The fleet size and mix pollution-routing problem

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.

A new heuristic for the fleet size and mix vehicle routing problem

The vehicle routing problem is a traditional combinatorial problem with practical relevance for a wide range of industries. In the literature, several specificities have been tackled by dedicated methods in order to better reflect real-world situations. Following this trend, this article addresses the fleet size and mix vehicle routing problem with time windows in which companies hire a third-party logistics company. The shipping charges considered in this work are calculated using step cost functions, in which values are determined according to the type of vehicle and the total distance traveled, with fixed values for predefined distance ranges. A mixed integer linear programming model is introduced and two sequential insertion heuristics are proposed. The introduced methods are examined through a computational comparative analysis in small-sized instances with known optimal solution, 168 benchmark instances from the literature, and 3 instances based on a real-world problem from the civil construction industry. The numerical experiments show that the proposed methods are efficient and show good performance in different scenarios.

ABSTRACTMost of the research on vehicle routing problems has focused on the operational or the tactical level. However, any decision made on a strategic level will affect the lower level decisions. One type of strategic decision that has been considered in the literature is to compose an appropriate fleet of different vehicles to perform transportation tasks, which yields the fleet size and mix vehicle routing problem (FSMVRP). This work defines a new variant of the FSMVRP where the customer demands may vary over a set of periods, for example by having different demands on each day of the week. The objective is to find the best fleet composition that can be used to repeatedly fulfil the customer demands, as well as the best routing with that fleet for each of the different periods in the planning horizon. Simple heuristics incorporating a tabu search are implemented to find the fleet composition. Computational results are reported on instances created from a set of standard FSMVRP test instances.

This paper introduces the Fleet Size and Mix Vehicle Routing Problem with Synchronized Visits (FSM-VRPS), an extension of the Vehicle Routing Problem with Synchronization (VRPS), where a mixed fleet composed of electric and conventional bikes, and passenger cars having different acquisition costs are considered. The problem consists of planning a set of different vehicle routes to serve a set of clients who may require more than one visit by different healthcare specialists, and some of these visits should be synchronized. Moreover, each client must be visited within a specified time window. In addition, the problem uses bikes to reduce Carbon Dioxide (CO2) emission for environmentally cleaner routing operations. This problem has many real-life applications, such as the scheduling of visits for homecare givers in the healthcare sector. We present a mixed integer linear-programming formulation and develop a Multi-Start Adaptive Large Neighborhood Search with Threshold Accepting algorithm. The results showed that our algorithm is highly effective on the FSM-VRPS, as well as on the heterogeneous VRPS. We also demonstrate the advantage of adopting different types of vehicles in terms of reducing the number of vehicles and costs. The analysis of the results also indicated that the new components added to the standard Adaptive Large Neighborhood Search algorithm enhanced intensification and diversification mechanisms during the search process.

Most paratransit agencies use a mix of different types of vehicles ranging from small sedans to large converted vans as a cost-effective way to meet the diverse travel needs and seating requirements of their clients. Currently, decisions on what types of vehicles and how many vehicles to use are mostly made by service managers on an ad hoc basis without much systematic analysis and optimization. The objective of this research is to address the underlying fleet size and mix problem and to develop a practical procedure that can be used to determine the optimal fleet mix for a given application. A real-life example illustrates the relationship between the performance of a paratransit service system and the size of its service vehicles. A heuristic procedure identifies the optimal fleet mix that maximizes the operating efficiency of a service system. A set of recommendations is offered for future research; the most important is the need to incorporate a life-cycle cost framework into the paratransit service planning process.

Logistics activity is both a major energy consumption user and an important CO₂ emission source. As logistics service activity rises in the city, it is crucial to improve the efficiency of fuel usage, as well as decrease the CO₂ emission of unit shipment using vehicle routing optimization. Based on the analysis of the characteristics of energy consumption and emission factors of CO₂ in the vehicle routing problem with multiple vehicles, this paper investigates the problem of fleet size and mixed vehicle routing problem considering CO₂ emissions cost (Green Fleet Size and Mixed Vehicle Routing Problem, G-FSMVRP ). A heuristic algorithm based on a genetic algorithm is given. Finally, a numerical simulation example is given to illustrate the optimization model and its algorithm. The findings show that: (1) the shortest route does not necessarily produce the least energy consumption; (2) compared with the traditional vehicle routing (based on shortest path), vehicle routing considering CO₂ emissions has a lower total cost, but longer distance travelled; and, (3) the genetic algorithm is an effective algorithm to solve the green vehicle routing problem.

