Truck Routing Problem Research Articles

Dynamic collaborative truck-drone delivery with en-route synchronization and random requests

Coordinated truck and drone delivery is gaining popularity in logistics as it can greatly reduce operation costs. However, existing studies on related operations management problems typically ignore the following important features: (i) the random appearance of requests, which require operators to dynamically respond to the requests; and (ii) the decisions of optimal launch and retrieval locations for trucks and drones instead of fixed to customer locations, which can significantly impact the overall time costs. To tackle these challenges, this study investigates the dynamic collaborative truck-drone routing problem with randomly arriving requests and synchronization on routes. We model the problem as a Markov Decision Process (MDP) and solve the MDP via a reinforcement learning (RL) approach. The proposed RL approach determines: (i) whether each request should be serviced upon arrival, (ii) which truck or drone should be assigned for the request, and (iii) the optimal en-route take-off and landing positions for paired trucks and drones. We further employ a framework of decentralized learning and centralized dispatching in RL to increase performance. Numerical experiments are conducted to assess the proposed solution approach on instances generated based on both the Solomon dataset and real-world operational data of a logistics operator in Singapore over several benchmark algorithms under various battery endurance levels of drones and distinct transportation scenarios including node-based dynamic collaborative truck-drone routing problem, dynamic non-collaborative truck and drone routing problem, and dynamic vehicle routing problem. The results show that our RL solution outperforms the benchmark algorithm in total profit by an average of 28.03 %, and our en-route takeoff and landing scenario outperforms the benchmark scenarios in total profit by an average of 8.43 % in multi-day instances. Additionally, compared to the traditional node-based landing scenario, employing our en-route takeoff and landing strategy can save 0.9 h/(drone*day) of waiting time on average.

A reinforcement learning-based multiobjective heuristic algorithm for multiple-truck routing problems with heterogeneous drones

As a result of new technological developments, drone usage has become common in last-mile logistics activities. Owing to the limited flight range of drones, drones may service customers by using trucks as hubs. Although the truck routing problem with drones (TRP-D) has been studied frequently, studies that have addressed this problem in a multiobjective manner are rare. In this study, multiobjective TRP-D is discussed. In this problem, multiple trucks are considered. Each truck is equipped with multiple heterogeneous drones. A multiobjective mixed-integer linear programming (MILP) model is proposed. Since the problem is NP-hard, a reinforcement learning (RL)-based multiobjective heuristic algorithm is proposed to obtain solutions in large-scale cases. A three-phase heuristic feasible-solution-generation algorithm is proposed. The variable neighbourhood descent (VND) algorithm with RL is proposed as a local search algorithm for the multiobjective optimization problem. The results of the proposed heuristic algorithm are compared with the Pareto optimal solutions for small-sized test problems via the augmented ε-constraint (AUGMECON) method and the CPLEX solver. The proposed algorithm is also compared with state-of-the-art multiobjective heuristic algorithms for large-scale problems. According to the results, the proposed algorithm is an efficient multiobjective heuristic algorithm for the addressed problem.

The cooperative algorithm with auxiliary objectives for the truck and trailer routing problem

<p>In this paper, a cooperative algorithm with auxiliary objectives is proposed to resolve the truck and trailer routing problem. In this proposal, each member of the population does not represent a complete solution as in almost any evolutionary algorithm. In addition, for each member, an aptitude is not possible to compute based only on its codification, because the member has only partial information of the solution. All the members of the population have partial information of the solution. Therefore, these members need to cooperate to obtain an aptitude for the entire population. This way of computing fitness is clearly a gap in the literature, and must be investigated. Moreover, the multi-objectivization approach incorporates an important feature to the proposed algorithm in order to improve its performance, i.e., the multi-objectivization approach permits to identify the best trips using the auxiliary objectives. Enough experimental results are shown that the cooperative algorithm is competitive against other current evolutionary algorithms. There no exist statistically significant difference between the cooperative algorithm and the others.</p>

An efficient and eco-friendly operation mode for container transshipments through optimizing the inter-terminal truck routing problem

