Trailer Routing Problem Research Articles

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>

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.

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.

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 two‐phase heuristic for a problem of food distribution with compartmentalized trucks and trailers

AbstractThis paper presents a new formulation for the routing problem in which the available fleet consists of trucks and trailers divided into compartments. Solving the model for large instances is computationally expensive. Therefore, we introduce and implemented a two‐phase heuristic algorithm. In the first phase, an initial solution is generated through a constructive heuristic algorithm based on concepts from the classic Clarke–Wright algorithm. In the second phase, the initial solution is improved by an iterated tabu search metaheuristic. Our algorithm was tested on 21 instances that were converted from the classic truck and trailer routing problem. The results of our computational study prove the effectiveness of our proposal; the algorithm always finds a feasible solution, which in small‐sized problems it is proven to be of good quality. In addition, the algorithm outperforms previous approaches for some truck and trailer routing problem instances. Furthermore, an application of the proposed model and heuristic is demonstrated in the field of agricultural logistics by comparing the obtained results.

A Hybrid Metaheuristic for Single Truck and Trailer Routing Problems

In this paper, we propose a general solution approach for a broad class of vehicle routing problems that all use a single vehicle, composed of a truck and a detachable trailer, to serve a set of customers with known demand and accessibility constraints. A more general problem, called the extended single truck and trailer routing problem (XSTTRP), is used as a common baseline to describe and model this class of problems. In particular, the XSTTRP contains, all together, a variety of vertex types previously considered only separately: truck customers, vehicle customers with and without parking facilities, and parking-only locations. To solve the XSTTRP, we developed a fast and effective hybrid metaheuristic, consisting of an iterative core part, in which routes that define high-quality solutions are stored in a pool. Eventually, a set-partitioning-based postoptimization selects the best combination of routes that forms a feasible solution from the pool. The algorithm is tested on extensively studied problems from the literature, such as the multiple depot vehicle routing problem, the location routing problem, the single truck and trailer routing problem with satellite depots, and the single truck and trailer routing problem. Finally, computational results and a thorough analysis of the main algorithm’s components on newly designed XSTTRP instances are provided. The obtained results show that the proposed hybrid metaheuristic is highly competitive with previous approaches designed to solve specific specialized problems, both in terms of computing time and solution quality.

Truck and Trailer Routing Problem Solving by a Backtracking Search Algorithm

AbstractTruck and trailer routing problem (TTRP) is one of the most frequently encountered problem in city distribution, particularly in populated and intensive downtown. This paper addresses this problem and designs a novel backtracking search algorithm (BSA) based meta-heuristics to solve it. The initial population is created by T-sweep heuristic and then based on the framework of backtracking search algorithm, four types of route improvement strategies are used as building blocks to improve the solutions of BSA in the process of mutation and crossover. The computational experiments and results indicate that the proposed BSA algorithm can provide an effective approach to generate high-quality solutions within the satisfactory computational time.

Parallel computation framework for optimizing trailer routes in bulk transportation

We consider a rich tanker trailer routing problem with stochastic transit times for chemicals and liquid bulk orders. A typical route of the tanker trailer comprises of sourcing a cleaned and prepped trailer from a pre-wash location, pickup and delivery of chemical orders, cleaning the tanker trailer at a post-wash location after order delivery and prepping for the next order. Unlike traditional vehicle routing problems, the chemical interaction properties of these orders must be accounted for to prevent risk of contamination which could impose complex product-sequencing constraints. For each chemical order, we maintain a list of restricted and approved prior orders, and a route is considered to be feasible if it complies with the prior order compatibility relationships. We present a parallel computation framework that envelops column generation technique for large-scale route evaluations to determine the optimal trailer-order-wash combinations while meeting the chemical compatibility constraints. We perform several experiments to demonstrate the efficacy of our proposed method. Experimental results show that the proposed parallel computation yields a significant improvement in the run time performance. Additionally, we perform sensitivity analysis to show the impact of wash capacity on order coverage.

