Applications of dynamic fleet management - Toepassingen voor dynamisch vloot beheer

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Delft University of Technology

FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING

Department Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

This report consists of 46 pages and 0 appendices. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology. Requests for consult are only taken into consideration under the condition that the applicant denies all legal rights on liabilities concerning the contents of the advice.

Specialization: Transport Engineering and Logistics Report number: 2017.TL.8122

Title: Applications of dynamic fleet management

Author: Daan Vossers

Title (in Dutch): Toepassingen voor dynamisch vloot beheer

Assignment: literature Confidential: no

Initiator (university): dr. R.R. Negenborn

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Delft University of Technology

FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING

Department Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

This report consists of 46 pages and 0 appendices. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology. Requests for consult are

Student: Daan Vossers Assignment type: Literature

Supervisor (TUD): R. Negenborn Creditpoints (ECTS): 10 Specialization: TEL

Report number: 2017.TL.8122 Confidential: no

Subject: Applications of dynamic fleet management

Fleet management is concerned with the planning and optimization of vehicles routes for a given set of customers. When the fleet management is dynamic, it considers scenarios in which not all customer information is known at the beginning of the planning horizon. Dynamic fleet management is used for several real-life applications, and there are multiple opportunities for further use.

The main research question that has to be answered:

• What is a promising future application for dynamic fleet management? Sub-questions:

• What is dynamic fleet management?

• What are important characteristics of dynamic fleet management? • Which mathematical models for fleet management have been proposed? • Which applications are currently considered for (dynamic) fleet management? • Which possibilities for future applications are possible?

• How can the existing models be used in realizing such future applications?

The report should comply with the guidelines of the section. Details can be found on the website. The professor,

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Abstract

Dynamic fleet management includes a wide range of functions, such as vehicle routing, fleet size determination, minimizing the overall costs and financing the vehicles, determining a maintenance schedule, providing information about waiting times and fuel consumption. Dynamic fleet management is needed for unexpected events. That is, to detect deviations from the initial dispatch plan and adjust the schedule.

Dynamic fleet management is applied to a broad variety of domains. It is applied for people transport, freight logistics and emergency vehicles. The objective and solution method are the main characteristics of dynamic fleet management. The most common objectives are minimizing the total travelled distance, the costs or the fleet size or maximizing the profit or service level. The are many mathematical methods proposed for solving those objectives, for instance, heuristic, goal programming, linear programming, Pareto approach, genetic algorithm, aggregation, local search, and colony optimization, and more. There are multiple combinations possible for generating a proper solution.

Electric vehicles are seen as a good alternative to conventional vehicles in terms of reduced en ergy consumption and emissions of air pollutant. However, there a few new challenges with electric vehicles, and especially the battery driven ones. The range is shorter than conventional vehicles and the charging takes more time. New electric vehicles generate more information which the fleet management system can use, like the state of charge of a battery or dynamic traffic information. Especially since the climate change is a global subject, the demand for environmental friendly vehicles is increasing.

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Samenvatting

Dynamisch vloot beheer beslaat een wijde variatie aan functies. Het kan onder andere bevatten: De routering van voertuigen, het aantal benodigde voertuigen bepalen, de totale kosten minimaliseren of een onderhoudsplan opstellen. Dynamisch vloot beheer voorziet ook beheerders en gebruikers van informatie, bijvoorbeeld over de aankomsttijden of het brandstofgebruik. Het systeem kan omgaan met onverwachte veranderingen, zelfs als een rit al begonnen is, en is daarom dynamisch.

Veel verschillende toepassingen gebruiken dynamisch vloot beheer. Het wordt bijvoorbeeld gebruikt voor personen en vrachtvervoer, maar ook door hulpdiensten. Elk vloot beheersysteem heeft een doel en een functie waarmee dit doel bereikt wordt. Meestal is het doel om de totaal afgelegde afstand, de totale kosten of de vloot grootte te minimaliseren. Het doel kan ook zijn om de winst of dienstverlening te maximaliseren. Er zijn veel oplosmethodieken zoals, heuristisch, doel programmering, lineair programmeren, Pareto aanpak, genetisch algoritmes, mierenkolonie optimalisatie en nog veel meer. Meerdere oplosmethodieken kunnen samen gebuikt worden om tot een oplossing te komen.

Duurzaamheid en het milieu worden steeds belangrijker. Elektrische voertuigen lijken een goede vervanging voor het conventionele wagenpark. Er zijn alleen wel nieuwe uitdagingen die overwonnen moeten worden met deze elektrische voertuigen, en dan voornamelijk voor de voertuigen die aangedreven worden door een batterij. De reikwijdte van deze voertuigen is beperkt en het opladen van de batterij kost meer tijd. Wel genereren deze voertuigen meer nuttige informatie, wat het beheerssysteem kan gebruiken, zoals het niveau van de batterij of de actuele verkeerssituatie.

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List of abbreviations

ACO Ant Colony Optimization BEV Battery Electric Vehicle

CCMQGA Cooperative Coevolutionary Multi-objective Quantum Genetic Algorithm DFM Dynamic Fleet Management

DFMS Dynamic Fleet Management System DVRP Dynamic Vehicle Routing Problem

DVRPFTW Dynamic Vehicle Routing Problem with Fuzzy Time Windows GA Genetic Algorithm

GPS Global Positioning System

GVRSP Green Vehicle Routing and Scheduling Problem

IoT Internet

MATSim Multi-Agent Transport Simulator MPLSFP Multi-Period Liner Ship Fleet Planning OV Openbaar Vervoer (public transport)

RDHFVRPTW Restricted Dynamic Heterogeneous Fleet Vehicle Routing Problem with Time Windows RDS Radio Data System

SoC State of Charge SUV Sports Utility Vehicle

SVRP Static Vehicle Routing Problem TMC Traffic Message Channel TSP Travelling Salesman Problem VDS Variable Direction Sign VRP Vehicle Routing Problem

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List of figures

Figure 1 Functions of fleet management... 9 Figure 2 Overview of the taxonomy adapted from Psaraftis [43] ...21

List of tables

Table 1 Overview of applications and objectives ...19 Table 2 Objectives and solution methods of the routing problem in literature (chronologi c)...25

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Chapter 1 Introduction

Fleet management is a term used for a wide range of solutions for different fleet-related applications in the field of transportation, logistics and distribution [1]. Fleet management is the coordination of a set of vehicles, including the target-based planning, supervision and control based on the available transport resources and constraints. Dynamic fleet management will focus on real-time management of a distribution system. If one has a fleet of multiple vehicles, it can always be useful to have a sort of fleet management. Fleet management is applicable for people transport (e.g. taxi’ s, busses, cyber cars), freight (e.g. delivery truck, trains, aircraft) or emergency vehicle (e.g. ambulances, fire trucks). Fleet management can include the (dynamic) routing of vehicles, the maintenance, the purchase or leasing of vehicles, customer administration etc.

