Integration of freight
transportation in Demand
Responsive Transport systems
DOMINIK FUCHS
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT
transportation in Demand Responsive Transport
systems
DOMINIK FUCHS
Master in Geoinformation and Transport Technology Date: June 12, 2020
Supervisor: Jonas Hatzenbühler Examiner: Erik Jenelius
School of Architecture and the Built Environment Host company: Trafficon - Traffic Consultants GmbH
Swedish title: Integration av godstransporter i Demand Responsive Transport system
Abstract
Demand-Responsive Transport (DRT) describes public transport modes, which do not run on a fixed schedule but the customers can order their trip including time windows, origin and destinations themselves. Especially for rural areas with lower demand for passengers, DRT systems seem to be suitable concepts.
On the other hand, high costs and frequent times, in which no passenger re- quests a trip, can make it difficult to operate these systems.
One idea to increase the efficiency of DRT systems is to integrate freight trans- portation and deliver products, which are ordered online from local shops, to the final customer. This thesis investigates the necessary data and the impacts following from the integration for the FLEXIBUS, a DRT system in the Bavar- ian town of Krumbach. The Adaptive Large Neighborhood Search (ALNS) is used as an optimization algorithm to create a model for the integration of freight transportation in the case of the FLEXIBUS. Different scenarios are tested on how the pickup and delivery could look like (e.g. with a central pickup station). The model demonstrates that the pickup of the product at the shop and delivery to the final customer is the most appropriate concept.
The model suggests that the increase in operational cost can be equaled by a low fare for the transportation, which makes this concept economically sus- tainable. On the other hand, the integration leads to higher waiting times per passengers although they are still within an acceptable range. In-vehicle times are not affected as much by the implementation of the system. The integration of freight transportation can lead to fewer emissions compared to costumers, which take the car to the shop. The actual results for emissions depend highly on the temporal and spatial distribution of the packages as well as their amount.
Sammanfattning
Demand-Responsive Transport (DRT) beskriver kollektivtrafiklägen, som inte körs enligt ett fast schema men kunderna kan beställa sin resa inklusive tids- fönster, ursprung och destinationer själva. Speciellt för landsbygden med lägre efterfrågan på passagerare verkar DRT-system vara lämpliga koncept. Å andra sidan kan höga kostnader och frekventa tider, där ingen passagerare begär en resa, göra det svårt att använda dessa system.
En idé för att öka effektiviteten i DRT-system är att integrera godstransporter och leverera produkter, som beställs online från lokala butiker, till slutkunden.
Denna avhandling undersöker den nödvändiga data och effekterna av integra- tion för FLEXIBUS, ett DRT-system i Tyskland i Krumbach. Adapative Large Neigborhood Search (ALNS) används som optimeringsalgoritm för att ska- pa en modell för integration av godstransport i fallet med FLEXIBUS. Olika scenarier testar hur pickup och leverans kan se ut (t.ex. med en central pickup- station). Modellen visar att hämtning av produkten i butiken och leverans till slutkunden är det mest lämpliga sättet att leverera paketet.
Modellen antyder att ökningen av driftskostnaderna kan jämställas med ett lågt pris, vilket gör detta koncept ekonomiskt hållbart. Å andra sidan leder in- tegrationen till högre väntetider per passagerare även om de fortfarande ligger inom ett acceptabelt intervall. Tiden som spanderas i fordon påverkas inte li- ka mycket av implementeringen av systemet. Integrationen av godstransporter kan leda till mindre utsläpp jämfört med kunder som tar bilen till butiken. De faktiska resultaten för utsläpp beror mycket på den temporära och rumsliga fördelningen av paketen såväl som deras mängd.
Acknowledgment
Without the contribution, time and helpful advice of many different people, this thesis would not have been possible. Foremost, I want to thank my super- visor, Jonas Hatzenbühler, who spent at least one hour in our weekly sessions together with me and helped me in crucial times although he had to work on his own licentiate thesis for his Phd. I really enjoyed our meetings every Tues- day, learned a lot and look forward to meet you someday again in Stockholm, Jonas.
Another special thanks belongs to Anja Höpping, Dr. Wolfgang Kieslich and the whole team of Trafficon, the host company of this thesis in Munich. Being able to write the thesis in such a friendly, communicative and productive en- vironment was a stroke of luck. Sitting together on the project and discussing every perspective taught me a lot and gave me new impression over and over again.