Dynamic truck and trailer routing problem for last mile distribution in disaster response

PurposeThe purpose of this paper is to investigate the application of the dynamic vehicle routing problem for last mile distribution during disaster response. The authors explore a model that involves limited heterogeneous vehicles, multiple trips, locations with different accessibilities, uncertain demands, and anticipating new locations that are expected to build responsive last mile distribution systems.Design/methodology/approachThe modified simulated annealing algorithm with variable neighborhood search for local search is used to solve the last mile distribution model based on the criterion of total travel time. A dynamic simulator that accommodates new requests from demand nodes and a sample average estimator was added to the framework to deal with the stochastic and dynamicity of the problem.FindingsThis study illustrates some practical complexities in last mile distribution during disaster response and shows the benefits of flexible vehicle routing by considering stochastic and dynamic situations.Research limitations/implicationsThis study only focuses day-to-day distribution on road/land transportation for distribution, and additional transportation modes need to be considered further.Practical implicationsThe proposed model offers operational insights for government disaster agencies by highlighting the dynamic model concept for supporting relief distribution decisions. The result suggests that different characteristics and complexities of affected areas might require different distribution strategies.Originality/valueThis study modifies the concept of the truck and trailer routing problem to model locations with different accessibilities while anticipating the information gap for demand size and locations. The results show the importance of flexible distribution systems during a disaster for minimizing the disaster risks.

A self-adaptive bat algorithm for the truck and trailer routing problem

PurposeThe purpose of this paper is to provide an effective solution method for the truck and trailer routing problem (TTRP) which is one of the important NP-hard combinatorial optimization problems owing to its multiple real-world applications. It is a generalization of the famous vehicle routing problem (VRP), involving a group of geographically scattered customers served by the vehicle fleet including trucks and trailers.Design/methodology/approachThe meta-heuristic solution approach based on bat algorithm (BA) in which a local search procedure performed by five different neighborhood structures is developed. Moreover, a self-adaptive (SA) tuning strategy to preserve the swarm diversity is implemented. The effectiveness of the proposed SA-BA is investigated by an experiment conducted on 21 benchmark problems that are well known in the literature.FindingsComputational results indicate that the proposed SA-BA algorithm is computationally efficient through comparison with other existing algorithms found from the literature according to solution quality. As for the actual computational time, the SA-BA algorithm outperforms others. However, the scaled computational time of the SA-BA algorithm underperforms the other algorithms.Originality/valueIn this work the authors show that the proposed SA-BA is effective as a method for the TTRP problem. To the authors’ knowledge, the BA has not been applied previously, as in this work, to solve the TTRP problem.

Branch-and-price and adaptive large neighborhood search for the truck and trailer routing problem with time windows

Motivated by a situation faced by infrastructure service providers operating in urban areas with accessibility restrictions, we study the truck and trailer routing problem with time windows (TTRPTW). In this problem the vehicle fleet consists of trucks and trailers which may be decoupled. A set of customers has to be served and some of the customers can only be accessed by the truck without the trailer. This gives rise to the planning of truck-and-trailer routes containing truck-only subroutes, in addition to truck-only routes and truck-and-trailer routes without subroutes. We propose a branch-and-price algorithm for the TTRPTW, using problem specific enhancements in the pricing scheme and alternative lower bound computations. We also tailor an adaptive large neighborhood search algorithm to the TTRPTW in order to obtain good initial columns. When compared to existing metaheuristic algorithms we obtain highly competitive results. Some instances with up to 100 customers are solved to optimality with the proposed branch-and-price algorithm.

The two-echelon time-constrained vehicle routing problem in linehaul-delivery systems considering carbon dioxide emissions

