The load-dependent vehicle routing problem and its pick-up and delivery extension

The present paper examines a Vehicle Routing Problem (VRP) of major practical importance which is referred to as the Load-Dependent VRP (LDVRP). LDVRP is applicable for transportation activities where the weight of the transported cargo accounts for a significant part of the vehicle gross weight. Contrary to the basic VRP which calls for the minimization of the distance travelled, the LDVRP objective is aimed at minimizing the total product of the distance travelled and the gross weight carried along this distance. Thus, it is capable of producing sensible routing plans which take into account the variation of the cargo weight along the vehicle trips. The LDVRP objective is closely related to the total energy requirements of the vehicle fleet, making it a credible alternative when the environmental aspects of transportation activities are examined and optimized. A novel LDVRP extension which considers simultaneous pick-up and delivery service is introduced, formulated and solved for the first time. To deal with large-scale instances of the examined problems, we propose a local-search algorithm. Towards an efficient implementation, the local-search algorithm employs a computational scheme which calculates the complex weighted-distance objective changes in constant time. Solution results are presented for both problems on a variety of well-known test cases demonstrating the effectiveness of the proposed solution approach. The structure of the obtained LDVRP and VRP solutions is compared in pursuit of interesting conclusions on the relative suitability of the two routing models, when the decision maker must deal with the weighted distance objective. In addition, results of a branch-and-cut procedure for small-scale instances of the LDVRP with simultaneous pick-ups and deliveries are reported. Finally, extensive computational experiments have been performed to explore the managerial implications of three key problem characteristics, namely the deviation of customer demands, the cargo to tare weight ratio, as well as the size of the available vehicle fleet.     

Design and development of a hybrid ant colony-variable neighbourhood search algorithm for a multi-depot green vehicle routing problem

The traditional distribution planning problem in a supply chain has often been studied mainly with a focus on economic benefits. The growing concern about the effects of anthropogenic pollutions has forced researchers and supply chain practitioners to address the socio-environmental concerns. This research study focuses on incorporating the environmental impact on route design problem. In this work, the aim is to integrate both the objectives, namely economic cost and emission cost reduction for a capacitated multi-depot green vehicle routing problem. The proposed models are a significant contribution to the field of research in green vehicle routing problem at the operational level. The formulated integer linear programming model is solved for a set of small scale instances using LINGO solver. A computationally efficient Ant Colony Optimization (ACO) based meta-heuristic is developed for solving both small scale and large scale problem instances in reasonable amount of time. For solving large scale instances, the performance of the proposed ACO based meta-heuristic is improved by integrating it with a variable neighbourhood search.     

A model and optimization-based heuristic for the operational aircraft maintenance routing problem

This paper investigates the Operational Aircraft Maintenance Routing Problem (OAMRP). Given a set of flights for a specific homogeneous fleet type, this short-term planning problem requires building feasible aircraft routes that cover each flight exactly once and that satisfy maintenance requirements. Basically, these requirements enforce an aircraft to undergo a planned maintenance at a specified station before accumulating a maximum number of flying hours. This stage is significant to airline companies as it directly impacts the fleet availability, safety, and profitability. The contribution of this paper is twofold. First, we elucidate the complexity status of the OAMRP and we propose an exact mixed-integer programming model that includes a polynomial number of variables and constraints. Furthermore, we propose a graph reduction procedure and valid inequalities that aim at improving the model solvability. Second, we propose a very large-scale neighborhood search algorithm along with a procedure for computing tight lower bounds. We present the results of extensive computational experiments that were carried out on real-world flight networks and attest to the efficacy of the proposed exact and heuristic approaches. In particular, we provide evidence that the exact model delivers optimal solutions for instances with up to 354 flights and 8 aircraft, and that the heuristic approach consistently delivers high-quality solutions while requiring short CPU times.     