To enhance efficiency and reduce carbon emissions of waterway-waterway transshipments for a multi-terminal port group, a crucial strategic planning issue lies in determining whether a centralized or distributed mode of feeder vessel service is more efficient and eco-friendly. This paper proposes a two-stage integer-optimized model to optimize intra- and inter-terminal operations and determine the most effective mode of operation for feeder vessel services. Our model integrates the multi-terminal berth allocation problem and inter-terminal transportation (ITT), considering different cases of transshipment flows. To address this optimization problem, we develop a heuristic approach based on genetic and adaptive large neighborhood search algorithms, which is ideal method for large-scale scenarios. In our case study, the proposed optimization model and heuristic methods were adopted to determine the best operation mode for North Operation Area in Shanghai Yangshan Deep-Water Port (namely Yangshan Phase V). The results indicate that Yangshan Phase V should operate as a feeder vessel service terminal, providing primary feeder vessel services and complementary liner vessel services. This development plan not only minimizes container transshipment delays and overall ITT costs, but also helps reduce approximately 707.46 tons of annual carbon emissions caused by ITT at Yangshan Deep-Water Port.

Solving the Inter-Terminal Truck Routing Problem for Delay Minimization Using Simulated Annealing with Normalized Exploration Rate

The growth in containerized shipping has led to the expansion of seaports, resulting in the emergence of multiple terminals. While multi-terminal systems increase port capacity, they also pose significant challenges to container transportation, particularly in inter-terminal movements. Consequently, the transportation delay of containers in inter-terminal operations demands crucial attention, as it can adversely affect the efficiency and service levels of seaports. To minimize the total transportation delays of the inter-terminal truck routing problem (ITTRP), we introduce simulated annealing with normalized acceptance rate (SANE). SANE improves the exploration capability of simulated annealing (SA) by dynamic rescaling of the transportation delay objective to modify the acceptance probability. To validate the quality of solutions provided by SANE, we have developed a mathematical model that provides a set of linear formulations for ITTRP constraints, avoiding the known set-partitioning alternative. Experimental results showed that for small-scale ITTRP instances, SANE achieved a solution close to the optimal. In larger instances with 100–120 orders, SANE found feasible suboptimal solutions within 15–21 seconds, which is unattainable using the exact solver. Further comparison with baselines indicates that SANE provides considerable improvements compared to both SA and Tabu search in terms of the objective value.

Environmental aspects in supplier networks-a bi-objective just-in-time truck routing problem

Freight transportation, including just-in-time (JIT) supplier networks, accounts for a substantial part of the global carbon dioxide (CO) emissions. The JIT truck routing problem (TRP-JIT) presented in the recent literature consists of several suppliers serving a single original equipment manufacturer (OEM). A logistics provider organises the milk-run routes. The shipments are available after their release dates at the suppliers and should be delivered on their due dates at the OEM with minimal total earliness-tardiness penalties (first objective). Unlike previous research on the TRP-JIT, we focus on its environmental impact: (1) We include the weight-distance (second objective), depending on the truck's curb weight, the load, and the transportation distance. (2) We adapt a state-of-the-art large neighbourhood search (LNS) from the literature considering both objectives. (3) The LNS is embedded in bi-criterial frameworks, i.e. ε-constraint and weighted sum methods. Thereby, we estimate Pareto frontiers with at least 60 solutions in less than 25 min for instances with 99 shipments. From a managerial perspective, increasing the difference between the release and due dates for a better JIT performance may worsen the environmental impact. Lighter trucks can reduce the environmental costs without affecting the JIT performance, whereas a smaller fleet negatively affects both objectives.

Time Window Oriented IoT Vehicle Pathway Study for the Dynamically Changing Needs of E-Commerce Customers

The main dynamic truck routing problem also presents a significant difficulty in the logistics sector, which is an unavoidable development trend of the contemporary technological changing society. A dynamic vehicle routing problem with time window model is suggested by the study in order to establish an effective and low-energy dynamic response method. The fundamental concept is to disrupt the conventional strategy of static dynamic consumers responding in time slots by dividing the dynamic time window into a static time window with several time slice intervals. The study makes use of cutting-edge ideas including dynamic attitude, before-and-after time slicing, and continuous optimisation while proposing a new method for model solution to optimise dynamic vehicle route issues effectively and affordably. The study employs the Solomon optimisation dataset and runs simulation studies on the Java platform to confirm its efficacy. The experimental findings demonstrated that the optimisation technique employed in the study reduced the cost of travelling by 83.8 miles while also considerably increasing the average vehicle utilisation by 3.6%. Because driving distance cost and vehicle number cost are typically positively connected with dynamic attitude, the study employs solutions that can increase dynamic response efficiency and save money. As a result, their robustness is higher.

