Route design for last-in,first-out deliveries with backhauling

The retail route design problem extends the capacitated vehicle routing problem with time windows by introducing several operational constraints, including order loading and delivery restrictions (last-in, first-out), order-dependent vehicle capacity, material handling limits at the warehouse, backhauling, and driving time bounds. In this paper, the problem is modeled on a directed network for an application associated with a major grocery chain. Because the corresponding mixed-integer program proved too difficult to solve with commercial software for real instances, we developed a greedy randomized adaptive search procedure (GRASP) augmented with tabu search to provide solutions. Testing was done using data sets provided Kroger, the largest grocery chain in the US, and benchmarked against a previously developed column generation algorithm. The results showed that cost reductions of $4887 per day or 5.58% per day on average, compared to Kroger’s corresponding solutions.     

The split-demand one-commodity pickup-and-delivery travelling salesman problem

This paper introduces a new vehicle routing problem transferring one commodity between customers with a capacitated vehicle that can visit a customer more than once, although a maximum number of visits must be respected. It generalizes the capacitated vehicle routing problem with split demands and some other variants recently addressed in the literature. We model the problem with a single commodity flow formulation and design a branch-and-cut approach to solve it. We make use of Benders Decomposition to project out the flow variables from the formulation. Inequalities to strengthen the linear programming relaxation are also presented and separated within the approach. Extensive computational results illustrate the performance of the approach on benchmark instances from the literature.     

Eco-routing problem considering fuel consumption and probabilistic travel time budget

Road transportation is one of the major sources of greenhouse gas emissions. To reduce energy consumption and alleviate this environmental problem, this study aims to develop an eco-routing algorithm for navigation systems. Considering that both fuel consumption and travel time are important factors when planning a trip, the proposed routing algorithm finds a path that consumes the minimum amount of gasoline while ensuring that the travel time satisfies a specified travel time budget and an on-time arrival probability. We first develop link-based fuel consumption models based on vehicle dynamics, and then the Lagrangian-relaxation-based heuristic approach is proposed to efficiently solve this NP-hard problem. The performance of the proposed eco-routing strategy is verified in a large-scale network with real travel time and fuel consumption data. Specifically, a sensitivity analysis of fuel consumption reduction for travel demand and travel time buffer is discussed in our simulation study.     

The impact of depot location,fleet composition and routing on emissions in city logistics

This paper investigates the combined impact of depot location, fleet composition and routing decisions on vehicle emissions in city logistics. We consider a city in which goods need to be delivered from a depot to customers located in nested zones characterized by different speed limits. The objective is to minimize the total depot, vehicle and routing cost, where the latter can be defined with respect to the cost of fuel consumption and CO₂ emissions. A new powerful adaptive large neighborhood search metaheuristic is developed and successfully applied to a large pool of new benchmark instances. Extensive analyses are performed to empirically assess the effect of various problem parameters, such as depot cost and location, customer distribution and heterogeneous vehicles on key performance indicators, including fuel consumption, emissions and operational costs. Several managerial insights are presented.     

The fleet size and mix pollution-routing problem

This paper introduces the fleet size and mix pollution-routing problem which extends the pollution-routing problem by considering a heterogeneous vehicle fleet. The main objective is to minimize the sum of vehicle fixed costs and routing cost, where the latter can be defined with respect to the cost of fuel and CO₂ emissions, and driver cost. Solving this problem poses several methodological challenges. To this end, we have developed a powerful metaheuristic which was successfully applied to a large pool of realistic benchmark instances. Several analyses were conducted to shed light on the trade-offs between various performance indicators, including capacity utilization, fuel and emissions and costs pertaining to vehicle acquisition, fuel consumption and drivers. The analyses also quantify the benefits of using a heterogeneous fleet over a homogeneous one.     

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.     

Heuristic approaches for solving large-scale bus transit vehicle scheduling problem with route time constraints

This paper presents new models for multiple depot vehicle scheduling problem (MDVS) and multiple depot vehicle scheduling problem with route time constraints (MDVSRTC). The route time constraints are added to the MDVS problem to account for the real world operational restrictions such as fuel consumption. Compared to existing formulations, this formulation decreases the size of the problem by about 40% without eliminating any feasible solution. It also presents an exact and two heuristic solution procedures for solving the MDVSRTC problem. Although these methods can be used to solve medium size problems in reasonable time, real world applications in large cities require that the MDVSRTC problem size be reduced. Two techniques are proposed to decrease the size of the real world problems. For real-world application, the problem of bus transit vehicle scheduling at the mass transit administration (MTA) in Baltimore is studied. The final results of model implementation are compared to the MTA's schedules in January 1998. The comparison indicates that, the proposed model improves upon the MTA schedules in all respects. The improvements are 7.9% in the number of vehicles, 4.66% in the operational time and 5.77% in the total cost.     