Multi-echelon distribution strategy is primarily to alleviate the environmental (e.g., energy consumption and emissions) consequence of logistics operations. Differing from the long-term strategic problems (e.g., the two-echelon vehicle routing problem (2E-VRP), the two-echelon location routing problem (2E-LRP) and the truck and trailer routing problem (TTRP)) that make location decisions in depots or satellites, the paper introduces a short-term tactical problem named the two-echelon time-constrained vehicle routing problem in linehaul-delivery systems (2E-TVRP) considering carbon dioxide (CO2) emissions. The linehaul level and the delivery level are linked through city distribution centers (CDCs). The 2E-TVRP, which takes CO2 emissions per ton-kilometer as the objective, has inter-CDC linehaul on the 1st level and delivery from CDCs to satellites on the 2nd level. The Clarke and Wright savings heuristic algorithm (CW) improved by a local search phase is put forward. The case study shows the applicability of the model to real-life problems. The results suggest that the vehicle scheduling provided by the 2E-TVRP is promising to reduce the CO2 emissions per ton-kilometer of the linehaul-delivery system. Adjusting the central depot location or developing the loaded-semitrailer demand among O-D pairs to eliminate empty-running of tractors will contribute to reduce the CO2 emission factor.

The two-echelon time-constrained vehicle routing problem in linehaul-delivery systems

Most of the studies address issues relating to the delivery from satellites to customers, which is throughout the end part of the linehaul-delivery system. Differing from the long-term strategic problems including the two-echelon vehicle routing problem (2E-VRP), the two-echelon location routing problem (2E-LRP) and the truck and trailer routing problem (TTRP) which make location decisions in depots or satellites, the paper introduces a short-term tactical problem named the two-echelon time-constrained vehicle routing problem in linehaul-delivery systems (2E-TVRP) that does not involve location decisions. The linehaul level and the delivery level are linked through city distribution centers (CDCs) located on the outskirts of cities. The 2E-TVRP has inter-CDC linehaul on the first level and urban delivery from CDCs to satellites on the second level. Vehicle routes on different levels are interacted by time constraints. A mixed integer nonlinear programming model for the 2E-TVRP is put forward, and a mixed integer linear programming model is used as the benchmark model. The Clarke and Wright savings heuristic algorithm (CW) improved by a local search phase is adopted. The 2E-TVRP formulations and the heuristic algorithm are tested by using 140 randomly-generated instances with up to 10 CDCs and 500 satellites. The computational results indicate that the heuristic can effectively solve various instances of the 2E-TVRP.

A Branch-and-Cut Algorithm for the Single Truck and Trailer Routing Problem with Satellite Depots

In the single truck and trailer routing problem with satellite depots (STTRPSD), a truck with a detachable trailer based at a main depot must serve the demand of a set of customers accessible only by truck. Therefore, before serving the customers, it is necessary to detach the trailer in an appropriate parking place (called either a satellite depot or a trailer point) and transfer goods between the truck and the trailer. This problem has applications in milk collection for farms that cannot be reached using large vehicles. In this work we present an integer programming formulation of the STTRPSD. This formulation is tightened with several families of valid inequalities for which we have developed different (exact and heuristic) separation procedures. Using these elements, we have implemented a branch-and-cut algorithm for the solution of the STTRPSD. A computational experiment with published instances shows that the proposed branch-and-cut algorithm consistently solves problems with up to 50 customers and 10 satellite depots, and it has also been able to solve instances with up to 20 satellite depots and 100 clustered customers.

The Combination Truck Routing Problem: A Survey

The combination-vehicle attributes of vehicle routing problems are additional characteristics that aim to consider more effectively the specificities of real logistics applications. Because various combination truck situations exist, the combination truck routing problem (CTRP) is supported by well-developed literature, especially with respect to the truck and trailer routing problem (TTRP), the rollon-rolloff vehicle routing problem (RRVRP), the tractor and semitrailer routing problem (TSRP), and a variety of heuristics. This article first reviews the three primary forms of the CTRP, providing a survey of problem foundations and heuristics for the TTRP, the RRVRP and the TSRP. Next, this report takes a closer look at comparing the three forms of the CTRP. The TTRP aims to efficiently apply trailers that can attach/detach trucks easily to serve less-than-truckload shipping, and the RRVRP and the TSRP aim to attain high use rates for tractors in different full truckload shipping practices. The three forms of the CTRP share a number of common features. In particular, most of the formulations and heuristic strategies developed for specific problems share many similar characteristics. The CTRP is an extremely rich and promising operations research field. More general formulations and more general-purpose solvers are necessary to address practical combination truck routing applications efficiently and in a timely manner.