In the well‐known vehicle routing problem (VRP), a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. An important variant of the VRP arises when a mixed fleet of vehicles, characterized by different capacities and costs, is available for distribution activities. The problem is known as fleet size and mix VRP with fixed costs FSMF and has several practical applications. In this article, we present a new mixed integer programming formulation for FSMF based on a two‐commodity network flow approach. New valid inequalities are proposed to strengthen the linear programming relaxation of the mathematical formulation. The effectiveness of the proposed cuts is extensively tested on benchmark instances. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009

To address the two urgent issues nowadays of protecting the environment and achieving energy sustainability, it is of strategic importance on a global scale to replace oil-dependent vehicles with electric drive vehicles (EDVs). Numerical simulation and optimization are essential to simulate the actual hardware and minimize the development procedure and cost. Accurate and efficient modeling, control, and optimization technologies have been the indispensable tools. EDVs have been continuously improved owing to the advancement of systematic control and power management, energy systems, batteries, and pack technologies, as well as economic and policy incentives, public awareness of energy sustainability/affordability, and environmental concerns. The primary goal of this special section is to provide timely solutions to technological and economic challenges in modeling, simulation, control, and optimization of EDVs. The accepted papers cover a range of different aspects of modeling, control, and optimization technologies for electric vehicles. A brief summary of them is given as follows. Most of papers are used to investigate the control and power management for EDVs. C. Lin and X. Cheng investigated a traction control strategy with an efficiency model in a distributed driving electric vehicle. S. Zhang et al. studied the optimal control strategy for a dual-motor coupling propulsion electric bus. The dynamic programming is applied to find the optimal control strategy including upshift threshold, downshift threshold, and power split ratio between the main motor and auxiliary motor. To improve the regenerative braking performance, J. Peng et al. provided a hierarchical control strategy for the cooperative braking system of an electric vehicle with separated driven axles. P. Lebeau et al. explored the possible integration of electric vehicles in urban logistics operations. A fleet size and mix vehicle routing problem with time windows for electric vehicles has been developed. In particular, an energy consumption model was integrated in order to consider variable range of electric vehicles. J.-J. Hwang et al. presented a novel charging strategy for fuel cell/battery electric vehicles. In comparison to the conventional switch control, a fuzzy control approach was employed to enhance the battery's state of charge (SOC). In terms of the batteries and grouping technology, S. Barcellona et al. proposed a simple method to investigate the effect of the duty cycle on the batteries lifetime through tests performed on different cells for different kinds of cycle. In this way, a generic complex cycle could be seen as a composition of elemental cycles by means of Rainflow procedures. Consequently, the ageing due to any cycle could be estimated starting from the knowledge of simpler cycles from their research results. For the research field of energy systems and networks, L. Niu and D. Zhang analyzed the actual operational data of electric taxis in Shenzhen, China. An electric taxis charging guidance model was established and guides the charging based on the positions of taxis and charging stations with adaptive mutation particle swarm optimization. The simulation results showed that electric taxis could be evenly distributed to the appropriate charging stations according to the charging pile numbers in charging stations after the charging guidance. In summary, the included seven papers cover the topics of modeling, control, and optimization technologies in EDVs with the new research achievements; we hope and are sure that the readers of this special issue could find valuable references to their research on EDVs.

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.

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.

Fleet sizing and deployment is a central decision problem of bulk shipping organizations. However, business and shipping market cycles induce significant asset price and transport demand volatility, making strategic fleet sizing extremely challenging. We propose a mixed integer programming (MIP) model of the multi-period fleet sizing and deployment problem. We extend the basic MIP model into a robust optimization model in order to account for the inherent uncertainty of the problem. Our approach can assist companies with varying degrees of risk tolerance in deciding the sale, purchase, chartering, lay-up, and scrapping of ships, as well as the deployment of the active ships to contracts and geographic markets. A realistic case study is presented.

SUMMARYA fleet sizing problem (FSP) in a road freight transportation company with heterogeneous fleet and its own technical back‐up facilities is considered in the paper. The mathematical model of the decision problem is formulated in terms of multiple objective mathematical programming based on queuing theory. Technical and economical criteria as well as interests of different stakeholders are taken into account in the problem formulation. The solution procedure is composed of two steps. In the first one, a sample of Pareto‐optimal solutions is generated by an original program called MEGROS. In the second step, this set is reviewed and evaluated, according to the Decision Maker's (DM's) model of preferences. The evaluation of solutions is carried out with an application of an interactive multiple criteria analysis method, called Light Beam Search (LBS). Finally, the DM selects the most desirable, compromise solution. Copyright © 2011 John Wiley & Sons, Ltd.

Service network design with mixed autonomous fleets

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.