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.     

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.     

Platinum,fuel cells,and future US road transport

The rate at which fuel cell vehicles (FCVs) might displace the conventional fleet is examined under constraints imposed by the limited availability of platinum. It concludes that a transition period as short as 31 years is not feasible. Under the most favorable circumstances, a complete transition of the US fleet to this new technology would require about 66 years and 10,800 net tonnes of platinum. Platinum demand for the US auto industry alone would amount to 48% of world production during much of that transition period. The effect of that demand on the price of platinum would add to the problem of reducing vehicle cost to a competitive range. If US platinum consumption were to remain at its current level of 16% of annual world production, fleet conversion would require 146 years. These results imply that, without alternative catalysts, fuel cells alone cannot adequately address the issues facing the current system of road transport.     

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.     

Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations

Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). This paper first proposes a new time-discretized multi-commodity network flow model for the VRPPDTW based on the integration of vehicles’ carrying states within space–time transportation networks, so as to allow a joint optimization of passenger-to-vehicle assignment and turn-by-turn routing in congested transportation networks. Our three-dimensional state–space–time network construct is able to comprehensively enumerate possible transportation states at any given time along vehicle space–time paths, and further allows a forward dynamic programming solution algorithm to solve the single vehicle VRPPDTW problem. By utilizing a Lagrangian relaxation approach, the primal multi-vehicle routing problem is decomposed to a sequence of single vehicle routing sub-problems, with Lagrangian multipliers for individual passengers’ requests being updated by sub-gradient-based algorithms. We further discuss a number of search space reduction strategies and test our algorithms, implemented through a specialized program in C++, on medium-scale and large-scale transportation networks, namely the Chicago sketch and Phoenix regional networks.     

A rolling horizon algorithm for auto-carrier transportation

This paper introduces a rolling horizon algorithm to plan the delivery of vehicles to automotive dealers by a heterogeneous fleet of auto-carriers. The problem consists in scheduling the deliveries over a multiple-day planning horizon during which requests for transportation arrive dynamically. In addition, the routing of the auto-carriers must take into account constraints related to the loading of the vehicles on the carriers. The objective is to minimize the sum of traveled distances, fixed costs for auto-carrier operation, service costs, and penalties for late deliveries. The problem is solved by a heuristic that first selects the vehicles to be delivered in the next few days and then optimizes the deliveries by an iterated local search procedure. A branch-and-bound search is used to check the feasibility of the loading. To handle the dynamic nature of the problem, the complete algorithm is applied repeatedly in a rolling horizon framework. Computational results on data from a major European logistics service provider show that the heuristic is fast and yields significant improvements compared to the sequential solution of independent daily problems.     

Optimal tank-trailer routing using the ILOG constraint programming – a Taiwan case study

Abstract

This paper investigates the routing of pressurized tank trailers and proposes a scheduling plan which ensures the practical delivery of industrial gases under the objective of reducing transportation costs. Using constraint programming, we solve a combinatorial optimization problem that incorporates both hard and soft constraints for routing and scheduling tank trailers. Hard constraints are resource and safety/regulation constraints, whereas soft constraints are utilization and efficiency constraints. This approach enables tank-trailer routing and scheduling management to consider different combinations of parameters and view the results in ‘real-time.’ The routing and scheduling results based on a case study in Taiwan fulfil the goals of avoiding risks associated with transporting industrial gases, and attaining efficient delivery while conforming to regulations and consistent with good business practice. The results also suggest that significant economies in distribution costs are possible.     