Partial recharge strategies for the electric vehicle routing problem with time windows

The Electric Vehicle Routing Problem with Time Windows (EVRPTW) is an extension to the well-known Vehicle Routing Problem with Time Windows (VRPTW) where the fleet consists of electric vehicles (EVs). Since EVs have limited driving range due to their battery capacities they may need to visit recharging stations while servicing the customers along their route. The recharging may take place at any battery level and after the recharging the battery is assumed to be full. In this paper, we relax the full recharge restriction and allow partial recharging (EVRPTW-PR), which is more practical in the real world due to shorter recharging duration. We formulate this problem as a 0–1 mixed integer linear program and develop an Adaptive Large Neighborhood Search (ALNS) algorithm to solve it efficiently. We apply several removal and insertion mechanisms by selecting them dynamically and adaptively based on their past performances, including new mechanisms specifically designed for EVRPTW and EVRPTW-PR. These new mechanisms include the removal of the stations independently or along with the preceding or succeeding customers and the insertion of the stations with determining the charge amount based on the recharging decisions. We test the performance of ALNS by using benchmark instances from the recent literature. The computational results show that the proposed method is effective in finding high quality solutions and the partial recharging option may significantly improve the routing decisions.     

Optimal solution to the vehicle routing problem by adopting a meta-heuristic algorithm

The delivery service provided by large-scale retailers continues to grow as online sales occupy an increasingly large share of the market. This study aims to tease out efficient vehicle scheduling times as well as optimal delivery routes by applying meta-heuristic algorithms. Monthly data on existing routes were obtained from a branch of Korea’s leading large-scale online retailer. The first task was to examine the status of existing routes by comparing delivery routes created using Dijkstra’s algorithm with existing delivery routes and their vehicle scheduling. The second task was to identify optimal delivery routes through a comparative analysis of the genetic algorithm and Tabu search algorithm, known for its superior applicability amongst other meta-heuristic algorithms. These findings demonstrate that the optimal vehicle routing problem not only has the potential to reduce distribution costs for operators and expedite delivery for consumers, but also the added social benefit of reduced carbon emissions.     

The tractor and semitrailer routing problem with many-to-many demand considering carbon dioxide emissions

The tractor and semitrailer routing problem with many-to-many demand (TSRP-MMD) is investigated in this study. The TSRP-MMD extends the existing studies on the rollon–rolloff vehicle routing problem (RRVRP) to a many-to-many problem with an intercity line-haul network background. To demonstrate and utilize the energy efficiency of the tractor and semitrailer combination, the TSRP-MMD takes carbon dioxide (CO₂) emissions per ton-kilometer as the objective. Because the problem is NP-hard, a modified Clarke and Wright Savings heuristic algorithm (CW) followed by an improvement phase and a local search phase is developed to solve the TSRP-MMD. The integer program is used to find optimum solutions for small-scale problems. The computational results show that the developed heuristics can be efficiently used to solve the problem.     

A tailored branch-and-price approach for a joint tramp ship routing and bunkering problem

This paper deals with a practical tramp ship routing problem while taking into account different bunker prices at different ports, which is called the joint tramp ship routing and bunkering (JSRB) problem. Given a set of cargoes to be transported and a set of ports with different bunker prices, the proposed problem determines how to route ships to carry the cargoes and the amount of bunker to purchase at each port, in order to maximize the total profit. After building an integer linear programming model for the JSRB problem, we propose a tailored branch-and-price (B&P) solution approach. The B&P approach incorporates an efficient method for obtaining the optimal bunkering policy and a novel dominance rule for detecting inefficient routing options. The B&P approach is tested with randomly generated large-scale instances derived from real-world planning problems. All of the instances can be solved efficiently. Moreover, the proposed approach for the JSRB problem outperforms the conventional sequential planning approach and can incorporate the prediction of future cargo demand to avoid making myopic decisions.     

A differential evolution approach for the vehicle routing problem with backhauls and time windows

This paper presents a differential evolution algorithm (DEA) to solve a vehicle routing problem with backhauls and time windows (VRPBTW) and applied for a catering firm. VRPBTW is an extension of the vehicle routing problem, which includes capacity and time window constraints. In this problem, customers are divided into two subsets: linehaul and backhaul. Each vehicle starts from a depot and goods are delivered from the depot to the linehaul customers. Goods are subsequently brought back to the depot from the backhaul customers. The objective is to minimize the total distance that satisfies all of the constraints. The problem is formulated using mixed integer programming and solved using DEA. Proposed algorithm is tested with several benchmark problems to demonstrate effectiveness and efficiency of the algorithm and results show that our proposed algorithm can find superior solutions for most of the problems in comparison with the best known solutions. Hence, DEA was carried out for catering firm to minimize total transportation costs. Copyright © 2013 John Wiley & Sons, Ltd.     