A Variable Neighborhood Search Method with a Tabu List and Local Search for Optimizing Routing in Trucks in Maritime Ports

Logistics problems represent an important class of real-world problems where even small improvements in solution quality can lead to significant decreases in operational costs. However, these problems are usually NP-hard; thus, they are mostly solved using metaheuristic methods. To improve their performance, there is substantial research on crafting new and refined metaheuristics to derive superior solutions. This paper considers a truck routing problem within a naval port, where the objective is to minimize the total distance traveled by all the vehicles to distribute a given set of containers. Due to the large volume of goods that are being transferred through ports, it is imperative to improve the operation times at such ports to improve the throughput. To achieve this goal, a novel variable neighborhood search method that integrates a tabu list, an iterative local search procedure, and parallelization of neighborhood generation is proposed and evaluated. The experimental results demonstrate that the proposed method achieves similar results to the state of the art, but in a smaller amount of time.

A granular iterated local search for the asymmetric single truck and trailer routing problem with satellite depots at DHL Group

AbstractTo plan the postal deliveries of our industry partner DHL Group (DHL), the single truck and trailer routing problem with satellite depots (STTRPSD) is solved to optimize mail carriers routes. In this application context, instances feature a high number of customers and satellites, and they are based on real street networks. This motivates the study of the asymmetric STTRPSD (ASTTRPSD). The heuristic solution methods proposed in the literature for the STTRPSD can either solve only the symmetric problem variant, or it is unclear whether they can also be used to solve the ASTTRPSD. We introduce an iterated local search, called ILS‐ASTTRPSD, which generates different first‐level tours in the perturbation phase, and improves the second‐level tours in the local search phase. To speed up the search, granular neighborhoods are used. The computational results on instances from the literature prove the capability of ILS‐ASTTRPSD to return high‐quality solutions. On DHL instances, ILS‐ASTTRPSD significantly decreases total travel times of the mail carriers and returns solutions with a different structure compared to the ones provided by DHL. Based on these differences, we give recommendations on how DHL could design more efficient mail carrier practices. Dedicated computational experiments reveal that considering parking and loading times when solving the ASTTRPSD leads to lower travel times, and that ignoring parking times is more counterproductive than ignoring loading times. Moreover, we assess the robustness of our solutions under parking time fluctuations. Finally, we derive properties of instances for which optimal solutions contain multiple second‐level tours rooted at the same parking spot and for which the optimal solutions of the ASTTRPSD correspond to the ones of a pure traveling salesman problem.

Reinforcement Learning Based Truck-and-Drone Coordinated Delivery

Coronavirus disease 2019 has brought a great challenge to the supply of daily necessities and medical items for home-quarantined people. Considering the unmanned operation, agility and use of clean energy of drones, we propose a novel truck-and-drone coordinated delivery system that does not require direct human contact during the delivery process. All final deliveries are completed by the drone while the truck acts as a movable charging station and a carrier, so that the contagion risks are reduced. Moreover, we spilt the whole delivery problem into the customer clustering problem and the routing problems of both the truck and the drone. An encoder-decoder framework combined with reinforcement learning is created to solve the routing problems without handcrafted designed heuristics. We design the different problem contexts specific to the truck routing problem and the drone routing problem. The experimental results show the proposed approach has good generality and can consequently be applied to problems of different scales with high time efficiency.

A hybrid large-neighborhood search for a truck and drone delivery system with stochastic customer existence and time windows

In recent years, e-commerce has become increasingly popular, and consumers expect quick and affordable delivery, placing additional pressure on city logistics activities. An innovative approach is proposed to coordinate ground vehicles and drones for delivery services, which has gained tremendous attention from academia and logistic service providers. This paper introduces a variant of this problem: the two-echelon truck and drone routing problem, characterized by stochastic demand existence and soft time windows. A Markov chain is used to model the problem, and a linear mathematical model is presented. This work employs a hybrid large-neighborhood search approach. Numerous computational experiments are conducted to evaluate the performance of the proposed solution method, and the results demonstrate its efficacy.