A relax-and-repair heuristic for the Swap-Body Vehicle Routing Problem

In this paper we address the Swap-Body Vehicle Routing Problem (SB-VRP), a variant of the truck and trailer routing problem. It was introduced in the VeRoLog Challenge 2014. We develop a solution approach that we coin Relax-and-Repair. It consists in solving a relaxed version of the SB-VRP and deriving a feasible solution by repairing the relaxed one. We embed this approach within a population-based heuristic. During computation we store all feasible routes in order to derive better solutions by solving a set-partitioning problem. In order to take advantages of nowadays multi-core machines, our algorithm is designed as a collaborative parallel population-based heuristic. Experimental results show that our relax-and-repair algorithm is very competitive and point the impact of each phase on the quality of the obtained solutions. The advantage of our approach is that it can be adapted to solve complex industrial routing problems.

Memetic Heuristic Approach for Solving Truck and Trailer Routing Problems with Stochastic Demands and Time Windows

Manufacturers and service providers often encounter stochastic demand scenarios. Researchers have, thus far, considered that the deterministic truck and trailer routing problem (TTRP) cannot address the prevailing demand uncertainties and/or other complexities. The purpose of this study is to expand the deterministic TTRP model by introducing stochastic demand and time window constraints to bring the TTRP model closer to reality and solve the model in a reasonable timeframe by administering the memetic algorithm (MA). This paper presents a model that can be applied in stochastic demand conditions. To employ the MA, various crossovers, mutations and local search approaches were applied. First, two experimental tests were carried out to show the validity and consistency of the MA for solving stochastic TTRPs. The results can be compared with the VRPSDTW (vehicle routing problem with stochastic demands (VRSPD) with time windows) solution obtained using large neighbourhood search (LNS) of earlier research. The average results from Tests 1 and 2 achieved by MA are 514.927 and 516.451. However, the average result obtained by LNS is 516.877. Therefore, the MA can generate results. Thus, MA is found to be suitable for solving truck and trailer routing problem(s) under stochastic demand with a time window (TTRPSDTW). Moreover, 54 benchmark instances were modified for this case and the initial feasible solutions were generated for this purpose. The solutions were significantly improved by the MA. Also, the problems were tested using sensitivity analysis to understand the effects of the parameters and to make a comparison between the best results obtained by MA and sensitivity analysis. Since the differences between the results are small, the MA was found to be appropriate and better for solving TTRPSDTW. The paper also gives some suggestions for further research.

Metaheuristic Approaches for Solving Truck and Trailer Routing Problems with Stochastic Demands: A Case Study in Dairy Industry

Manufacturers and service providers often encounter stochastic demand scenarios. Researchers have, thus far, considered the deterministic truck and trailer routing problem (TTRP) that cannot address ubiquitous demand uncertainties and/or other complexities. The purpose of this study is to model the TTRP with stochastic demand (TTRPSD) constraints to bring the TTRP model closer to a reality. The model is solved in a reasonable timeframe using data from a large dairy service by administering the multipoint simulated annealing (M-SA), memetic algorithm (MA), and tabu search (TS). A sizeable number of customers whose demands follow the Poisson probability distribution are considered to model and solve the problem. To make the solutions relevant, first, 21 special TTRPSD benchmark instances are modified for this case and then these benchmarks are used in order to increase the validity and efficiency of the aforementioned algorithms and to show the consistency of the results. Also, the solutions have been tested using sensitivity analysis to understand the effects of the parameters and to make a comparison between the best results obtained by three algorithms and sensitivity analysis. Since the differences between the results are insignificant, the algorithms are found to be appropriate and relevant for solving real-world TTRPSD problem.

Solving the Truck and Trailer Routing Problem with Fuzzy Constraints

AbstractThe Truck and Trailer Routing Problem consists of a heterogeneous fleet composed of trucks and trailers to serve a set of customers. This problem has been solved previously considering accurate data available. But in a real-world the available knowledge about some data and parameters involves a vague nature. In this study, we propose the application of the Soft Computing to model and solve the TTRP when capacity constraints are imprecise. Numerical examples are presented to illustrate the proposed method.