For companies with multiple vehicles, it is important to have some kind of fleet management. A reason can be to reduce the operation costs or to track all vehicles. Also, fleet management can be useful to reduce the ecologic footprint of a company, by reducing the driven kilometres or by the smart use of electric vehicles.

The number of electric vehicles is increasing [2]. The battery capacity is getting higher and the investment costs are decreasing. These vehicles have the potential to reduces fossil fuel dependency and CO2 emissions. Therefore, it is necessary to investigate if fleet management can be helpful for future applications.

1.1 Research question

In this report, the main question that is answered is:

What is a promising future application for dynamic fleet management?

1.2 Sub-questions and approach

To get an answer to this main question, several sub-questions are examined. To start with, it is important to know what fleet management is and which applications are currently using it. This will be answered by the first two sub-questions.

1. What is dynamic fleet management?

2. Which applications are currently considered for (dynamic) fleet management?

Thereafter, an answer is given to the more mathematical background of fleet management. Proposed models from literature are discussed, as well as the key characteristics of dynamic fleet management.

3. What are important characteristics of dynamic fleet management?

4. Which mathematical models for dynamic fleet management have been proposed?

After answering these questions, the possible future application need to be investigated. Two questions will be answered.

5. Which possibilities for future applications are possible?

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1.3 Contents of this report

Chapter 1 gives a general introduction of dynamic fleet management. Multiple themes are discussed, such as the purchase, the maintenance and the routing problem. In Chapter 2 are the various functions of fleet management described. Thereafter, in Chapter 3, current applications of fleet management are described, separated into three domains: people, freight and emergency vehicles. In Chapter 4 the main characteristics of fleet management and their objectives are denominated. The different solutions methods are also discussed. In Chapter 5 possible application for fleet management are given. The clever use of batteries is important here. Finally, in Chapter 6 the main research question is answered and the conclusion is given, followed by some recommendations for further research.

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Chapter 2 Functions of fleet management

Fleet management can include a range of functions, the most common examples are vehicle routing, vehicle financing and vehicle maintenance. But also, driver, health and speed management, fuel consumptions and vehicle telematics of possible functions. The central task is to route vehicles to the customer, and this is what I focus on in this report. Some of these functions are described here below, whereby the routing problem is the most important and comprehensive. The applications described in Chapter 3 and objectives in Chapter 4 are mainly about this problem, although also the other functions are shortly described.

Figure 1 Functions of fleet management

2.1 Routing

Approaches to the planning of a fleet of vehicles typically focus on the development of near-optimal plans. The most effective vehicle routing algorithms can be either static or dynamic.

2.1.1 Static Vehicle Routing Problem (SVRP)

Static vehicle routing is concerned with the planning of optimal vehicles routes for providing a given set of customers. It generalizes the Travelling Salesman Problem (TSP), in which a salesman is to visit a set of cities and return to the city he started in. The first introduction of the VRP was in 1959 by Dantzig and Ramser, where they concerned the optimum routing of a fleet of gasoline delivery trucks between a bulk terminal and a large number of service stations supplied by the terminal [3]. A VRP model a transportation problem whose objective is to deliver and/or pick products to geographically distributed customers with a fleet of vehicles. Minimizing the total route costs is the overall objective problem. The resolution aims generally at minimizing the total travel time, the travel distance, the vehicles used, the costs, etc. There are also some constraints such as; not overloading the vehicle, maximum waiting time and serving each customer only once. The SVRP is a well-studied problem in literature, for a comprehensive overview, see Toth and Vigo [4]. A good definition of the SVRP is given by Larsen [5]:

• All information relevant to the planning of the routes is assumed to be known by the planner

before the routing process begins.

• Information relevant to the routing does not change after the routes have been constructed. Billhardt gives the following definition for SVRP [1]:

• All relevant data is known before the planning starts, short- and long- term decisions have the

same importance, and the time available for creation, verification, and implementation of route plans is of minor importance. The use of an initial fleet schedule, although necessary, is by no means sufficient because it might not cope adequately with unexpected events during

Fleet management Chapter 2 Routing Section 2.1 Static Section 2.1.1 Dynamic Section 2.1.2 Purchase Section 2.2 Fleet size Section 2.2 Maintenance Section 2.3 Battey level Section 2.3 Environmental impact Section 2.4 Information services Section 2.5

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execution, such as traffic delays, vehicle break- downs, road works, and new customer requests or the cancellation of pre-existing ones, which causes fleet delays, unexpected costs, and poor customer service.

2.1.2 Dynamic Vehicle Routing Problem (DVRP)

In contrast with the Static Vehicle Routing Problem, Dynamic Vehicle Routing considers scenarios in which not all customer information is known at the beginning of the planning horizon. For instance, traffic and weather conditions can change, new requests can arise, vehicles can break down, etc. So, the routers must be re-planned when this new information becomes available. This makes the DVRP harder to solve then the SVRP [6]. A description of the dynamic routing problem by Billhardt [1] and Larsen [5]:

• Dynamic vehicle routing is needed to handle unexpected events. That is, to detect deviations

from the initial dispatch plan and adjust the schedule accordingly by suggesting effective re- routing immediately. In this context, timely decisions are very important because the time available for verification, correction, and implementation of changed route plans is often very short.

• Not all information relevant to the planning of the routes is known by the planner when the

routing process begins.

• Information can change after the initial routes have been constructed.

Nowadays the DVRP is a well-known and studied problem, but until the millennium there wasn’t done much research. In the late seventies the first papers were published, in the time period after 2000 a real explosion of related papers were published [7]. Pillac et al. summarize these papers in his publication.

According to Psafartis [8][9] there are 12 main advantages of dynamic vehicle routing over static vehicle routing:

1. Time dimension is essential. 2. The problem may be open-ended.

3. Future information may be imprecise or unknown. 4. Near-term events are more important.

5. Information update mechanisms are essential.

6. Re-sequencing and reassigning decisions may be warranted. 7. Faster computation times are necessary.

8. Indefinite deferment mechanisms are essential. 9. Objective function may be different.

10. Time constraints may be different.

11. Flexibility to vary vehicle fleet size is lower. 12. Queueing considerations may become important.

Powel et al. [10] argue that there is a difference between the dynamics of a problem, a model and an application. These are their conclusions:

• A problem is dynamic if one or more of its parameters are a function of time. This includes models with dynamic data that change constantly as well as problems with time-dependent data which are known in advance.

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• A model is dynamic if it explicitly incorporates the interaction of activities over time. Here one should distinguish between deterministic dynamic models and stochastic models.

• An application is dynamic if the underlying model is solved repeatedly as ne w information is received. Consequently, solving models within dynamic applications require huge computational resources.

So, to conclude, there are advanced options with a dynamic routing problem, although the static vehicle problem is mostly the start of the problem.

