Backhaul Customers Research Articles

An assignment-based decomposition approach for the vehicle routing problem with backhauls

In the context of the Vehicle Routing Problem with Backhauls, which involves delivering to linehaul and picking up from backhaul customers, we propose a novel mathematical model that can decompose the main problem into three sub-problems: two Open Vehicle Routing Problems and one Assignment Problem. In our proposed model, Open Vehicle Routing Problems optimize routes for homogeneous vehicles serving linehaul/backhaul customers, while the Assignment Problem matches linehaul and backhaul routes. We utilize Lagrangian decomposition approach and solve subproblems in parallel and sequential layouts. We measure the performance of the foregoing arrangements (in terms of solution quality and computational efficiency) by testing our model on two benchmark datasets, proposed by Goetschalckx and Jacobs-Blecha (1989) and Toth and Vigo (1997) and are known as GJ and TV datasets in the extant literature, respectively. Our model matches best known solutions in 35 % and 33 %, with most within 2 % deviation, for GJ and TV instances, respectively. We also showcase our model on a real-world transportation network containing 100, 250, and 500 customers and geographically located in Lansing, Michigan. To reduce the computational burden of solving the Vehicle Routing Problem with Backhauls on the Lansing dataset, we present a cluster first-route second algorithm and then analyze the impact of vehicle capacity on the solution quality of our proposed algorithm.

Deep Reinforcement Learning for Solving Vehicle Routing Problems With Backhauls.

The vehicle routing problem with backhauls (VRPBs) is a challenging problem commonly studied in computer science and operations research. Featured by linehaul (or delivery) and backhaul (or pickup) customers, the VRPB has broad applications in real-world logistics. In this article, we propose a neural heuristic based on deep reinforcement learning (DRL) to solve the traditional and improved VRPB variants, with an encoder-decoder structured policy network trained to sequentially construct the routes for vehicles. Specifically, we first describe the VRPB based on a graph and cast the solution construction as a Markov decision process (MDP). Then, to identify the relationship among the nodes (i.e., linehaul and backhaul customers, and the depot), we design a two-stage attention-based encoder, including a self-attention and a heterogeneous attention for each stage, which could yield more informative representations of the nodes so as to deliver high-quality solutions. The evaluation on the two VRPB variants reveals that, our neural heuristic performs favorably against both the conventional and neural heuristic baselines on randomly generated instances and benchmark instances. Moreover, the trained policy network exhibits a desirable capability of generalization to various problem sizes and distributions.

Energy-Efficient Dispatching of Battery Electric Truck Fleets with Backhauls and Time Windows

<div>The adoption of battery electric trucks (BETs) as a replacement for diesel trucks has potential to significantly reduce greenhouse gas emissions from the freight transportation sector. However, BETs have shorter driving range and lower payload capacity, which need to be taken into account when dispatching them. This article addresses the energy-efficient dispatching of BET fleets, considering backhauls and time windows. To optimize vehicle utilization, customers are categorized into two groups: linehaul customers requiring deliveries, where the deliveries need to be made following the last-in-first-out principle, and backhaul customers requiring pickups. The objective is to determine a set of energy-efficient routes that integrate both linehaul and backhaul customers while considering factors such as limited driving range, payload capacity of BETs, and the possibility of en route recharging. We formulate the problem as a mixed-integer linear programming model and propose an algorithm that combines adaptive large neighborhood search and simulated annealing metaheuristics to solve it. The effectiveness of the proposed strategy is demonstrated through extensive experiments using a real-world case study from a logistics company in Southern California. The results indicate that the proposed strategy leads to a significant reduction in total energy consumption compared to the baseline strategy, ranging from 11% to 40%, while maintaining reasonable computational time. In addition, the proposed strategy provides solutions that are better than or comparable with those obtained by other metaheuristics. This research contributes to the development of sustainable transportation solutions in the freight sector by providing a novel approach for dispatching BET fleets. The findings emphasize the potential of deploying BETs to achieve energy savings and advance the goal of green logistics.</div>