A blockchain‐based framework to optimize shipping container flows in the hinterland

AbstractWe address two interrelated issues affecting the hinterland portion of the maritime container supply chain: reducing the movement of empty containers and reducing empty trips by trucks carrying these containers. In this paper, we show that empty container flow optimization can be implemented via a blockchain based on the proof‐of‐useful‐work concept where the proof of work requires the solution of an ‐hard optimization problem whose solution benefits the blockchain participants. Accordingly, we propose that anonymous miners compete to solve the container truck routing problem, which seeks to find the most efficient routes for trucks. We show that this problem is ‐hard. Miners must also solve the problem of optimally matching consignees and shippers, which will reduce transportation and storage costs for empty containers. In essence, the proposed framework turns blockchain into a massive optimization engine that directly benefits the hinterland container supply chain ecosystem.

Trailer allocation and truck routing using bipartite graph assignment and deep reinforcement learning

AbstractTrailer allocation and truck routing are critical components of truck transportation management. However, in real‐world applications, inter‐influence between selecting the best trailers and trucks, strict fulfillment of Pickup or Delivery (PD) orders, and the size of the fleet are some of the challenges that need to be dealt with in a large truck company. In addition, trailer allocation and truck routing problems are considered to be NP‐hard combinatorial optimization (CO) problems. Therefore, we use deep reinforcement learning (DRL), which has the capability of solving routing problems with a single set of hyperparameters. This is significant progress toward finding strong heuristics for a special case of the trailer allocation to customers and truck routing problem presented in this article. Given a set of trailers, trucks, customers, and orders we propose a novel two‐phase framework based on Bipartite Graph Assignment (BGA) and attention‐based DRL to minimize the total traveling distance traveled from trucks to trailers and then to customers. The BGA heuristic finds the minimum traveling distance from the trailers to the customers based on the edge information and the encoder‐decoder helps DRL to get useful node and graph feature representations and trains the model to find the proper solutions for the trailer allocation and truck routing problem. Our experiments on three different problem sizes showcase the effectiveness of ARTT‐DRL. The results indicate that ARTT‐DRL produces desirable outcomes and has strong generalization capabilities.

The Profitable Single Truck and Trailer Routing Problem with Time Windows: Formulation, valid inequalities and branch-and-cut algorithms

The Profitable Single Truck and Trailer Routing Problem with Time Windows (PSTTRPTW) is defined by a fleet of trucks and trailers and a set of customers that reward a profit if their supply is collected within a time window. Trailers can be attached to trucks in order to raise capacity, at the expense of increasing travel time and cost. Trailers can be decoupled from trucks at satellite depots, after which the truck performs subtours, visiting customers inaccessible by trailers. A route may include any number of subtours, as long as the vehicle’s capacity is respected. The goal is to find a route for a single choice of truck and trailer maximizing the difference between the collected profit and the route cost. We introduce an Integer Programming formulation, preprocessing tests, valid inequalities and investigate two PSTTRPTW Branch-and-cut (BC) algorithms, one of them based on the basic formulation and the other, on the strengthened model. Our numerical results show that these preprocessing tests reduced the number of variables by about 30%. In addition, the Linear Programming relaxations provided by the strongest model are, on average, 25% sharper than those given by the basic model. As a result, the reinforced BC algorithm has the edge: it is faster, solves all instances solved by its competitor and 13 additional ones, and provides optimality gaps 14% smaller when optimality is not certified.

Truck and rotary-wing drone routing problem considering flight-level selection

Last-mile logistics is one of the most promising areas for rotary-wing drone (RWD) applications. In the literature, routing variants that use drones in collaboration with trucks assume that both drones and trucks move along arcs in two-dimensional networks. There is a need for methodological innovations to cater to more practical and general scenarios involving flight-level decisions of RWDs in the three-dimensional network. In this study, flight level is defined as the specified height at which an RWD is allowed to fly. We introduce the truck and RWD routing problem considering flight-level selection and time windows (TDRP-FT). The TDRP-FT is characterized by RWD flight-level selection, time windows, direct delivery, multiple trucks, and multiple RWDs carried by each truck. We develop a mixed-integer linear programming model and propose a hybrid algorithm based on a greedy randomized adaptive search procedure and an adaptive large neighborhood search. We experimentally evaluate the effectiveness of the TDRP-FT model and the applicability of the hybrid algorithm to small-, medium- and large-scale instances. The computational experiment results indicate that the TDRP-FT model can be used to determine how flight levels of RWDs should be selected.