2.2 Purchase and fleet size

Fleet replacement is a valuable expense. Timely prediction of this expense is very important for companies with a large fleet of vehicles. However, fleet replacement can also save the company money, for instance by replaces the vehicles for energy efficient ones. In this report are multiple examples given of models that account for the replacement.

Of course, the fleet is size important. Too many vehicles lead to a lower utilization rate. Also, the right composition of a fleet important, sometimes it is better to have all uniform vehicles and sometimes a combination of different is desirable. Different scenarios are described further in this report.

2.3 Maintenance or fuel/battery levels

With the use of fleet management, it is possible to make a good maintenance plan. Most of the vehicles have an onboard computer which can send the current status of the vehicle to a central management system. Vehicles who need maintenance can be scheduled.

Also, the fuel level or the state of capacity (SoC) of the vehicles can be monitored with a management system. In chapter 4 of this report can more information found about the use of batteries in a fleet of electric vehicles.

2.4 Environmental impact

By implementing fleet management environmental impact can be reduced. This can be realized in multiple ways, by minimizing the travelled distance or avoiding traffic jams, but also by clever use of electric vehicles. In chapter 3 are some examples given of environmental friendly ways of implementing dynamic fleet management.

2.5 Information services

Dynamic fleet management can generate a lot of useful data. For companies, but also for the customers. By combining data received from the tracking system is it possible to make a profile for any given driver, such as average speed, detours, speeding. Also vehicles characteristics can be monitored by the fleet management system. For customers is relevant information about the arrival time or occupancy rate available.

2.6 Concluding

Dynamic fleet management includes a width range of functions. The most common function is about the vehicle routing problem, this problem can be static or a dynamic. However, fleet management can also include fleet size determination, minimizing the overall costs and financing the vehi cles, determining a maintenance schedule, providing information about waiting times and fuel consumption and a lot more. Fleet management can also be used to minimize the environmental impact of the

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vehicles. Dynamic fleet management is needed to unexpected events. That is, to detect deviations from the initial dispatch plan and adjust the schedule. In this context, timely decisions are very important because of the time available for verification, correction and implementation of changed route plans is often very short.

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Chapter 3 Current applications of fleet management

In the previous chapter the functions of fleet management are described. In this chapter various applications are described with these functions. There are multiple applications for dynamic fleet management known in literature. In this report, the applications are divided into three domains; people transport, freight logistics and emergency vehicles. This gives the answer to the second sub-question:

• Which applications are currently considered for (dynamic) fleet management?

In the first section, the applications of fleet management concerning people transport are mentioned. There are examples given of bus, bike, car and taxi. In the second part the applications concerning the freight transport are described. This section is divided into road, rail, air and water transport. The third section is about emergency vehicles. This chapter ends with a summarizing table of all the current applications of fleet management.

3.1 People transport

In public transport the transport-vehicle can be shared with other passengers, and so the solution of the routing problem is an optimum between multiple requests. On the other hand, with private transport, only one person (or group with the same objective) is in the vehicle, thus the solution is based on your objective. Not always is the objective of the fleet management to find the shortest path or travel times, it can also be minimizing the waiting time of optimizing the allocation of vehicles.

3.1.1 Bus

With the introduction of technologies as the Global Positioning Systems (GPS), the constant improvement of telematic infrastructure and technologies, the possibilities for fleet management are significantly increased in the recent years [11]. Also, the introduction of better communication tools like VDS (Variable Direction Sign and text panels) and warming message via broadcast (RDS/TMC or cellular-phone-based services) provide real-time information to the operators and the users of the transport services.

The iBus system in London is a good example of dynamic vehicle management in real-life [12]. The busses are equipped with an automatic vehicle location system to improve the efficiency of the transport system. Satellite-based location and communication systems, in this case, GPS, provide the location of each vehicle. This information is used for real-time passenger, fleet management and operations. In the paper of Hounsell et al., this information is used to calculate the dwell times estimations and for a bus performance analysis.

For the largest bus company in Hong Kong, Li et al. have introduced another objective of the fleet optimization [13][14]. Their goal is not consumer orientated, but rather environmental. Transportation, in general, is a major cause of the pollutant emissions and the exhaust gasses of busses in particular. Updating the fleet of busses to the newer emissions standards can reduce the contribution of emissions substantial. The proposed model of Li et al. analyses the total net profit by either retrofitting or by early-retiring the current busses. Since the emissions standards change faster than the lifespan of a bus, this becomes a dynamic model. With a remaining life, additional benefit-cost analysis, the most beneficial management scheme for the bus fleet can be identified.

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3.1.2 Bike

Dynamic fleet management is also applicable for bike sharing. By bike sharing, people can rent a bike at several depots and return it at a different depot. An example of this is the OV-fiets in the Netherlands or the Santander-Cycles in London, but this concept is widely spread through the world. The demand for each bike-depot is different during daytime even as the depot where the bikes are returned. Caggiani and Ottomanelli made a simulation model for the repositioning of the bikes [15]. Their objective is to minimize repositioning costs, with a high customer satisfaction level. The customer satisfaction level is determined by the time it takes to find an available bike or a free docking depot for returning the bike to any depot at any time.

3.1.3 Cyber cars

The amount of private cars in big cities all over the world increased greatly last few years. The highly-disorganized behaviour of the human drivers of these cars are causing severe problems, like many accidents, frequent congestion and increasing energy consumption and pollution. Due to these problems, the quality of life has been degraded in these cities. Multiple car manufacturers and it-companies, such as Google and Tesla, are working on the development of self -driving autonomous cars, the so-called cyber cars. One of the targets of the use of cyber cars is the to minimize the ownership of cars, with other words, multiple people share the same car(s), with the result that fewer cars are needed and a higher occupation level of each car. Dynamic fleet management must be used for coordination of the fleet of cyber cars. The difference to bikes is that empty cars can drive towards the customer by itself, while the customer must move to the bike.

An overview of the literature on cyber cars is made by Luo [16]. One of the first researches on using fleet management in real-life is done by Melki and Hammadi [17]. Here, a fleet of cyber cars drives in an urban environment and new requests are generated by persons with a PDA. The system has to integrate these requests into the process of transportation strategy. The Dijkstra Algorithm is used to calculate the optimal path.

3.1.4 Taxi

Taxi dispatching is a typical dynamic vehicle routing problem. In big cities, enormous amounts of taxies and passengers have to be dispatched every day. Traditional this dispatching was done with macroscopic models, while nowadays with the increasing computing power, also the microscopic ones are implemented. Maciejewskie et al. [18][19] have done a lot of research into the taxi dispatching, with case studies in Barcelona [20], Berlin [21], Mielic (Poland) [22] and Singapore [23]. A Multi-Agent Transport Simulator Dynamic Vehicle Routing Problem (MATSim DVRP) is used in these four cities for simulating the taxi dispatching. Only immediate requests with unknown destinations are considered in this model. For new requests the nearest idle taxi is dispatched.