A diversity-enhanced memetic algorithm for solving electric vehicle routing problems with time windows and mixed backhauls

The electric vehicle routing problem (EVRP) has been studied increasingly because of environmental concerns. However, existing studies on the EVRP mainly focus on time windows and sole linehaul customers, which might not be practical as backhaul customers are also ubiquitous in reality. In this study, we investigate an EVRP with time windows and mixed backhauls (EVRPTWMB), where both linehaul and backhaul customers exist and can be served in any order. To address this challenging problem, we propose a diversity-enhanced memetic algorithm (DEMA) that integrates three types of novel operators, including genetic operators based on adaptive selection mechanism, a selection operator based on similarity degree, and modification operators for tabu search. Experimental results on 54 new instances and two classical benchmarks show that the proposed DEMA can effectively solve the EVRPTWMB as well as other related problems. Furthermore, a case study on a realistic instance with up to 200 customers and 40 charging stations in China also confirms the desirable performance of the DEMA.

Inventory routing problem with backhaul considering returnable transport items collection

The Inventory Routing Problem (IRP) has been highlighted as a valuable strategy for tackling routing and inventory problems. This paper addresses the IRP but considers the forward delivery and the use of Returnable Transport Items (RTIs) in the distribution strategy. We develop an optimization model by considering inventory routing decisions with RTIs collection (backhaul customers) of a Closed-Loop Supply Chain (CLSC) within a short-term planning horizon. RTIs consider reusable packing materials such as trays, pallets, recyclable boxes, or crates. The RTIs represent an essential asset for many industries worldwide. The solution of the model allows concluding that if RTIs are considered for the distribution process, the relationship between the inventory handling costs of both the final goods and RTIs highly determines the overall performance of the logistics system under study. The obtained results show the efficiency of the proposed optimization scheme for solving the combined IRP with RTIs, which could be applied to different real industrial cases.

Optimizing electric vehicle routing problems with mixed backhauls and recharging strategies in multi-dimensional representation network

Electric vehicles are environmental transportation modes that are widely applied in green logistics systems. To guarantee the energy efficiency, the impacts of customer service modes and recharging strategies need to be integrated into the optimization of electric logistics resource. This paper proposes an electric vehicle routing problem with mixed backhauls, time windows, and recharging strategies (EVRPMBTW-RS), minimizing the total travel cost with sophisticated constraints on the time-dependent pickup and delivery requests, limited recharging station capacity, and battery remaining capacity of electric vehicles. Mixed service sequences of linehaul and backhaul customers is allocated for the routing planning, with the synchronous optimization of recharging strategies including the selection of recharging stations and determination of recharging time. A time-discretized multi-commodity network flow model is constructed based on an extended space–time-state modeling framework, which is formulated as a quadratic 0–1 programming model by using the augmented Lagrangian relaxation technique. After the dualization and linearized transformation, we decompose the model into a sequence of least-cost path subproblems based on the alternating direction multiplier method (ADMM). The subproblems are alternately minimized and solved using the time-dependent forward dynamic programming algorithm. The solution quality can be guaranteed through calculating the optimality gap between the best lower bound and upper bound for each iteration. The proposed solution approach is examined on examples of a simple 7-node network and real-world Yizhuang road network. This paper provides a theoretical foundation for the route optimization method of electric logistics vehicles, and contributes to improve the operational efficiency of electric logistics systems.

A bilevel approach for the collaborative transportation planning problem

The integration of the outbound and the inbound logistics of a company leads to a large transportation network, allowing to detect backhauling opportunities to increase the efficiency of the transportation. In collaborative networks, backhauling is used to find profitable services in the return trip to the depot and to reduce empty running of vehicles. This work investigates the vertical collaboration between a shipper and a carrier for the planning of integrated inbound and outbound transportation. Based on the hierarchical nature of the relation between the shipper and the carrier and their different goals, the problem is formulated as a bilevel Vehicle Routing Problem with Selective Backhauls (VRPSB). At the upper level, the shipper decides the minimum cost delivery routes and the set of incentives offered to the carrier to perform integrated routes. At the lower level, the carrier decides which incentives are accepted and on which routes the backhaul customers are visited. We devise a mathematical programming formulation for the bilevel VRPSB, where the routing and the pricing problems are optimized simultaneously, and propose an equivalent reformulation to reduce the problem to a single-level VRPSB. The impact of collaboration is evaluated against non-collaborative approaches and two different side payment schemes. The results suggest that our bilevel approach leads to solutions with higher synergy values than the approaches with side payments.