Design and development of a hybrid artificial bee colony algorithm for the environmental vehicle routing problem

The vehicle routing problem (VRP) is a critical and vital problem in logistics for the design of an effective and efficient transportation network, within which the capacitated vehicle routing problem (CVRP) has been widely studied for several decades due to the practical relevance of logistics operation. However, CVRP with the objectives of minimizing the overall traveling distance or the traveling time cannot meet the latest requirements of green logistics, which concern more about the influence on the environment. This paper studies CVRP from an environmental perspective and introduces a new model called environmental vehicle routing problem (EVRP) with the aim of reducing the adverse effect on the environment caused by the routing of vehicles. In this research, the environmental influence is measured through the amount of the emission carbon dioxide, which is a widely acknowledged criteria and accounts for the major influence on environment. A hybrid artificial bee colony algorithm (ABC) is designed to solve the EVRP model, and the performance of the hybrid algorithm is evaluated through comparing with well-known CVRP instances. The computational results from numerical experiments suggest that the hybrid ABC algorithm outperforms the original ABC algorithm by 5% on average. The transformation from CVRP to EVRP can be recognized through the differentiation of their corresponding optimal solutions, which provides practical insights for operation management in green logistics.     

Robust weekly aircraft maintenance routing problem and the extension to the tail assignment problem

In this paper, we study two closely related airline planning problems: the robust weekly aircraft maintenance routing problem (RWAMRP) and the tail assignment problem (TAP). In real life operations, the RWAMRP solution is used in tactical planning whereas the TAP solution is implemented in operational planning. The main objective of these two problems is to minimize the total expected propagated delay (EPD) of the aircraft routes. To formulate the RWAMRP, we propose a novel weekly line-of-flights (LOF) network model that can handle complex and nonlinear cost functions of EPD. Because the number of LOFs grows exponentially with the number of flights to be scheduled, we propose a two-stage column generation approach to efficiently solve large-scale real-life RWAMRPs. Because the EPD of an LOF is highly nonlinear and can be very time-consuming to accurately compute, we propose three lower bounds on the EPD to solve the pricing subproblem of the column generation. Our approach is tested on eight real-life test instances. The computational results show that the proposed approach provides very tight LP relaxation (within 0.6% of optimal solutions) and solves the test case with more than 6000 flights per week in less than three hours. We also investigate the solutions obtained by our approach over 500 simulated realizations. The simulation results demonstrate that, in all eight test instances, our solutions result in less EPDs than those obtained from traditional methods. We then extend our model and solution approach to solve realistically simulated TAP instances.     

Vehicle routing problem and driver behaviour: a review and framework for analysis

Vehicle routing problems (VRPs) whose typical objective is to minimise total travel costs over a tour have evolved over the years with objectives ranging from minimising travel times and distances to minimising pollution and fuel consumption. However, driver behaviour continues to be neglected while planning for vehicle routes. Factors such as traffic congestion levels, monotonous drives and fatigue have an impact on the behaviour of drivers, which in turn might affect their speed-choice and route-choice behaviours. The behaviour of drivers and their subsequent decision-making owing to these factors impact the revenue of transport companies and could lead to huge losses in extreme cases. There have been studies on the behaviour of drivers in isolation, without inclusion of the objectives and constraints of the traditional routing problem. This paper presents a review of existing models of VRP, planner behaviour models in the VRP context and driver behaviour models and provides a motivation to integrate these models in a stochastic traffic environment to produce practical, economic and driver-friendly logistics solutions. The paper provides valuable insights on the relevance of behavioural issues in logistics and highlights the modelling implications of incorporating planner and driver behaviour in the framework of routing problems.     

A reinforcement learning framework for the adaptive routing problem in stochastic time-dependent network

Most previous work in addressing the adaptive routing problem in stochastic and time-dependent (STD) network has been focusing on developing parametric models to reflect the network dynamics and designing efficient algorithms to solve these models. However, strong assumptions need to be made in the models and some algorithms also suffer from the curse of dimensionality. In this paper, we examine the application of Reinforcement Learning as a non-parametric model-free method to solve the problem. Both the online Q learning method for discrete state space and the offline fitted Q iteration algorithm for continuous state space are discussed. With a small case study on a mid-sized network, we demonstrate the significant advantages of using Reinforcement Learning to solve for the optimal routing policy over traditional stochastic dynamic programming method. And the fitted Q iteration algorithm combined with tree-based function approximation is shown to outperform other methods especially during peak demand periods.     