3.1.5 Car rental or sharing

Car rental is very similar to the bike sharing problem. People can hire a car at one location and return the car elsewhere (single-trip) or they return at the start location (round-trip). Therefore an unbalance can arise between multiple cities [24]. Li and Toa [25] developed a dynamic programming model where first the initial car distribution is determined and afterwards the vehicle transfer policy. For the solving of this problem, they use a heuristic method which compares a series of linear programming problems. The heuristic method for the initial set-up of car distribution performs well, however, the

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corresponding vehicle relocation policy is not appropriate. The overall performance of their solution can decline drastically even with the optimal fleet size.

Car sharing is a slightly different problem then car rental, although they have many similarities. Like the car renting there are models for single-trips and round trips, although more models are possible such as one-way-free-floating trips, where cars can be returned to any legal on-street parking space, or peer-to-peer models, where car owners make their private vehicle available instead of an operator. Hu and Liu [26] describe this situation as a mixed queuing network model with the objective to maximize the profit by optimizing the fleet size and station capacities. All constraints are modelled as a queue, like the rental station, each route, the road congestions and the booking process. The conclusion of their analysis is that a higher customer service rate will generate the optimal de sign with lower fleet size and lower parking capacities.

3.2 Freight logistics

The best-known freight logistics problem for dynamic fleet management is the Traveling Salesman Problem (TSP) (or the Traveling Repairman Problem), however, there are much more applications for DFM. For transport on the road, the TSP applicable is, but freight can also be transported over water, through the air or by rail. Furthermore, DFM is used for some other applications, like the coordination of shipping containers.

3.2.1 Road

The traveling salesman problem is the most described DFM for freight transport on the road, for a complete literature overview see Matai [27]. Most fleet management algorithms focus on the development of near-optimal distribution plans, with the goal to minimize the distributions costs. In an urban environment, however, the transportation costs are more dependent upon unexpected costs and delays, which arise during the execution of a delivery plan. According to Zeimpekis and Giaglis there are three main types of accidents which cause the most costs and/or delays [28].

• Incidents originating from the clients served; for instance, order cancellation, new customer request, delivery time changes and lack of unloading or parking space at the customer site. • Incidents related to the road infrastructure; for instance, traffic congestion, weather conditions

and road construction.

• Incidents related to the delivery vehicle; for instance, empty batteries, accidents and mechanical failures.

In several cities vehicles have access restrictions for freight transport in the city centre. These limitations can apply at a certain time and/or on vehicle characteristics, like engine type, CO2 emissions, noise, etc. Often small green vehicles are allowed because they satisfy the conditions. Franceschetti et al. [29] study the vehicle routing problem for a heterogeneous fleet for city logistics. They formulate the problem as a dynamic program and a mixed integer l inear problem. The result of their model is that the restrictions can be counterproductive and may lead to an increase of vehicles in the service area. They also found out that it is better to have a homogenous fleet then a heterogeneous fleet because the costs are slightly higher for a homogenous fleet, however, the complexity of the logistical modal increased enormously for a heterogeneous fleet.

Also Zhao et al. share this conclusion, and they have an addition to this conclusion [30]. In scenarios where the demand is high and with a low fuel economy, hybrid vehicles are preferred to fulfill the daily

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requirements. With a low demand and a high fuel economy, current diesel trucks are capable with reasonable low costs. However, more electric trucks are of course better when tailpip e emissions constraints become more important.

Giglio et al. [31] have modelled the real-time management for a fleet of tank trucks in the north of Italy. These trucks deliver fuel to multiple gas stations through the country. Weather and traffic conditions, truck failure and new urgent orders (which must be immediately dispatched) are the dynamical factors for their model. There are two stages proposed, first trip re-scheduling and subsequently trip optimization. The trucks are equipped with GPS so the re -scheduling of the trucks can be done real-time. All tests have shown that the proposed strategy is effective for shorter delivery times.

3.2.2 Water

The increasing globalization and inter-dependence of various economies caused an increase of seaborne trade. However, this was the scenario before 2008, when the economic crisis s tarted. Especially the containerized trade by liner shipping was the fastest growing sector in seaborne transportation.

3.2.2.1 Ships

Each liner container shipping company has to make a suitable fleet management system, in order to seize market share in the very competitive market. Meng et al. developed a multi-period liner ship fleet planning (MPLSFP) to determine the optimal fleet seize within a multi-period planning horizon [32]. The fleet management plan identifies the current and future quantities and types of ships required, and it is used to determine to assignment and operation of the fleet. The objective of the algorithm is to maximize the profit with a given container shipment demand. The model is solved by a shortest path algorithm on an acyclic network. Results show that purchasing ships seems to be a more profitable in long-term than chartering ships. On the short-term chartering is much cheaper than buying ships. Ming et al. made a more extensive model for the fleet planning of a shipping company [33]. The forecast for demand is based on a Grey-Markov chain, so the demand is more uncertain. These uncertainties play an important role in the decision-making of the shipping companies. According to Ming the results of this model are much better.

Christiansen proposed a fleet management model for a specific case; routing and scheduling a fleet of fuel supply vessels [34]. The model is based on a real-life operational problem of the Hellenic oil company in the broader area of Piraeus Port where their supply ships have to fuel anchored customer ships. The problem is formulated as a rich multi-trip vehicle routing problem. The researchers developed and compared a path-flow model and an arc-flow model. The path-flow model can best be used in real planning situations according to computational studies.

3.2.2.2 Containers

The world container fleet size keeps growing according to Dong [35]. However, there is an unbalance in trade from most of the geographical locations. The result is that there are a lot of empty containers is Europe. Repositioning the empty containers from one port to another is essential. At least 20% of the global port handling is accounted for the handling of empty containers. For repositioning the empty containers, a dynamic fleet management system with multi-vessel, multi-port and multi-voyage shipping are considered. With a Genetic Algorithms (GA) the optimal solution is calculated, with the

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transportation costs and lost-sale penalty costs). The proposed model can save from 24% to 69% of the total costs.

Shintani et al. propose a solution that can save even more costs; with the use of foldable containers [36]. They model the empty container flow as an integer programming problem with different strategies. This container fleet management carries out numerical experiments for optimizing the repositioning of the empty containers. The objective is to minimize the total costs as well.

3.2.3 Air

Fleet management is also very important in the air. Airliners have complex logistic problems for scheduling their aircrafts and crews, which are both very expensive resources. Each flight should, of course, be covered by one aircraft and by one crew, and they both need to be at the right location at minimum costs. Salazar-González describes this situation for a regional carrier operating in the Canary Islands region [37]. This paper gives a solution approach for an integrated fleet-assignment, aircraft-routing and crew-pairing problem. The solution approach is a heuristic algorithm based on an integer programming model. This approach is a success, the airline is currently using this approach.

