A Simulated Annealing Heuristic for the Heterogeneous Fleet Pollution Routing Problem

The vehicle routing problem (VRP) is a crucial group of transportation problems, and traditional capacitated VRP (CVRP) directly handles external logistics with a homogeneous vehicle fleet. This paper examines the CVRP from an in-plant logistic view with a heterogeneous fleet in an automotive factory. The homogeneous and heterogeneous vehicle fleets are compared to address the factory's actual in-plant logistics issues. Firstly, simulated annealing (SA), tabu search (TS) algorithms and mathematical modeling were utilized. Then, a hybrid approach was proposed, and all suggested meta-heuristic algorithms were evaluated for homogeneous and heterogeneous vehicle fleets. According to the results, the reduction rates using CVRP with the heterogeneous fleet are 17% and 36% for fleet area and distribution costs, respectively. Also, to examine the effect of the hybrid algorithm parameters on the result, traveling distance was calculated for different scenarios, and multiple regression analyses were applied. According to the multiple regression analysis, the hybrid algorithm's most affected parameter was the cooling coefficient.

In most classic vehicle routing problems, the main goal is to minimise the total travel time or distance while, the green vehicle routing problem, in addition to the stated objectives, also focuses on minimising fuel costs and greenhouse gas emissions, including carbon dioxide emissions. In this research, a new approach in Pollution Routing Problem (PRP) is proposed to minimise the CO2 emission by investigating vehicle weight fill level in length of each route. The PRP with a homogeneous fleet of vehicles, time windows, considering the possibility of split delivery and constraint of minimum shipment weight that must be on the vehicle in each route is investigated simultaneously. The mathematical model is developed and implemented using a simulated annealing algorithm which is programmed in MATLAB software. The generated results from all experiments demonstrated that the application of the proposed mathematical model led to the reduction in CO2 emission.

In Southeast Asian cities, it is common for logistic companies to operate a heterogeneous fleet of delivery vehicles with motorcycles being the preferred vehicle to handle the final phase of delivery. In such scenarios, heterogeneous fleet vehicle routing problem (HFVRP) is generally applied to plan an optimal delivery. However, in many downtown cores of large and rapidly developing Southeast Asian cities, HFVRP is neither viable nor reliable because of road usage restrictions. The purpose of this article is to develop and test a different approach that accurately takes these restrictions into account and provides viable and more sustainable results. Restrictions in this paper refer to situations of urban areas in Vietnam where (i) certain vehicle types are prohibited in specified areas or where narrow alleyways limit the utilization of vehicles that exceed the road capacity and (ii) certain roads are exclusive to certain vehicle types. In networks, limited access and exclusive lanes are represented as links, or arcs, exclusive to one or another. Taking these limitations into consideration, we have developed a unique model, which we have termed Vehicle Routing Problem with Exclusive Links (VRP-EL). The model was validated and tested for its performance on scenarios with varying ratios of exclusive links. Scenarios up to 500 customers were tested on a meta-heuristic algorithm, simulated annealing. VRP-EL produces realistic outcomes. Limiting certain links to be selected according to vehicle types increases overall travel distance. However, this increase outweighs the cost of re-planning and rerouting had they not been constrained initially. The reduction in traveling distance leads to fossil fuel reduction for the overall system. The estimation of reduced carbon emissions through applying the proposed model is presented. Considering the severe traffic congestion and carbon emissions caused by motorcycles in Vietnam, the proposed model leads to a sustainable road environment.

This paper presents a novel bi-objective multi-product capacitated vehicle routing problem with uncertainty in demand of retailers and volume of products (UCVRP) and heterogeneous vehicle fleets. The first of two conflict fuzzy objective functions is to minimize the cost of the used vehicles, fuel consumption for full loaded vehicles and shortage of products. The second objective is to minimize the shortage of products for all retailers. In order to get closer to a real-world situation, the uncertainty in the demand of retailers is applied using fuzzy numbers. Additionally, the volume of products is applied using robust parameters, because the possible value of this parameter is not distinct and belongs to a bounded uncertainty set. The fuzzy-robust counterpart model may be larger than the deterministic form or the uncertain model with one approach and it has with further complexity; however, it provides a better efficient solution for this problem. The proposed fuzzy approach is used to solve the bi-objective mixed-integer linear problem to find the most preferred solution. Moreover, it is impossible to improve one of the objective functions without considering deterioration in the other objective functions. In order to show the conflict between two objective functions in an excellent fashion, a Pareto-optimal solution with the e-constraint method is obtained. Some numerical test problems are used to demonstrate the efficiency and validity of the presented model.