Vehicle Routing Problem with Simultaneous Pickup and Delivery

This paper focuses on the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD) issue. VRPSPD is one of the extended problems related to the usual Vehicle Routing Problem (VRP). VRPSPD consists of both linehaul customers and backhaul customers with a known demand. In VPRSPD, only a single depot can receive and supply the loads. The vehicles can only visit each customer once and can serve all customers simultaneously by delivering or picking up the loads within a limited capacity. VPRSPD is a NP-hard problem. The huge data size has increased the difficulty for it to be solved by using mathematical programming or combinatorial optimisation. A heuristic approach based on the Variable Neighbourhood Search (VNS) is proposed. Heuristic based solutions offer feasible solutions that are approximately accurate to the exact solution. It is one of the most popular solutions to solve a complex problem. In this research, the algorithm solution consists of two main phases. A simple heuristic is used to generate the initial solution in the first phase. Then, the feasible solution obtained in the first phase will become the initial input for the improvement phase which applied the VNS algorithm. The proposed algorithm is tested using a list of benchmark dataset. The result obtained is compared with the best solution that can be found from the literature research. The comparison result shows that the heuristic algorithm is favourable to be used for this kind of vehicle routing problem.

A robust optimization approach for the vehicle routing problem with selective backhauls

The Vehicle Routing Problem with Selective Backhauls (VRPSB) aims to minimize the total routing costs minus the total revenue collected at backhaul customers. We explore a VRPSB under uncertain revenues. A deterministic VRPSB is formulated as a mixed-integer programming problem and two robust counterparts are derived. A novel method to estimate the probabilistic bounds of constraint violation is designed. A robust metaheuristic is developed, requiring little time to obtain feasible solutions with average gap of 1.40%. The robust approach studied demonstrates high potential to tackle the problem, requiring similar computing effort and maintaining the same tractability as the deterministic modeling.

A hybrid algorithm for the vehicle routing problem with three-dimensional loading constraints and mixed backhauls

In this paper, a variant of the vehicle routing problem with mixed backhauls (VRPMB) is presented, i.e. goods have to be delivered from a central depot to linehaul customers, and, at the same time, goods have to be picked up from backhaul customers and brought to the depot. Both types of customers can be visited in mixed sequences. The goods to be delivered or picked up are three-dimensional (cuboid) items. Hence, in addition to a routing plan, a feasible packing plan for each tour has to be provided considering a number of loading constraints. The resulting problem is the vehicle routing problem with three-dimensional loading constraints and mixed backhauls (3L-VRPMB). The simultaneous transport of linehaul and backhaul items presents a particular challenge of the problem. We consider two different loading variants in order to avoid any reloading during the tour: (i) rear loading with separate linehaul and backhaul sections and (ii) loading at a long side. In order to solve the problem, we propose a hybrid metaheuristic consisting of a reactive tabu search for the routing problem and different packing heuristics for the loading problem. Numerical experiments are reported with benchmark instances from the literature for the one-dimensional VRPMB to examine the performance of the routing algorithm and with newly generated instances for the 3L-VRPMB.