Not only the scheduling of the crew and aircrafts is important for fleet management tools but also keeping the costs as low as possible. Environmental charges for air pollution, noise and fuel consumption are a major cost driver. Khoo et al. describe in their paper a bi-objective dynamic programming approach for airline green fleet management [38]. The objective is to find an optimal aircraft acquisition, purchase or lease, with minimizing the costs. With this method, the profit of the airlines is affected, however, this could be recovered from environmental costs savings. So, this method could assist airlines to become a little bit greener.

3.2.4 Rail

Railcars are a significant investment in the chemical industry. These railcars with chemicals transported are according to Kallrath 8% of all transported goods [39]. Through safety regulations, the transport of many products is simply prohibited for road transport. As well are the railcars superior to trucks in terms of the maximum volume that can be transported. Also, are the railcars much more environmental friendly and a reliable option. Therefore, the chemical companies are continuously trying to optimize the fleet. The model of Kallrath is based on the German chemical company BASF and derives the optimum number and size of different rail cars. This approach of the fleet management is done with a mixed integer linear programming model. With this tool, the cost savings are nearly 2 million euros so far.

3.3 Emergency vehicles

The last domain of applications for fleet management are the emergency vehicles. Ambulances, fire trucks and humanitarian operations are discussed.

3.3.1 Ambulances

Ambulances are strategically located over the territory they serve. However, the distribution of emergency calls is very dynamic and uncertain. It can even happen that the vehicles available to respond to these calls no longer cover their region properly, even if the allocation of these vehicle is carefully planned with initial information. Re-allocation is then necessary. According to Bélanger et al. [40], there are multiple static and dynamic vehicle routing problems used, and they have analyzed their effectiveness. In most of the cases, a dynamic model is used. The result shows that the dynamic models

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achieve a higher service level compared with the static models, but it also shows that the costs of re -allocating are significantly higher.

Billhardt has done a case study in the coordination of ambulances in Madrid [1]. The objective is to reduce the time between an incoming emergency call and the moment the ambulance arrives since shorter response time are directly correlated with lower mortality rates. A dynamic fleet management system is proposed, in which the ambulances are the vehicles and the calling patients the tasks. 29 hospitals and 29 ambulances are used. The Dimitri Bertseka’s auction algorithm assures an assignment that minimizes the average ambulance response time. The average response time decreases with 15,8% compared with the currently used static management tool.

3.3.2 Fire trucks

Most of the cities have multiple fire stations, where the fleet of vehicles remains fixed at their own station. However, seasonal patterns suggest the frequency of fire alerts changes according to their geographical distribution. Santiago is such a city, with a lack of a dynamic fleet management strategy for their fleet. Pérez et al. [41] propose a model with the goal of maximizing the amount of standards responses, within as short as possible time of arrival. The model they used is an allocation model with multiple periods, a fixed number of fire trucks and a restricted number of re-allocations of the vehicles. With respect to the current situation, the number of standard responses is increased between 6% and 20%.

Unplanned fire occurs not only in cities but also in woods, forest, bush and grass. In Australia bushfire has been a recurring problem according to Shahparvari et al. [42]. Since short-notice emergency response and rescue operations are very important, a dynamic vehicle routing model is introduced. The model computes not only for fire trucks but also for evacuation vehicles, the safest routes and schedules for late evacuees under various time windows and road disruption risks. With the use of a heuristic solution method, the best solution is calculated. Compared with the 2009 Black Saturday bushfires in Victoria, Australia, the model outputs are useful in the development of an emergency evacuation plan.

3.3.3 Humanitarian operations

One of the most critical operations in humanitarian development programs is the last-mile distribution according to Eftekhar et al. [43]. Multiple vehicles, typically SUV’s, transport food, materials and humanitarian workers. Fleet management is needed for allocating the right types of vehicles to different missions, and purchasing and reselling the right quantity of vehicles with the features needed for each situation. According to Eftekar it is impossible to use one algorithm for this vehicle management since all situations are very different. Therefore, better data and analysis is needed for making applicable fleet management tool.

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3.4 Overview of the literature

An overview of the applications described in this chapter is listed in Table 1. As earlier mentioned in the introduction, there are multiple objectives possible for fleet management. The objectives mentioned in the discussed papers are:

• Vehicle routing. Fleet management is used for determining the optimal route for the vehicles.

• Environmental impact. The CO2 emissions are being minimized. • Vehicle purchase. The optimal vehicle composition is determined. • Customer satisfaction. Customer satisfaction must be as high as possible.

• Travel information. The fleet management gives information about arrival-, travel- and waiting times.

• Relocating vehicles. The unbalance of vehicles between multiple stations is handled by the fleet management system.

• Minimizing the costs. The overall costs are kept as low as possible.

• Minimizing the travelled time. The travelled time of each vehicle is minimized. • Determine the fleet size. The optimal number of vehicles is determined.

Table 1 Overview of applications and objectives

Application Objective Author, Year

V e h ic le r o u ti n g En vi ro n m e n ta l im p ac t V e h ic le p u rc h as e C u sto m e r sa ti sf ac ti o n Tr av e l in fo rm ati o n R e lo ca ti n g ve h ic le s M in im iz in g th e c o st M in im iz in g tr av e lle d ti m e D e te rm in e f le e t si ze Pe o p le tr an spo rt

Bus x x Belmonte et al., 2008 [11]

x x Hounsell et al., 2012 [12] x Li et al., 2015 [13] [14]

Bike x x x Caggiani and Ottomanelli,

2013 [15]

Cyber cars x Melki and Hammadi, 2008 [17]

Taxi x x x Maciejewski et al., 2016 [18]

x x x Maciejewski and Nagel, 2012 [19]

x x x Grau and Romeu, 2015 [20] x x x Maciejewski and Bischoff,

2015 [21]

x x x x Maciejewski and Nagel, 2013 [22]

x x x Seow et al., 2010 [23] Car rental x Oliveira et al., 2016 [24]

x x Li and Tao, 2010 [25] x x Hu and Liu, 2016 [26]

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Fr e ig h t l o gi st ic s

Road freight transport x Matai et al., 2010 [27] x x Zeimpekis et al., 2008 [28] x x x Franceschetti et al., 2017 [29] x Giglio et al., 2004 [31]

Ships x x Meng and Wang, 2011 [32]

x x Ming et al., 2009 [33] x Christiansen et al., 2016 [34] Containers x x x x Dong and Song, 2009 [35]

x x x x Shintani et al., 2010 [36] Aircrafts x x x Salazar-González, 2014 [37]

x x x Khoo and Teoh, 2014 [38]

Train x Kallrath et al., 2016 [39]

Em e rg e n cy ve h ic le s

Ambulances x x Bélanger et al., 2016 [40] x x Billhardt et al., 2014 [1] Fire trucks x x Pérez et al., 2016 [41]

x x Shahparvari et al., 2017 [42] Humanitarian vehicles x x Eftakgar and Wassenhove,

2016 [43]

3.5 Concluding

Dynamic fleet management is applied to a broad variety of domains. Is it applied for people transport, including bus, bike, taxi, etc. Also for commercial delivery vehicles, courier fleets, ships, aircrafts and trains is fleet management applied. Furthermore, it is applied for emergency vehicles (ambulances, fire trucks and humanitarian operations). The objective can differ for each application. Also, the fleet management can have multiple objectives for each application.