Dynamic green bike repositioning problem – A hybrid rolling horizon artificial bee colony algorithm approach

This paper introduces a new dynamic green bike repositioning problem (DGBRP) that simultaneously minimizes the total unmet demand of the bike-sharing system and the fuel and CO₂ emission cost of the repositioning vehicle over an operational period. The problem determines the route and the number of bikes loaded and unloaded at each visited node over a multi-period operational horizon during which the cycling demand at each node varies from time to time. To handle the dynamic nature of the problem, this study adopts a rolling horizon approach to break down the proposed problem into a set of stages, in which a static bike repositioning sub-problem is solved in each stage. An enhanced artificial bee colony (EABC) algorithm and a route truncation heuristic are jointly used to optimize the route design in each stage, and the loading and unloading heuristic is used to tackle the loading and unloading sub-problem along the route in a given stage. Numerical results show that the EABC algorithm outperforms Genetic Algorithm in solving the routing sub-problem. Computation experiments are performed to illustrate the effect of the stage duration on the two objective values, and the results show that longer stage duration leads to higher total unmet demand and total fuel and CO₂ emission cost. Numerical studies are also performed to illustrate the effects of the weight and the loading and unloading times on the two objective values and the tradeoff between the two objectives.     

Order-first split-second methods for vehicle routing problems: A review

Cluster-first route-second methods like the sweep heuristic (Gillett and Miller, 1974) are well known in vehicle routing. They determine clusters of customers compatible with vehicle capacity and solve a traveling salesman problem for each cluster. The opposite approach, called route-first cluster-second, builds a giant tour covering all customers and splits it into feasible trips. Cited as a curiosity for a long time but lacking numerical evaluation, this technique has nevertheless led to successful metaheuristics for various vehicle routing problems in the last decade. As many implementations consider an ordering of customers instead of building a giant tour, we propose in this paper the more general name of ordering-first split-second methods. This article shows how this approach can be declined for different vehicle routing problems and reviews the associated literature, with more than 70 references.     

Recent advances in automotive technology and the cost-effectiveness of fuel economy improvement

The potential for improving the fuel economy of conventional, gasoline-powered automobiles through optimized application of recent technology advances is analyzed. Results are presented at three levels of technical certainty, ranging from technologies already in use to technologies facing technical constraints (such as emissions control problems) which might inhibit widespread use. A fleet-aggregate, engineering-economic analysis is used to estimate a range of U.S. new car fleet average fuel economy levels achievable given roughly 10 years of lead time. Technology cost estimates are compared to fuel savings in order to determine likely cost-effective levels of fuel economy, which are found to range from 39 miles per gallon to 51 miles per gallon depending on technology certainty level. The corresponding estimated increases in average new car price range from $540 to $790 (1993$). Estimated fuel savings payback times average less than 3 years and the cost of conserved energy averages $0.50 per gallon, indicating that these levels of fuel economy improvement are cost-effective over a vehicle lifetime. A vehicle stock turnover model is used to project the reductions in gasoline consumption and associated emissions that would follow if the estimated fuel economy levels are achieved. Potential trade-offs regarding vehicle performance, safety, and emissions are also discussed.     

Real-time energy-efficient traffic control via convex optimization

This article proposes a macroscopic traffic control strategy to reduce fuel consumption of vehicles on highways. By implementing Greenshields fundamental diagram, the solution to Moskowitz equations is expressed as linear functions with respect to vehicle inflow and outflow, which leads to generation of a linear traffic flow model. In addition, we build a quadratic cost function in terms of vehicle volume to estimate fuel consumption rate based on COPERT model. A convex quadratic optimization problem is then formulated to generate energy-efficient traffic control decisions in real-time. Simulation results demonstrate significant reduction of fuel consumption on testing highway sections under peak traffic demands of busy hours.     

Integrating a heterogeneous fixed fleet and a flexible assignment of destination depots in the waste collection VRP with intermediate facilities

We consider a complex recyclable waste collection problem that extends the class of vehicle routing problems with intermediate facilities by integrating a heterogeneous fixed fleet and a flexible assignment of destination depots. Several additional side constraints, such as a mandated break period contingent on tour start time, multiple vehicle capacities, and site dependencies are also included. This specific problem was inspired by a real-world application and does not appear in the literature. It is modeled as an MILP which is enhanced with several valid inequalities. Due to the rich nature of the problem, state-of-the-art solvers are only able to tackle instances of small to medium size. To solve realistic instances, we propose a multiple neighborhood search heuristic capable of systematically treating all problem features and general enough to respond to the varying characteristics of the case study regions for which it is intended. The results show that the heuristic achieves optimality on small instances, exhibits competitive performance in comparison to state-of-the-art solution methods for special cases of our problem, and leads to important savings in the state of practice. Moreover, it highlights and quantifies the savings from allowing a flexible depot assignment. The data from the state of practice comes from a company in the waste collection industry in Geneva, Switzerland.