Developing the Inventory Routing Problem with Backhauls, Heterogeneous Fleet and Split Service

One of the most important points in a supply chain is customer-driven modeling, which reduces the bullwhip effect in the supply chain, as well as the costs of investment on the inventory and efficient transshipment of the products. Their homogeneity is reflected in the Inventory Routing Problem, which is a combination of distribution and inventory management. This paper expands the classical Inventory Routing Problem based on the Multiple Delivery Strategy along with one of the functionalities of routing problem, namely, backhauls, with a priority consideration for linehaul customers. Then it has been modeled in the form of a problem with Multi-period, multi-product, and multi- vehicle planning horizons in which stock out is not allowed. Moreover, for an optimal use of the vehicle capacity to serve the linehaul and backhaul customers, this study adopted a “split service” problem to the model, which also increases the complexity of the problem. First, considering the above-mentioned assumptions, a new mathematical model is proposed in the form of mixed integer programming for the problem defined in this paper. Then, since the stated problem can be considered among the non-deterministic polynomial-time hard, an efficient meta-heuristic genetic algorithm is provided for solving it. At the end, the numerical results obtained by this algorithm are analyzed using the randomized test problems. The result shows that by adopting a split service approach, 70% of the test problems will demonstrate cost reduction.

Variable neighborhood search algorithms for the vehicle routing problem with two‐dimensional loading constraints and mixed linehauls and backhauls

AbstractIn this paper, we explore a vehicle routing problem with two‐dimensional loading constraints and mixed linehauls and backhauls. The addressed problem belongs to a subclass of general pickup and delivery problems. Two‐dimensional loading constraints are also considered. These constraints arise in many real‐world situations and can improve efficiency since backhaul customers do not need to be delayed in a route when it is possible to load their items earlier and without rearrangements of the items. To tackle this problem, we report extensive computational experiments to assess the performance of different variants of the variable neighborhood search approaches. The initial solution relies on an insertion heuristic. Both shaking and local search phases resort to 10 neighborhood structures. Some of those structures were specially developed for this problem. The feasibility of routes is heuristically obtained with a classical bottom‐left based method to tackle the explicit consideration of loading constraints. All the strategies were implemented and exhaustively tested on instances adapted from the literature. The results of this computational study are discussed at the end of this paper.

Heuristics for vehicle routing problems with backhauls, time windows, and 3D loading constraints

In this paper, we consider vehicle routing problems with backhauls and time windows (VRPBTW). Different backhaul variants are studied, namely clustered backhauls (CB), mixed linehauls and backhauls, and variants with simultaneous delivery and pickup and with divisible delivery and pickup. Three dimensional loading constraints are assumed. A two-phase approach following the principle packing first, routing second is proposed. In the first phase, the packing of goods is carried out by solving a 3D strip packing problem for each customer using tabu search. The resulting VRPTW instance is solved in the second phase using first a multi-start evolutionary strategy to minimize the number of vehicles while again tabu search is applied to minimize the total travel distance. We show that the various backhaul types can be incorporated into this framework. For the backhaul variants different from CB, unloading and reloading efforts are taken into account. Moreover, side loading and a separation of the loading space into separate compartments for goods of linehaul and backhaul customers are proposed. Computational results for benchmark instances and new randomly generated problem instances are presented that demonstrate that the heuristics determine high-quality solutions in a short amount of computing time. The unloading and reloading strategies outperform the strategies based on two separate compartments.

A parallel variable neighborhood search for the vehicle routing problem with divisible deliveries and pickups

A well-known variant of the vehicle routing problem involves backhauls, where vehicles deliver goods from a depot to linehaul customers and pick up goods from backhaul customers to the depot. The vehicle routing problem with divisible deliveries and pickups (VRPDDP) allows vehicles to visit each client once or twice for deliveries or pickups. In this study, a very efficient parallel approach based on variable neighborhood search (VNS) is proposed to solve VRPDDP. In this approach, asynchronous cooperation with a centralized information exchange strategy is used for parallelization of the VNS approach, called cooperative VNS (CVNS). All available problem sets of VRPDDP have been successfully solved with the CVNS, and the best solutions available in the literature have been significantly improved.