Without the help of Josef Brandner and Daniel Mayer from the FLEXIBUS KG, this project would have never been possible. Their data and willingness to help me understand the FLEXIBUS was the foundation of this thesis. Work- ing with them on the project "Autobus.Schwaben" was a pleasure and I am looking forward to see the concept that we have been working on together for half a year to be implemented.
Dominik Fuchs, Munich, June 2020
Declaration of contribution
The research motivation and the conceptualization of the research project were done in close discussion with Erik Jenelius and Jonas Hatzenbühler. The research design, implementation, computational experiments, result analysis and writing were done mainly by me. Jonas Hatzenbühler helped me with the development and critical assessment of the chosen methodology.
1 Introduction 1
1.1 Challenges of transportation in rural areas . . . 1
1.2 Objective . . . 4
1.3 Scope and limitation . . . 5
2 Review of literature 8 2.1 DRT systems and freight transportation . . . 8
2.2 Vehicle Routing Problems . . . 10
2.3 Optimization Algorithms . . . 11
3 Methodology 14 3.1 Problem Definition . . . 14
3.2 Mathematical Model . . . 15
3.3 Adaptive Large Neighborhood Search . . . 18
3.3.1 Basic ideas . . . 18
3.3.2 Removal of requests . . . 19
3.3.3 Insertion of requests . . . 21
3.3.4 Choosing Heuristics using adaptive weighs . . . 24
3.3.5 Differences to other ALNS Models . . . 25
4 Application 27 4.1 Case Study - Project "Autobus.Schwaben" . . . 27
4.1.1 Chances of Integration of freight in rural areas . . . . 27
4.1.2 Use Cases . . . 29
4.1.3 Operational requirements . . . 33
4.2 Data collection . . . 35
4.2.1 Overview . . . 35
4.2.2 Definition of time-windows . . . 37
4.3 Data processing . . . 41
4.3.1 Definition of parameters . . . 41
vii
4.3.2 Comparison Passenger and Package . . . 42
4.3.3 Scenarios for Transporting Packages . . . 43
4.3.4 Package demand sets . . . 47
5 Results 50 5.1 Validation of the Model . . . 50
5.2 Analysis of Scenarios . . . 56
5.2.1 Set 5S . . . 57
5.2.2 Set 10S . . . 60
5.2.3 Set 10M . . . 62
5.2.4 Resume . . . 65
5.3 Analysis of the impact of the demand set . . . 67
5.3.1 Magnitude . . . 67
5.3.2 Relationship between customers and shops . . . 70
5.3.3 Temporal closeness of arrival times . . . 72
5.3.4 Spatial closeness of destinations . . . 75
5.3.5 Resume . . . 77
5.4 Comparison Integration and Separation . . . 79
5.4.1 Results of options for separation . . . 79
5.4.2 Comparison of costs and CO2 emissions . . . 80
5.4.3 Analysis of operational costs of the DRT system . . . 82
6 Discussion and conclusion 84
Bibliography 88
Appendices 92
Introduction
1.1 Challenges of transportation in rural ar- eas
Since the beginning of the 19th century, more and more people tend to accu- mulate in bigger cities. This movement of people to group in cities is called urbanization and is one of the dominant social trends of the late 20th and be- ginning 21st century. Since 2007 and for the first time in history, more than half of the world’s population has been living in cities (Madlener and Sunak, 2011).
Urbanization shows some encouraging opportunities when it comes to the re- duction of CO2 emissions and therefore tackling climate change. Using the official income and expenditure survey of 2013, (Gill and Moeller, 2018) ex- amined that the main advantage of urban areas is that daily points of interests like supermarkets, working places and spaces for leisure activities are in the close range to each other and easier to reach. In this case, a well-developed network for public transport (metros, busses and trains) provides the citizens with a sustainable, easy, fast and rather cheap alternative to the usage of cars.
Because of current debates of not only CO2 emissions caused by the transport sector but also discussions about air quality and sustainable usage of spare space in cities, many cities try to decrease the number of cars within cities.
Policies include a fee for cars driving into the city (e.g. Stockholm), the re- duction of parking lots and an increased fee for their usage, the construction of wider bike lanes and lanes for busses in the city and many more.