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Chapter 4 Characteristics of dynamic fleet management

In this chapter the main characteristics of dynamic fleet management are discussed. According to Psaraftis [44] there are 11 main criteria in the taxonomy of fleet management, see Figure 2. This taxonomy is a guide-line for this chapter, although a different categorisation is used. The main domains that are described in this chapter, are the objective function, the time constraints, the nature of stochasticity and some mathematical models.

Figure 2 Overview of the taxonomy adapted from Psaraftis [43]

The sub questions that are answered is this chapter are:

• What are important characteristics of dynamic fleet management?

• Which mathematical models for dynamic fleet management have been proposed?

First the objective functions of fleet management are introduced. Thereafter, the mathematical solutions proposed in literature are discussed. With both these two variables, a table with relevant literature studies is compiled. Since the majority of the papers is about the vehicle routing problem, and especially about the routing problem with time windows, a separate section is dedicated to this subject.

4.1 Objective function

The objectives for the routing problem can be multiple and diverse. The most common objectives are minimizing the travel distance, the travel time, the total costs, environmental emissions and/or the fleet size, and maximizing the profit, customer satisfaction and/or level of service [45].

4.1.1 Minimizing the travelled distance

Minimizing the travelled distance is also known as the shortest path problem and is one of the best-known objectives for the routing problem, for a complete overview of the shortest path literature, see Cherkassky and Gallo [46][47]. The Dijkstra algorithm is the basic strategy for solving the problem with non-negative edge lengths [48]. Since the Dijkstra algorithm is from 1959, many improvements are supposed, particularly in speeding up the calculation process, see Wagner [49]. The Dijkstra algorithm can also be used for other objectives by replacing the distance for instance for time or costs.

4.1.2 Minimizing the costs

Minimizing the costs can be achieved in multiple ways [50]. It is often a combination of multiple variables, such as minimizing the travelled distance or the amount of vehicles or by increasing the loading rate of a vehicle. Furthermore, this can be achieved for instance by replacing old vehicles with newer more fuel-efficient ones, which have lower operational costs. Also, lowering the maintenance costs can be effective, this can be done by monitoring the vehicle behaviour. Minimizing the overhead costs has also the effect of lower costs. Overhead costs, or indirect costs, are for instance costs for management and administrative staff, buildings and areas, fuel sites, computer systems and

Taxonomy of fleet management

Type of

problem Logistical context Transportation mode Objection function Fleet size constraintsTime

Vehicle capacity constraints Ability to reject customers Nature of dynamic element Nature of

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environmental taxes. Various models are described in literature with one of these methods for minimizing the total costs, see Table 2.

4.1.3 Minimizing the number of vehicles

The goal of minimizing the number of vehicles explains itself. Although there are several reasons for minimizing the number of vehicles, for instance for lowering the investment costs or operational costs. Another example is humanitarian operations, where a transport ship has a limited capacity, thus the amount of vehicles should be as low as possible [43].

4.1.4 Maximizing the profit

This goal explains itself, the profit must be as high as possible. It can be achieved in several ways, but most of the time by combining solutions from the previously mentioned goals.

4.1.5 Maximizing the service level

The goal of the solution presented by Djadane et al. [51] is to provide the customer a given level of service. For qualifying the level of service a balance between service quality and risk-taking has to be found. The time window and travel times are subject to variations. Each time a new request arrives the model has to choose between accepting the new order in the current route, which results in a longer total travel time, or planning the order in a new route, which gives that specific order a longer travel time.

4.1.6 Minimum CO2 emissions

The environmental impact of transport received increasing attention from governments and organizations. Smart and green vehicle routing can help to minimize the emissions of these polluting vehicles. Lin made an overview of the papers about green vehicle routing [52]. Environmental, ecological and social effects are important for green vehicle routing. The increasing amount of publications about green vehicle routing is the paper of Lin.

Xiao and Konak [53] have suggested a new objective function, the Gree n Vehicle Routing and Scheduling Problem (GVRSP). The goal of this function is to minimize the CO2 emissions. The function has hierarchical objectives and weighted tardiness. The function is composed out of earlier mentioned functions, i.e. the minimum distance and minimum travel time function. The performance of the GVRSP is tested on large-sized problems up to 100 nodes. A reduction of 50% of CO2 emissions can be achieved compared with minimum distance functions (on average 12%) and minimum travel time functions (on average 28%).

Another solution for reducing the CO2 emissions is obviously the use of an environmental friendly vehicle. However, it can be very expensive to renew the total fleet of vehicles. And since the vehicles are becoming more and more environmental friendly, it becomes very costly the keep the whole fleet with the latest technology. Yang et al. [54] and Helfert et al. [55] propose a solution of the Vehicle Routing Problem with (soft) Time-Window for multiple environmental vehicle types. This is called the Hybrid Fleet Vehicle Routing Problem. A hybrid genetic algorithm (GA) is used for this problem. There are three main objectives examined; distribution costs, customer satisfaction and environmental pollution. After a sensitivity analysis, the results show that speed has a strong correlation with the environmental pollution and the operating costs.

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4.1.7 Other objectives

In the literature discussed in this research two other objectives, namely maximizing the equalization of vehicle travel time and optimize makespan, are mentioned. These objectives are very rare.

4.2 Mathematical solutions

In this section possible mathematical methods are explained. Furthermore, in Table 2 an overview of the most used mathematical methods is given.

4.2.1 Heuristic

A heuristic mathematical method is a practical method which is sufficient for immediate goals. The solution is not necessarily the perfect or the most optimal, but a he uristic method is used to speed up the process. Heuristic means “find” or “discover” in the ancient Greek (εὑρίσκω).

4.2.2 Linear programming

Linear programming is a method for finding the best solutions for requirements that are represented by linear relationships. Is it a good method for minimizing the costs or maximizing the profit. The standard form consists of three parts, a linear function (1), constraints (2) and non-negative variables (3):

(1) 𝑓(𝑥1,𝑥2) = 𝑐1𝑥1+ 𝑐2𝑥2

(2) 𝑎11𝑥1+ 𝑎12𝑥2≤ 𝑏1

𝑎21𝑥1+ 𝑎22𝑥2≤ 𝑏2

(3) 𝑥1≥ 0, 𝑥2≥ 0

The linear problem then becomes:

max⁡{𝑐𝑇_{𝑥⁡I⁡𝐴𝑥 ≤ 𝑏 ∧ 𝑥 ≥ 𝑜}}

Linear programming was founded in 1939 by Leonid Kantorovich, for which he received the Nobel prize in economics [56].