A biased‐randomized metaheuristic for the vehicle routing problem with clustered and mixed backhauls

This article analyzes the Vehicle Routing Problem with Backhauls, where delivery and pick‐up customers are served from a central depot. Initially, we focus in the version with clustered backhauls (VRPCB), where all the customers in the delivery group of the same route have to be served before the first customer in the pick‐up group can be visited. The article presents a relatively simple‐to‐implement yet efficient metaheuristic algorithm that integrates a biased‐randomized version of the popular savings heuristic within a metaheuristic framework. A skewed probability distribution is used to induce a biased (oriented) randomization effect on the savings list of routing edges, and a penalty cost is assigned to those edges connecting delivery customers with pick‐up customers in order to promote a sequential order in delivery and pick‐up activities. In the proposed approach, the fleet size constraint is implicitly relaxed. This feature allows the perturbation process to explore unfeasible but promising regions in the solution space. Then, whenever the number of routes does not match the number of available vehicles, a “recursive corrective operator” is employed to transform the new solution into a feasible one. Some classical benchmark instances for the VRPCB are selected in order to compare our approach with other state‐of‐the‐art algorithms, and a new best‐know solution for a classical benchmark set is obtained. Finally, we analyze the flexibility of our approach by employing it, after a minor adaptation, in the Vehicle Routing Problem with Mixed Backhauls, where linehaul and backhaul customers might appear in any order during a route. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 69(3), 241–255 2017

Preface: Special issue on the VeRoLog 2015 conference

VeRoLog is the annual conference sponsored by the EURO Working Group on Vehicle Routing and Logistics Optimization within EURO, the Association of the European Operational Research Societies. It brings together the large community of researchers and practitioners interested in vehicle routing optimization and its relations with logistics. The conference is open to high-quality methodological contributions as well as relevant real-world applications and case studies from the industry and service sectors. VeRoLog 2015, which forms the basis of the current special issue, was organized in Vienna. The former conferences were located in Bologna (2012), Southampton (2013), and Oslo (2014). Researchers in the field of Vehicle Routing and Logistics from many parts of Europe and beyond met at the University of Vienna from June 8th to June 10th, 2015. There were 181 participants from 29 countries (). The conference was organized into two plenaries (given by Martin Savelsbergh and Tolga Bektas) and 37 sessions including 123 presentations. strong focus was on rich and real-world routing, especially in the field of green and electric vehicle routing problems, city logistics and bike sharing, and safe and secure routing. In total 28 presentations focused on one of these topics. VeRoLog now also has a solver challenge on rich vehicle routing. The paper of the winner is also included in the special issue. The following seven papers are a selection of the best papers presented during the conference. The paper by Belloso, Juan, Faulin, and Martinez, entitled A Biased-Randomized Metaheuristic for the Vehicle Routing Problem with Clustered and Mixed analyzes the Vehicle Routing Problem with Backhauls, where delivery and pickup customers are served from a central depot. Initially, it focusses on the version with clustered backhauls (VRPCB), where all delivery customers on a route have to be served before the first pickup customer can be visited. This is motivated by the fact that vehicles are often rear loaded. The paper presents a relatively simple to implement yet efficient metaheuristic algorithm that employs a biased randomized version of the popular savings heuristic within a metaheuristic framework. skewed probability distribution is used to induce a biased (oriented) randomization effect on the savings list of routing edges, and the sequencing constraints are considered via penalty costs. On some classical benchmark instances for the VRPCB, competitive results are obtained and a new best-known solution is found. In order to show the robustness of the proposed approach, it is also applied-after a minor adaptation-to the Vehicle Routing Problem with Mixed Backhauls, where line-haul and backhaul customers might appear in any order during a route. The second paper, entitled An Adaptive and Diversified Vehicle Routing Approach to Reducing the Security Risk of Cash-in-Transit Operations and authored by Bozkaya, Salman, and Telciler, considers the new problem class of inconsistent vehicle routing problems. The authors consider the transportation of valuables (e.g., cash). Due to the high-risk nature of this operation (e.g., robberies), they consider a bi-objective function where they

A simulated annealing algorithm for solving multi-depot location routing problem with backhaul

This paper presents a method for solving a multi-depot location-routing problem with backhaul (MDLRPB). In the suggested problem, there are two subsets of customers including linehaul and backhaul customers. Linehaul customers require a delivery of stock from the depot, whereas backhaul customers need to deliver stock from their location to the depot. A mathematical model and a heuristic method based on the simulated annealing (SA) algorithm have been proposed for solving the problem. Test problems from the literature have been used for generating a new test problem for the MDLRPB problem. Computational results show that the CPU time for the SA is reasonable while this value for the LINGO increase dramatically in large size problems. In the worst case, the gap between objective function value of SA algorithm and optimal solution is equal 3%. The results indicate that suggested algorithm can reach the optimal or near optimal solution in small and medium size problems in a reasonable computational time.