An integrated modelling approach for the bicriterion vehicle routing and scheduling problem with environmental considerations

The consideration of pollution in routing decisions gives rise to a new routing framework where measures of the environmental implications are traded off with business performance measures. To address this type of routing decisions, we formulate and solve a bi-objective time, load and path-dependent vehicle routing problem with time windows (BTL-VRPTW). The proposed formulation incorporates a travel time model representing realistically time varying traffic conditions. A key feature of the problem under consideration is the need to address simultaneously routing and path finding decisions. To cope with the computational burden arising from this property of the problem we propose a network reduction approach. Computational tests on the effect of the network reduction approach on determining non-dominated solutions are reported. A generic solution framework is proposed to address the BTL-VRPTW. The proposed framework combines any technique that creates capacity-feasible routes with a routing and scheduling method that aims to convert the identified routes to problem solutions. We show that transforming a set of routes to BTL-VRPTW solutions is equivalent to solving a bi-objective time dependent shortest path problem on a specially structured graph. We propose a backward label setting technique to solve the emerging problem that takes advantage of the special structure of the graph. The proposed generic solution framework is implemented by integrating the routing and scheduling method into an Ant Colony System algorithm. The accuracy of the proposed algorithm was assessed on the basis of its capability to determine minimum travel time and fuel consumption solutions. Although the computational results are encouraging, there is ample room for future research in algorithmic advances on addressing the proposed problem.     

Application specific instance generator and a memetic algorithm for capacitated arc routing problems

Capacitated arc routing problem (CARP) is a well known combinatorial problem that requires identifying minimum total distance traveled by a fleet of vehicles in order to serve a set of roads without violating the vehicles’ capacity constraints. A number of optimization algorithms have been proposed over the years to solve basic CARPs and their performance have been analyzed using selected benchmark suites available in literature. From an application point of view, there is a need to assess the performance of algorithms on specific class of instances that resemble realistic applications, e.g., inspection of electric power lines, garbage collection, winter gritting etc. In this paper we introduce a benchmark generator that controls the size and complexity of the underlying road network resembling a target application. It allows generation of road networks with multiple lanes, one-way/two-way roads and varying degree of connectedness. Furthermore, an algorithm capable of solving real life CARP instances efficiently within a fixed computational budget of evaluations is introduced. The proposed algorithm, referred to as MA-CARP, is a memetic algorithm embedded with a similarity based parent selection scheme inspired by multiple sequence alignment, hybrid crossovers and a modified neighborhood search to improve its rate of convergence. The mechanism of test instance generation is presented for three typical scenarios, namely, inspection of electric power lines, garbage collection and winter gritting. The code for the generator is available from http://seit.unsw.adfa.edu.au/research/sites/mdo/Research-Data/InstanceGenerator.rar. The performance of the algorithm is compared with a state-of-the-art algorithm for three generated benchmarks. The results obtained using the proposed algorithm are better for all the above instances clearly highlighting its potential for solving CARP problems.     

A decision support system for integrated hazardous materials routing and emergency response decisions

Hazardous materials routing constitutes a critical decision in mitigating the associated transportation risk. This paper presents a decision support system for assessing alternative distribution routes in terms of travel time, risk and evacuation implications while coordinating the emergency response deployment decisions with the hazardous materials routes. The proposed system provides the following functionalities: (i) determination of alternative non-dominated hazardous materials distribution routes in terms of cost and risk minimization, (ii) specification of the hazardous materials first-response emergency service units locations in order to achieve timely response to an accident, and (iii) determination of evacuation paths from the impacted area to designated shelters and estimation of the associated evacuation time. The proposed system has been implemented, used and evaluated for assessing alternative hazardous materials routing decisions within the heavily industrialized area of Thriasion Pedion of Attica, Greece. The implementation of the aforementioned functionalities is based on two new integer programming models for the hazardous materials routing and the emergency response units location problems, respectively. A simplified version of the routing model is solved by an existing heuristic algorithm developed by the authors. A new Lagrangean relaxation heuristic algorithm has been developed for solving the emergency response units location problem. The focus of this paper is on the exposition of the proposed decision support system components and functionalities. Special emphasis is placed on the presentation of the two new mathematical models and the new solution method for the location model.     