The fleet size and mix pollution-routing problem

A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints

In the last decade interest in environment preservation is increasing and environmental aspects play an important role in strategic and operational policies. Therefore, environmental targets are to be added to economic targets, to find the right balance between these two dimensions. Green logistics extend the traditional definition of logistics by explicitly considering external factors associated mainly with climate change, air pollution, noise, vibration and accidents. Among the logistical activities, the vehicle routing problem (VRP) is one of the most widely researched and has mainly focused on economic objectives, not considering explicitly environmental issues. In this chapter, a realistic variant of the VRP with heterogeneous vehicle fleets in which vehicles are characterized by different capacities and costs, has been considered and external costs have been estimated using international research projects, and have been included as part of a mixed-integer linear programming model to solve a realistic variant of the VRP. To solve medium to large-size VRP instances, heuristic approaches are necessary. An impressive number of heuristic have been proposed for the VRP in the literature. In this chapter, one heuristic is developed to find good solutions to the proposed eco-efficiency model: a savings heuristic when time windows are not considered. Since there are no instances for this problem variant, the algorithm is validated with benchmarking problems adapted from the literature, offering good solutions and quickness. The selection of eco-efficiency routes can help to reduce the emissions of air pollutants, noises and greenhouse gases, without losing competitiveness in transport companies.KeywordsVehicle routing problemSustainabilityExternalitiesGreen logisticsEnvironmental costs

In this paper, we consider the waste collection problem from customers’ location with assumptions that are closer to real life applications of the problem. The fleet of vehicles is heterogeneous and vehicles have separated compartments, namely they have different capacity for each type of waste. Also, the vehicles have different traveling time limitation and different variable and fixed cost according to their types. As well as, the multi-depot vehicle routing problem and the mixed close-open vehicle routing problem are combined together. The objective of the problem is minimizing the cost of servicing to customers with respect to customers’ demands and available constraints. A new mathematical MIP model is proposed and to deal with this problem, three meta-heuristic algorithms are investigated and the results are compared with the results of CPLEX solver. The results of experiments show that the proposed Meta-heuristic algorithms are able to produce satisfied solutions with regard to the MIP solver CPLEX.

In real life situations most companies that deliver or collect goods own a heterogeneous fleet of vehicles. Their goal is to find a set of vehicle routes, each starting and ending at a depot, making the best possible use of the given vehicle fleet such that total cost is minimized. The specific problem can be formulated as the Heterogeneous Fixed Fleet Vehicle Routing Problem (HFFVRP), which is a variant of the classical Vehicle Routing Problem. This paper describes a variant of the threshold accepting heuristic for the HFFVRP. The proposed metaheuristic has a remarkably simple structure, it is lean and parsimonious and it produces high quality solutions over a set of published benchmark instances. Improvement over several of previous best solutions also demonstrates the capabilities of the method and is encouraging for further research.

This work considers a complex logistics routing issue about vehicle pollution, which is connected to the Pollution Routing Problem (PRP). In the PRP, the direct fuel costs and the resulting Greenhouse Gas (GHG) emissions depend on the distance traveled, on the road slopes, and finally, on the speed of a heavy-duty vehicle. In order to solve this problem, a study of the routing for the urban solid waste (USW) collection was carried out in the Miraporanga district, managed by the municipality of Uberlândia, Brazil. Thus, by using free software in a GIS environment, this paper considers to optimize the waste collection routes in order to minimize GHG emissions into the atmosphere. Because it is a complex problem with multifactorial checks in the logistics study, a Process Hierarchy Analysis (AHP) was developed with the functionality to rank the project variables. During the development of the research, a mathematical equation was formulated to estimate the implementation cost (IC) for a USW collection service according to its logistical variables. Related to route optimization, algorithms inserted into QGIS software were used so as to determine the shortest distance path. The results indicated that there was a reduction of 8.31% in GHG emissions per collection. As for the optimization of the PRP, a reduction of 16.44% in fuel consumption was verified, in terms of distance, speed, payload and road slopes

