A list based threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem

The purpose of this paper is to present a new method to solve the heterogeneous fixed fleet vehicle routing problem (HFFVRP) based on structure-redesign-based bacterial foraging optimization (SRBFO). The HFFVRP is a special case of the heterogeneous vehicle routing problem (HVRP), in which the number of each type of vehicles is fixed. To deal with this combinatorial optimization problem, two improved SRBFOs (SRBFOLDC and SRBFONDC) are presented by integrating the same time decreasing chemotaxis step size mechanism of BFOLDC and BFONDC into the optimization process of SRBFO. SRBFOLDC and SRBFONDC are successfully applied though encoding the position of bacteria by 2N dimensions. The first N dimensional vectors indicate the corresponding vehicle, and the next N dimensional vectors present the execution order of the corresponding vehicle routing. In the simulation experiments, it is demonstrated that SRBFONDC and SRBFOLDC are efficient to solve the heterogeneous fixed fleet vehicle routing problem with lower transportation cost and get better vehicle routing. Besides, SRBFONDC performs best compared with other five bacterial foraging optimization algorithms.

An adaptive memory programming metaheuristic for the heterogeneous fixed fleet vehicle routing problem

Abstract. One of the most significant extension problems of Vehicle Routing Problem (VRP) is the Heterogeneous Fixed Fleet Vehicle Routing Problem (HFFVRP) that aims to provide service to a specific customer group using a limited number of vehicles. HFFVRP consists of determining the minimum cost routes for a fleet of vehicles in order to satisfy the demand of the customer population. The fleet composition consists of various types of vehicles that differ with respect to their maximum carrying load and variable cost per distance unit. This paper proposes a metaheuristic algorithm based on Ant Colony System (ACS) for solving the HFFVRP in which two local search algorithms are used as improving methods. The proposed algorithm is tested on 8 standard instances available from the literature. Computational experiments yield high quality solutions, illustrating the effectiveness of the approach and to be competitive of the ACS with other metaheuristic algorithms.

Product distribution is one of the most important problems in supply chain management. The heterogeneous fixed fleet vehicle routing problem (HFFVRP) is a variant of VRP that aims to determine the routes for a fleet of vehicles while satisfying demand and minimizing cost. The fleet composition is fixed and it consists of various types of vehicles. These vehicles differ according to their variable cost. In this paper, a reactive adaptive memory metaheuristic was developed which made use of the Tabu Search as an improvement procedure (ReAMTS) in order to solve the HFFVRP. The method was implemented and evaluated on two sets of test problems, which are used in the literature. In addition, its performance was compared with an exact method and a set of tractable instances. The computational results demonstrated high-quality results within a reasonable time.

Logic-based Benders decomposition for the heterogeneous fixed fleet vehicle routing problem with time windows

This paper discussed the heterogeneous fixed fleet vehicle routing problem with pick-up and delivery, which different type vehicles have different...

In the current economy, companies are increasingly interested in optimizing their logistics operations to reduce costs and increase agility. Transport logistics is one of the processes to be optimized, since companies have a limited fleet of heterogeneous vehicles, with particular capacities and costs, and have to attend to their customers within restricted periods. These features characterize the problem as a Heterogeneous Fixed Fleet Vehicle Routing Problem with Time Window (HFVRPTW). To solve this problem, this work proposes a method based on the Adaptive Large Neighborhood Search (ALNS) metaheuristic particularly focused on selecting vehicles that reduce the costs of the used fleet. The experiments showed that the proposed method improved <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">\(69.6\%\)</tex-math> </inline-formula> of the benchmark instances compared with the literature state-of-the-art, with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">\(0.44\%\)</tex-math> </inline-formula> of average reduction in the total cost. Besides that, the implemented ALNS algorithm was around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">\(35\)</tex-math> </inline-formula> times faster to run than the most relevant compared work.

Public consciousness on environmental sustainability and industry impact on environment has been increasing for the last few decades. As a result, more and more companies are taking pollution factor into account when planning their logistic activities. Pollution Routing Problem (PRP) is an extension of the classical Vehicle Routing Problem with Time Windows by determining a set of optimal routes and vehicle speed on each route segment for a fleet of vehicles serving a set of customers within specific time windows. In practice, many vehicle routing problems are addressed by a fleet of heterogeneous vehicles with different capacities and travel costs. Emission levels vary by vehicle type due to differences in curb weight and capacity. Therefore, Heterogeneous Fleet Pollution Routing Problem (HFPRP) has been proposed as an extension of Pollution Routing Problem (PRP). Its goal is to minimize the total costs of fuel, greenhouse gas (GHG) emissions, and vehicle variable cost put together in a more comprehensive objective function. This research developed a mathematical model and proposed a Simulated Annealing (SA) heuristic for HFPRP. The performance of the proposed SA heuristic was first verified using benchmark data of the Pollution Routing Problem. The result shows that SA performs better for 7 instances than previous method. SA was then used to solve HFPRP and the results were compared to those obtained by CPLEX. We found that the consideration of a heterogeneous fleet reduces total costs for all instances.

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 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.

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

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.

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 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.

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