Exact and meta-heuristic approach for a general heterogeneous dial-a-ride problem with multiple depots

Dial-a-ride problems are concerned with the design of efficient vehicle routes for transporting individual persons from specific origin to specific destination locations. In real-life this operational planning problem is often complicated by several factors. Users may have special requirements (e.g. to be transported in a wheelchair) while service providers operate a heterogeneous fleet of vehicles from multiple depots in their service area. In this paper, a general dial-a-ride problem in which these three real-life aspects may simultaneously be taken into account is introduced: the Multi-Depot Heterogeneous Dial-A-Ride Problem (MD-H-DARP). Both a three- and two-index formulation are discussed. A branch-and-cut algorithm for the standard dial-a-ride problem is adapted to exactly solve small problem instances of the MD-H-DARP. To be able to solve larger problem instances, a new deterministic annealing meta-heuristic is proposed. Extensive numerical experiments are presented on different sets of benchmark instances for the homogeneous and the heterogeneous single depot dial-a-ride problem. Instances for the MD-H-DARP are introduced as well. The branch-and-cut algorithm provides considerably better results than an existing algorithm which uses a less compact formulation. All seven previously unsolved benchmark instances for the heterogeneous dial-a-ride problem could be solved to optimality within a matter of seconds. While computation times of the exact algorithm increase drastically with problem size, the proposed meta-heuristic algorithm provides near-optimal solutions within limited computation time for all instances. Several best known solutions for unsolved instances are improved and the algorithm clearly outperforms current state-of-the-art heuristics for the homogeneous and heterogeneous dial-a-ride problem, both in terms of solution quality and computation time.     

Quadratic approximation and convergence of some bush-based algorithms for the traffic assignment problem

This paper first shows that LUCE (Gentile, 2012), a recent addition to the family of bush-based algorithms, is closely related to OBA (Bar-Gera, 2002). LUCE’s promise comes mainly from its use of the greedy method for solving the quadratic approximation of node-based subproblems, which determines the search direction. While the greedy algorithm accelerates the solution of the subproblems and reduces the cost of line search, it unexpectedly disrupts the overall convergence performance in our experiments, which consistently show that LUCE failed to converge beyond certain threshold of relative gap. Our analysis suggests that the root cause to this interesting behavior is the inaccurate quadratic approximation constructed on faulty information of second-order derivatives. Because the quadratic approximations themselves are inaccurate, the search directions generated from them are sub-optimal. Unlike OBA, however, LUCE does not have a mechanism to correct these search directions through line search, which explains why its convergence performance suffers the observed breakdowns. We also attempt to improve LUCE using the ideas that have been experimented for the improvement of OBA. While these improvements do work, their effects are not enough to counteract the inability to adjust sub-optimal search directions. Importantly, the fact that the search direction has to be corrected in line search to ensure smooth convergence attests to the limitation of origin-based flow aggregation shared by both OBA and LUCE. These findings offer guidelines for the design of high performance traffic assignment algorithms.     

A cooperative waiting strategy based on elliptical areas for the Dynamic Pickup and Delivery Problem with Time Windows

The purpose of this paper to present a cooperative scheduling algorithm for solving the Dynamic Pickup and Delivery Problem with Time Windows (DPDPTW). The idea behind cooperative waiting strategies is to calculate simultaneously the waiting times for all nodes in the solution. Classical non‐cooperative scheduling algorithms perform the scheduling for each route independently of the scheduling of the other routes. We present the Cooperative Scheduling Problem (CSP) based on the elliptical areas generated by vehicles waiting at their nodes. The CSP is solved by means of a genetic algorithm and is evaluated by using a set of benchmarks based on real‐life data found in the literature. Initially, two waiting strategies are presented: Wait‐Early‐Time scheduling and Balanced‐Departure scheduling. Extensive empirical simulations have been carried out by analyzing the degree of dynamism and the average waiting time, a new concept defined to take into account the gap between the time windows of pickup and delivery nodes. Copyright © 2016 John Wiley & Sons, Ltd.