This paper addresses the issue of ship routing design for collecting and transporting the oily liquid waste from a number of ports to a waste treatment center. The aim is simultaneously to construct a set of ship routes and to determine the number and the types of ships in a fleet at the minimum total cost. The problem is considered as a vehicle routing problem with heterogeneous fleet of vehicles and multiple trips (VRPHMT). The VRPHMT is a combination of two variants of the classical vehicle routing problem (VRP) by including two additional features. The first is the heterogeneous fleet of vehicles where number and types of vehicles have to be determined, and the second is multiple trips where vehicles may perform more than one route or trip as long as the total duration of each vehicles does not exceed the planning period.

The Vehicle Routing Problem (VRP) is a well-known combinatorial optimization problem where a number of customers must be served with a fleet of vehicles. The classical variation of the VRP is the Capacicated Vehicle Routing Problem (CVRP) with the additional constraint that each vehicle must have uniform capacity. Many Decision Support Systems (DSS) have been implemented to solve real life problems of the VRP and its’ variants, but they do not allow multiple decision makers to explore several scenarios of a given problem simultaneously and collaborate with each other in order to find the best possible solution. In this paper, we extend our previous work [35] and incorporate in our spatial DSS four variants of the CVRP: (i) Distance Constrained Vehicle Routing Problem (DVRP), (ii) Vehicle Routing Problem with Time Windows (VRPTW), (iii) Vehicle Routing Problem with Backhauls (VRPB), and (iv) Vehicle Routing Problem With Pickup and Delivery (VRPPD). This extension allows decision makers to solve specific routing problems according to their needs. The proposed collaborative spatial DSS allows two decision makers to collaborate with each other in order to find the best possible solution through a tangible interface. The locations are added through interactive Google Maps and other parameters through user-friendly forms that can be manipulated via tangible interfaces. The proposed DSS has been implemented using Java, TUIO protocol, jsprit, and Google Maps.

Although urban freight transport is a significant contributor to the development of a country, it has adverse effects on the environment and the quality of life in urban areas. To reduce these adverse effects, we can deploy sustainable city logistic strategies. Scheduling and routing of vehicles is a crucial decision in city logistic strategies. Hence, in this paper, we solve the Multi-Depot Two Echelon Capacitated Vehicle Routing Problem (MD2E-CVRP), which is a variant of Vehicle Routing Problem (VRP) with heterogeneous fleets at both levels. Since VRP is NP-hard, we have proposed a Simulated Annealing (SA) based heuristic solution algorithm and have tested it on the standard 2E- CVRP and MD2E-CVRP instances. The results obtained from SA have a good solution quality at just one-fiftieth of computational time using CPLEX and was found to be faster than Adaptive Large Neighborhood Search (ALNS) with only a marginal drop in solution quality.

Nowadays genetic algorithms stand as a trend to solve NP-complete and NP-hard problems. In this paper, we present a new hybrid metaheuristic which combines Genetic Algorithms and Scatter Search coupled with a decomposition-into-petals procedure for solving a class of Vehicle Routing and Scheduling Problems. Its performance is evaluated for a heterogeneous fleet model, which is considered a problem much harder to solve than the homogeneous vehicle routing problem.

Real life distribution problems present high degree of complexity mostly derived by the need to respect a variety of constraints. Moreover they are not considered by the classical models of the vehicle routing literature. In this paper we consider a vehicle routing problem with heterogeneous vehicle fleet with different capacity, multi-dimensional capacity constraints, order/vehicle, item/vehicle, and item/item compatibility constraints, different start and end locations for vehicles, and multiple time windows restrictions. We propose an evolutionary algorithm based on the combination of a genetic algorithm and local search heuristics. We investigated the performance of the implemented algorithm in the large-scale retail and in the waste collection industries.