A simulated annealing algorithm for solving multi-depot location routing problem with backhaul

This paper presents a method for solving a multi-depot location-routing problem with backhaul (MDLRPB). In the suggested problem, there are two subsets of customers including linehaul and backhaul customers. Linehaul customers require a delivery of stock from the depot, whereas backhaul customers need to deliver stock from their location to the depot. A mathematical model and a heuristic method based on the simulated annealing (SA) algorithm have been proposed for solving the problem. Test problems from the literature have been used for generating a new test problem for the MDLRPB problem. Computational results show that the CPU time for the SA is reasonable while this value for the LINGO increase dramatically in large size problems. In the worst case, the gap between objective function value of SA algorithm and optimal solution is equal 3%. The results indicate that suggested algorithm can reach the optimal or near optimal solution in small and medium size problems in a reasonable computational time.

Exact Method for the Vehicle Routing Problem with Mixed Linehaul and Backhaul Customers, Heterogeneous Fleet, time Window and Manufacturing Capacity

Due to concerns over food safety, quality, and transparency, the food industry has been challenged to deal with an increased complexity in its logistics and production planning. This complexity is mostly associated to the task of optimally exploring a highly constrained solution space. This paper addresses the problem of designing a set of vehicle routes satisfying the delivery and the collection requirements of a set of geographically scattered linehaul and backhaul customers. Each customer has a known demand for delivery and/or pickup, and it must be serviced within a predefined time window, representing the earliest and the latest times service time, by a vehicle of a heterogeneous fleet of depot-returning capacitated vehicles. Additionally the proposed model, aiming at minimizing the logistics costs, also takes manufacturing capacities and driving hour's regulations into consideration. The proposed algorithm was embedded in a native application. This digital tool, enabling the support of a holistic production and logistics planning, was implemented in a food company.

Fuzzy multi-objective programming algorithm for vehicle routing problems with backhauls

The vehicle routing problem with backhauls (VRPB) is an extension of the standard vehicle routing problem. VRPB has two sets of customers: linehaul customers and backhaul customers. The aim of this study is to propose a new algorithm based on fuzzy multi-objective programming (FMOP-VRPB algorithm) to solve the VRPB. The FMOP-VRPB algorithm has three phases; clustering, routing and local search. In the clustering phase, customers are assigned to vehicles by the proposed multi-objective programming (MOP) model with two objective functions: minimizing the total distance and maximizing the total savings value. The proposed MOP model is solved by fuzzy operators. The weights of the objectives are also calculated by a fuzzy two-person zero-sum game with mixed strategies using membership functions in a fuzzy pay-off matrix. In the routing phase, each vehicle is routed as a traveling salesman problem with backhauls. The local search phase is used to improve the routes.The primary contributions of the FMOP-VRPB algorithm are to consider the two objectives, to determine the weights of objectives using the proposed fuzzy pay-off matrix in the clustering phase and to use only mathematical programming in both the clustering and routing phases through many customers in an acceptable CPU time. The algorithm will also show that the proposed MOP model defines the seed customers itself in the clustering phase and will always generates feasible clusters, contrary to the reports in the literature.Benchmark problems from the literature are solved to test the performance of the FMOP-VRPB algorithm. The results indicate that the FMOP-VRPB algorithm generates sufficient solutions, and CPU times are within acceptable limits. In addition, a weekly routing problem for a logistics department of a ceramics firm in Turkey is solved by the FMOP-VRPB algorithm. Additionally, this study is the first to solve a real world VRPB; the solution shows that the FMOP-VRPB algorithm is suitable and effective for real world problems.