4.2.3 Goal programming

Goal programming is an optimization program which can be seen as an extension or generalization on the earlier mentioned linear programming. It can handle multiple, even conflicting, objectives, by given each goal a target value to be achieved. The function minimizes the unwanted deviations of this target value. Dependent on the goal programming variant used, this can be or a weighted sum or a vector. Goal programming is introduced by Charnes and Cooper [57].

4.2.4 Genetic algorithm

A genetic algorithm (GA) is an adaptive heuristic search algorithm. It is based on the evolutionary idea of natural selection and genetics. GA is often used for solving optimization problems, they represent an intelligent exploitation of a random search [58]. Though a GA is not random at all, it uses historical data to direct the search, within the search space, into the region of better performance. It uses Darwin’s principle “survival of the fittest”, so the fittest solutions are dominating over the weaker ones [59].

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4.2.5 Pareto approach

The Pareto approach is frequently used in multi-objective vehicle routing problems. This approach is mainly introduced by Goldberg for genetic algorithms [60]. It can be a useful aid for decision-making since it does not allow one compromise to be favored over another.

4.2.6 Aggregation

An aggregation function is a function where the values of multiple rows are grouped together. With this groups of values, one new criterion is created to form more significant meaning of just a single input.

4.2.7 Local search

Local search is also a heuristic method. It moves from solution to solution in the space of candidate solutions based on specified criterion. The local search continues the search for new solutions until the current best solution can’t be improved by any transformation of the solutions or when a time bound is elapsed.

4.2.8 Ant colony optimization

Ant colony optimization (ACO) is one of the newer mathematical methods. It is based on the behaviour of ants seeking a path between a source of food and their colony. Marco Dorigo proposed this method in 1992, and nowadays it is widely used [61]. The ACO is a good method for minimizing the travelled distance. It is used for near-optimal solutions to the travelling salesman problem. Ant colony systems are used to solve problems on graphs. It is defined by a target function depending on edge costs and possibly other information about the graph. Ant systems are specially designed for scenarios where the topology of the graph of the edge costs changes during the operation. The advantage of ACO over a GA is that an ACO can be run continuously and adapt to changes in real time, which occur often in dynamic routing problems.

4.2.9 Other

There are also some mathematical methods that were only used once, their method of working is not explained in this report. This are those methods: Lexicographic method, scalarizing function, weighted sum program, attractor, branch and cut algorithm, tabu search, weighted sum, tree recourse problem and longest path policy.

4.3 Nature of Dynamic Element

4.3.1 Requests

In the paper of Azi et al. [62] is described a vehicle routing problem with a delivery operation where new customer request occur dynamically. The solution method is based on an adaptive large neighborhood search heuristic. The method decides if the new request can be added to the current solution. However, the real-time decision is only about the acceptance of the new request, not about including the request in the current service, because in this case the delivery route is fixed when the vehicle departs from the depot.

4.3.2 Travel time and/or service time

The travel time is not always a certainty. When a vehicle has to operate in public, other vehicles do play a part in the travel time. One problem, for instance, is traffic congestion. With traffic congestion,

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Travel time and distance can change both dynamically and stochastically over time. Kim et al. [63] describe this in their report. They propose a Markov decision process model to solve the problem.

4.3.3 Moving demands

A special case of the vehicle routing problem is the one described by Bopardikar et al . [64]. They introduce a VRP in which the demands move with a specified speed upon arrival. For instance, in the automation industry where the demand are parts that are on a conveyor belt and a robot arm has to pick the parts from it. The service vehicle (in the example the robot arm) must have a higher speed to fulfill the translating demands. To solve this problem, they propose a translational minimum Hamiltonian path (TMHP). The results of this method are that when the demands move a lot slower than the service vehicle, the conditions on the arrival rate are within a constant factor.

4.3.4 Multiple dynamic elements

Cheung et al. [65] have developed a mathematical model for the dynamic fleet management. The model is based on the static problem but is re-analysed the solution if new information arrives as travel time, vehicle locations and incoming orders. The new solution is, according to computational experiments, near-optimal.

4.4 Overview of literature

Table 2 gives an overview of all objectives and solutions for the fleet management, most of the papers are about the vehicle routing problem. The objectives and methods in the category other, have a footnote with corresponding objective or method. These are mentioned just one time in the discussed papers and are not discussed in detail.

Table 2 Objectives and solution methods of the routing problem in literature (chronologic)

Year, Author Problem Objective Method

M in . th e tr av e lle d d is ta n ce M in . th e tr av e lle d ti m e M in . th e c o sts M in . th e n u m b e r o f ve h ic le s M ax . th e p ro fi t O p ti m iz e th e b al an ce o f th e lo ad M ax . cu sto m e r sa ti sf ac ti o n O th e r H e u ri sti c G o al p ro gr am m in g Li n e ar p ro gr am m in g P ar e to a p p ro ac h G e n e ti c A lg o ri th m A gg re ga ti o n Lo ca l se ar ch A n t co lo n y o p ti m iz ati o n O th e r 1985, Keller et al. [66]

Traveling salesman problem with profit

x x x 1

1986, Park and Koelling [67][68]

Vehicle routing problem x x x 1990, Sutcliffe an

Board [69]

Vehicle routing problem x 2_x

1996, Cherkassky et al. [46]

Vehicle routing problem x 1998, Lee and Ueng

[70]

Vehicle routing problem x x x x

1_{Lexicographic method}

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1998, Sessomboon et al. [71]

Vehicle routing problem with time windows

x x x x 1999, Hong and Park

[72]

x x x 2000, Hansen [73] Multi-objective traveling

salesman problem

x x 3

2001, Geiger [74] Vehicle routing problem with time windows

x x 2001, Rahoual et al.

[75]

x x 2001, Ribeiro and

Lourenco [76]

Multi-period vehicle routing problem x x x x 2002, Borges and Hansen [77] Multi-objective traveling salesman problem x 4 2003, Baràn and Schaerer [78]

x x 2003, Paquete and Stützle [79] Multi-objective traveling salesman problem x x x 2003, Zhou et al. [80] Vehicle routing problem

with time windows

x x x 2003, Zhenyu et al.[81] Multi-objective traveling salesman problem x x x 2004, Angel et al. [82] Multi-objective traveling salesman problem x x 2004, Chitty and Hernandez [83]

Dynamic vehicle routing problem

x x 2005, Alvarenga [84] Dynamic vehicle routing

problem with time windows

x x 2005, Song et al. [85] Bi-objective traveling

salesman problem x x 5 2005, Murata and Itai [86] Multi-objective vehicle routing problem 6_{x x} 2005, Riera-Ledesma and Salazar-González [87] Traveling purchaser problem x x x 7 2006, Housroum et al. [88]

Dynamic vehicle routing problem with time windows

x x 8

3_{Scalarizing function} 4_{Weighted sum program} 5_Attractor

6_{Optimize makespan} 7

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2006, Ombuki et al. [89]

x x x 9

2008, Ahmmed et al. [90]

x x x 2008, Moreira et al.

[91]

x x x x 2009, Smith et al.

