose a solution approach based on variable neighborhood search algorithm combined with pairing and insertion heuristics, as well as with variable neighborhood descent and tabu search methods. Optimization has then been embedded into a simulation model which designs the rail/road terminal. To be more specific, this optimization model can be used to evaluate several distribution policies, which results in a set of routing decisions and can adopt the best policy in a distribution network with competing rail and road transport services. Finally, we test the proposed model on real and generated instances characterizing several scenarios to highlight the performance and efficiency of our approach.

Impact analysis of different container arrival patterns on ship scheduling in liner shipping

ABSTRACT Different transportation modes interrelate in intermodal transportation. Previous researches on intermodal transportation mainly investigate policy, network design, cargo routing or drayage operations. In order to explore the coordination between two connected transportation modes, this paper considers the connection between inland transportation and maritime container transportation. By making use of different container arrival patterns resulted from inland transportation, this paper focuses on liner ship scheduling with sailing speed optimization, as well as considering the container storage cost at each port. The studied problem is formulated as a mixed-integer nonlinear programming model, which is efficiently solved by using an outer-approximation method. Numerical results show that the optimal ship schedule varies with different container arrival patterns, and this influence is also related to the container storage cost and the bunker price.

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.

The impact of foldable containers on the cost of empty container relocation in the hinterland of seaports

This study analyses the impact of using foldable containers in terms of cost savings of truck drayage operations, of both loaded and empty containers, in the hinterland of a seaport. We model a vehicle routing problem to optimise empty container relocation. A simulated annealing algorithm is developed to solve the problem. Numerical experiments are carried out in realistic empty container relocation scenarios. We find that, under certain conditions, foldable containers can offer higher truck productivity compared with standard containers, hence resulting in substantial cost savings. This paper provides managerial insights into how foldable containers can help reduce the costs of hinterland transport.

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.

Intermodal Container Routing: Integrating Long-Haul Routing and Local Drayage Decisions

Intermodal logistics service providers decide on the routing of demand through their service network. Long-haul routing decisions determine the selected departure and arrival terminals for containers and imply corresponding drayage tasks. Traditionally, given these long-haul routes and fixed drayage tasks, drayage operations are planned in a second phase by establishing truck routes to transport containers to and from terminals by truck. In this paper, operational decisions on local drayage routing in large-volume freight regions with multiple terminals on the one hand, and intermodal long-haul routing on the other hand are merged into an integrated intermodal routing problem. Different long-haul routing decisions imply different drayage tasks to be performed and thus impact total trucking costs. The approach aims at reducing the number of road kilometres and increases bundling opportunities by maximising the long-haul capacity utilisation. In this way, it contributes to the modal shift towards intermodal transport and a more sustainable transport system. As a weekly planning horizon is used, a maximum daily active time and a minimum overnight’s rest are included for multi-day drayage routing. A large neighbourhood search heuristic is proposed to solve the integrated intermodal routing problem. This integrated planning approach provides decision support for routing customer orders throughout the intermodal network with the aim of minimising total transport costs and maximising capacity utilisation. Experiments show the added value of the integrated approach, which uses more information to make better-informed decisions and increase the capacity utilisation. The largest savings in trucking costs are obtained for clustered instances with demand characteristics closest to real-life cases. Finally, a real-life case study analyses the impact of tactical service network design decisions on the total operational costs.

Integrated scheduling of drayage and long-haul operations in synchromodal transport

We study the problem of the integrated scheduling of drayage operations and long-haul transport in synchromodality. Although different in time span and characteristics of execution, these two processes have an impact on each other and their interaction has a direct influence on the overall performance of the transport network over time. We propose a simulation based integration of a Mixed-Integer Linear Programming model for the drayage operations and a Markov Decision Process model for the long-haul transport. We analyze the interfaces between these models, outline the challenges of integrating them, and design a heuristic approach to the simulation based integration. In a series of numerical experiments, we evaluate the cost savings compared to a non-integrated approach, using various transport network configurations. We show that our approach achieves average cost savings between 4 and 24% on networks with a majority of pre-haulage freights. Furthermore, we discuss limitations of our model and experiments, and provide guidelines for further research for the integrated scheduling of drayage and long-haul operations in synchromodal transport.

Truck appointment systems considering impact to drayage truck tours

This paper proposes a novel approach for designing a Truck Appointment System (TAS) intended to serve both the maritime container terminal operator and drayage operators. The aim of the proposed TAS is to minimize the impact to both terminal and drayage operations. In regard to terminal operations, the TAS seeks to distribute the truck arrivals evenly throughout the day to avoid gate and yard congestion. In regard to drayage operations, the TAS explicitly considers the drayage truck tours and seeks to provide appointment times such that trucks do not have to deviate greatly from their original schedule. The proposed TAS is formulated as a mixed integer nonlinear program (MINLP) and the model is solved using the Lingo commercial software. Experimental results indicate that the proposed TAS reduces the drayage operation cost by 11.5% compared to a TAS where its aim is only to minimize gate queuing time by making truck arrivals uniform throughout the day.

Kink in the intermodal supply chain: interorganizational relations in the port economy

ABSTRACTThe intermodal logistics supply chain is designed to move goods from the point of production to the point of consumption as quickly and as cheaply as possible. The ability to accomplish this objective has allowed for the wholesale geographic relocation and offshoring of basic manufacturing and assembly. As a chain of linked and integrated organizations characterized by sequential interdependence, interorganizational relations play a key role in determining the level of integration and seamlessness. Yet there is one critical interorganizational link in the chain that deviates from this vision. This is the relationship between the shipping container terminal and drayage trucking operations which is better described as a form of intermodal disintegration. The weakness in this link of the supply chain is explained by the divergent industrial structures and labor market conditions, the unique nature of the transaction, and the externalization of costs to subordinate workers.