A Radial Hybrid Estimation of Distribution Algorithm for the Truck and Trailer Routing Problem

The truck and trailer routing problem (TTRP) has been widely studied under different approaches. This is due to its practical characteristic that makes its research interesting. The TTRP continues to be attractive to developing new evolutionary algorithms. This research details a new estimation of the distribution algorithm coupled with a radial probability function from hydrogen. Continuous values are used in the solution representation, and every value indicates, in a hydrogen atom, the distance between the electron and the core. The key point is to exploit the radial probability distribution to construct offspring and to tackle the drawbacks of the estimation of distribution algorithms. Various instances and numerical experiments are presented to illustrate and validate this novel research. Based on the performance of the proposed scheme, we can make the conclusion that incorporating radial probability distributions helps to improve the estimation of distribution algorithms.

The road train optimization problem with load assignment

This paper studies the road train optimization problem with load assignments (RTOP–LA). The RTOP–LA deals with assigning customers’ demands to trailers delivered via regular trucks or road trains and determining the routing of these trucks through final customers. Road trains leave the origin terminal to reach intermediate ones, where the trailers can later be dismantled and sent to customers by regular trucks. We formulate the problem to minimize the total cost. A commercial solver is used to solve small-size instances of the problem, and we develop a multi-start iterated local search (MS-ILS) algorithm to obtain high-quality solutions. The results of our experiments show that MS-ILS provides optimal solutions for most instances. For small size instances MS-ILS outperforms the commercial solver, but its performance becomes more evident when the number of customers increases. Moreover, MS-ILS provides excellent solutions for larger instances in short computation times. Finally, a slightly adapted version of our algorithm has been proved efficient to solve the single truck and trailer routing problem. Compared to state-of-the-art algorithms on a set of 32 instances, our adapted algorithm obtained five new best known solutions.

A new experimental technique for the trailer and truck routing problem

A new experimental technique for the trailer and truck routing problem

A new experimental technique for the trailer and truck routing problem

A new experimental technique for the trailer and truck routing problem

Rich arc routing problem in city logistics: Models and solution algorithms using a fluid queue-based time-dependent travel time representation

City logistics, as an essential component of the city operation system, aims at managing the complex flow of goods and services from providers to customers efficiently. Delays associated with peak-period traffic congestion exists in both large and small metropolitan areas. As many of the service tasks in city logistics are needed to be performed during peak hours, operators of urban management movement should consider reducing the total trip time and delay when designing service plans. Equally important, the congestion impact of service vehicles to other road users should also be considered. In this paper, we focus on formulating and solving rich arc routing problems (RARPs) in city logistics with a congested urban environment. We highlight the needs of embedding a structurally parsimonious time-dependent travel time model in RARP for producing high-quality and practically useful solutions. A fluid queue model based analytical approach is presented for link travel time calibration in the form of polynomial arrival rate functions. Accordingly, system-wide (societal) impact of vehicles routing is analytically derived and incorporated into the RARP models which enables traffic managers to systematically consider operation costs and societal impacts when designing routing policies in real-life city logistics applications. Additionally, we develop two new representation schemes for time-dependent travel time modeling in RARPs, including a discretized time-expanded representation scheme and a nonlinear polynomial representation scheme. Three modeling approaches for RARPs are proposed, with different perspectives of capturing time-dependent travel time and formulating problem-specific constraints. With a real-life sprinkler truck routing problem as the representative example of RARP, we develop two efficient exact solution algorithms, including a Lagrangian relaxation-based method and a branch-and-price based method. The latter one is embedded with an enhanced parallel branch-and-bound algorithm. Extensive numerical experiments are conducted based on real-world networks and traffic flow data to demonstrate the effectiveness of the proposed methods.