[64]

Vehicle routing problem 10 11

2013, Armas et al. [92]

x x 2013, Gao and Sheng

[93]

x x x 12

2013, Ghannadpour et al. [94][95]

Dynamic vehicle routing problem with fuzzy time windows

x x x x x

2013, Shi et al. [96] Dynamic fleet management x 13

2014, Albareda-Sambola et al. [97]

Dynamic vehicle routing problem with unknown time constraints

x x

2014, Afshar-Nadjafi [51]

x x 2014, Bopardikar et

al. [98]

x 14

2014, Elhassania et al. [58]

x x 2015, Beheshti et al.

[99]

x x 2015, Helfert et al.

[55]

x x 15_x

2015, Yang et al. [54] Dynamic vehicle routing problem with time windows

x x 16_x

4.5 The vehicle routing problem with time windows

Most of the vehicle routing problems listed in Table 2 have time windows. In these time windows the deliveries or visits have to be made. Since there are so much routing problems with a time window, a

9_{Weighted sum}

10_{Fulfilling translating demans}

11_{Translational minimum Hamiltonian path} 12_{Computer simulation}

13_{Tree recourse problem} 14_{Longest path policy}

15_{Minimizing environmental pollution} 16_{Minimizing environmental pollution}

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short overview of the papers is given. The vehicle routing problem with Time Windows (VRPTW) is a well-known and complex combinatorial problem. Here a literature overview of this problem is given.

4.5.1 Time windows

One of the first solutions to the dynamic vehicle routing problem is to use the static version of this problem. In this case, the algorithm is restarted when the initial route is changed. However, this restart doesn’t use the memory to improve the quality of the optimized results. Alvarenga et al. [84] propose a better solution, a modification of the hybrid CGH Column Generation Heuristic.

Housroum et al. [88] were also early adopters of the dynamic vehicle problem. Their dynamic factor was the arrival of new customers over time only. They propose a solution based on a genetic algorithm (GA). The solution was tested with the Solomon benchmarks and the results were similar compared to other metaheuristic approaches.

In the research of Bopardikar et al. [98], a situation with time constraints is described. The conditions are: demands are sequent generated and these demands need to be fulfilled within a fixed finite time after its generation. The computation of this problem is based on a longest-path logarithm. The demands are generated in time with a Poisson process.

A courier service company in the Canary Islands, Spain, uses the Vehicle Routing Problem with Time Windows (VRPTW) to solve their routing problems. [92] The request from customers are known at the start of the day or can even be dynamically added during the day. This gives a Restricted Dynamic Heterogeneous Fleet Vehicle Routing Problem with Time Windows (RDHFVRPTW) as a real -world application. The solution proposed to solve this is problem is a Metaheuristic Solution Approach. Another dynamic vehicle routing problem with time constraints is the Ant Colony Optimization. Ahmmed et al. [90] present a solution with multiple ant colonies which work hierarchy. Their solution is called MACS-DVRPTW, Multiple Ant Colony Solution – Dynamic Vehicle Routing Problem with Time Windows. The first ant colony minimizes the number of vehicles, the second ant colony minimizes the travel distances. These two colonies communicated through pheromone updating. The proposed solution has the same average number of vehicles with the known best.

The vehicle routing problem of Fernández and Laporta [97] has a time constraint, only is this constraint unknown. The probability distribution of the time constraint is available. Multiple requests must be satisfied within a given time window. Therefore, an adaptive service policy that aims at the best time period to serve each request within its associated time window is proposed. The goal of this method is to reduce the distribution costs. With computational experiments is the effectiveness of this policy compared with two other basic policies.

In the paper of Shi et al. [96], another variation of the DVRP with Time Constraints is described. Here the customer can choose its service level that varies in travel time. In their case, the travel time a customer can choose is 1 day, 2 days or 3 days. E-commercial companies like amazon.com, bol.com, coolblue.nl provide this kind of service level to their customers. The researchers transform this problem into a dynamic network with partially dependent random arc capacities. A structural decomposition method is developed and this method decomposes the problem into a three recourse problems. All three recourse problems have their own efficient algorithm, so it can solve the solution

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very efficiently. The solution is compared with two other methods and the results are quite encouraging.

Another option for the vehicle routing problem is described by Beseshti et al. [99]. In their problem, each request has a certain time window. However, it is not possible to handle all request within its time window, with the result of a reduction of the customer’s satisfaction. But not all customer’s satisfaction is even important to the distributer, so a trade-off has to be made. The proposed solution of Beseshti is a Cooperative Coevolutionary Multi-objective Quantum-Genetic Algorithm (CCMQGA). A model with a hard time window is described by Afshar-Nadjafi [100]. They describe a constructive heuristic for time-dependent multi-depot DVRPTCTW and heterogeneous fleet. The goal is to minimize the total fleet costs. There is a maximum number of vehicle allowed in the depots and the travel time only depends on the departure time. The proposed solution is a constructive heuristic procedure and after evaluating the procedure can obtain a satisfying solution.

Gao [93] proposed a solution for the DVRPTW for a real city environment, a fresh food distributor in Nanjing, China. For this special case, the real-time road traffic and random new requests are considered as the dynamic factor. A simulation model is constructed by both improved ant colony optimization (ACO) and a computer simulation method. Results show that this is an efficient and effective model.

4.5.1.1 Fuzzy time windows

In most of the above-mentioned reports, the time windows and travel times are known in advance, or there is deterministic or probabilistic information available. With the concept of fuzzy time windows

ant travel times these data is not known until new requests arrive. This is called the Dynamic Vehicle

Routing Problem with Fuzzy Time Windows (DVRPFTW). Ghannadpour et al . [94][95] considered the situation with these fuzzy data. The travel times are fuzzy because of for example traffic and weather conditions, accidents. The satisfaction level of the customers, the maximum time window, is also modelled as fuzzy travel time. The objective of the model is multidimensional; minimizing the waiting time, travel distance and fleet size and maximizing the customer's satisfaction. The proposed solution is based on a genetic algorithm (GA) and three basic modules. The results are compared with static instances in the literature and show the effectiveness of this approach.

4.6 Concluding

There are multiple combinations of problems, objectives and solutions possible, see Table 2. Some problems have even more than one objective or solution method. Most of the problems consider the routing of the vehicles, this can be explained because this was the focus of this research. The most common objective is minimizing the travelled distance. The method for this objective can differ, all proposed solutions are applicable for minimizing the travelled distance. Minimizing the costs and the amount of vehicles are the second most common objectives. Although, while minimizing the travelled distance, the costs are also reduced in most of the cases. The most used solution method is the genetic algorithm, and most of the time this method is used for minimizing the travelled distance. It is also used for minimizing the travelled time, the total costs and maximizing the customer satisfaction. The objective and solution method are the main characteristics of dynamic fleet management. The most common objectives are minimizing the total travelled distance, the costs or the fleet size or maximizing the profit or service level. Other objectives are minimizing the environmental impact.