Urbanization does not only affect cities but rural areas as well. Eurostat, the institutions responsible for statistics in the European Union, defines the typol- ogy of areas (urban areas, intermediate areas and rural areas) in a three-step
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methodology (EUROSTAT, 2020). First, rural areas are defined as all areas outside of urban clusters, which are areas with a density higher than 300 in- habitants per km2 and a minimum population of 5000 people. Secondly, the Nomenclature of Territorial Units for Statistics (NUTS) regions defines re- gions based on the share of their population in rural areas into the following categories
• Predominantly rural: Share higher than 50 percent
• Intermediate: Share between 20 percent and 50 percent
• Predominately urban: Share lower than 20 percent
The third and last step takes the size of the urban center in the region into account, where rural and intermediate regions can advance into intermediate and urban areas respectively if there is an urban center with 200.000 people (for rural areas) or 500.000 people (for intermediate areas) and they make at least 25 percent of the regional population.
In recent years much focus of research regarding a more environmentally friend- ly way of transportation was drawn to urban mobility and the integration of the suburbs as will be later discussed in the literature review, with the main rea- sons being the previously explained opportunities in the city to construct a more sustainable transport. On the other hand, rural areas face a difficult chal- lenge to maintain a sustainable transport network. Rural areas are often char- acterized by low population density and disperse settlement structures with low accessibility (Gross-Fengels and Fromhold-Eisebith, 2018). This means for example that the demand for supermarkets, doctors or leisure activities is relatively small resulting in small supply and high distances between those public services. Due to these long distances and low densities, rural trans- portation networks are marked by high operating expenses (ibid). Another threat, which will most likely hit rural areas more intense than urban regions, will be the demographic change in countries like Germany. Because of longer reaction times, decreasing eyesight and less stamina available for walking and biking old people are in special need for a well equipped public transport. This means that public transport is facing a difficult challenge: How is it possible to sustain a reliable and good service for the decreasing number of customers, which depend even more on a well-equipped network than before?
One approach to solve this issue is demand-responsive transportation (DRT).
In contrast to usual public transport with a timetable and predefined stops, the concept of DRT waives those constraints and lets the customer decide where
and when they need to be picked up. A public transport service can be regarded as DRT system if the following criteria are met (Wang et al., 2015).
• The service is available to the general public (i.e. it is not restricted to particular groups of users according to age or disability criteria)
• The service is provided by low capacity road vehicles such as small busses, vans or taxis
• The service responds to change in demand by either altering its route and/or its timetable
• The fare is charged on a per passenger and not per vehicle basis
Therefore, DRT tries to combine the advantages of different transport modes.
The concept aims for a reliable, affordable and efficient public transport sys- tem, which reduces the need for owning a car and bundle up demands of people to reduce emissions to a minimum. Different approaches of Demand Respon- sive Transport have been around for a while with varying success, where the main reason for its failure is that it is quite expensive to operate a system like this (Ryley et al., 2014). The driver is the main cost factor in this case and only transports few people during the day, which makes the cost recovery in many cases difficult and the necessity of high subsidies arises. Another point is that the demand varies a lot during the day, which leads to many time-slots in which the vehicle is not used and does not gain any profit for the bus com- pany.
One promising idea to increase the efficiency of DRT systems is to transport other goods in the vehicle next to passengers. As an easy to transport and not for the passengers disturbing good, packages have been identified as freight, which could fit in the concept of DRT systems. With the integration of freight transportation in the DRT system, not only bus companies get the opportunity to establish a new business model but local retailers are able to increase their clientele. This concept strengthens local economic cycles and improves the situation for retailers in the competition with big online shops like Amazon.
The customers can benefit by an attractive service and the possibility of same- day delivery of their local products. Because the customer does not need to take the car to get to the shop, the integration of freight logistics in the DRT might lead to environmental benefits as well.
1.2 Objective
The integration of freight transportation in DRT system is assumed to have economical as well as environmental benefits due to lower overall travelled distances resulting in less emissions and the fare of transporting the goods.
On the other hand, a decrease in service for the passengers of the DRT as well as higher operational costs might be the result of this concept as well.
Therefore, four different Key Performance Indexes (KPIs) will be discussed in this thesis
• Number of required busses
• Service time of passengers
• Profit
• Emissions
Demand Responsive Transport operates only if there is customer demand. In general, this demand is rather difficult to predict and can vary a lot. The bus company has a limited capacity of busses, which operate during the day and pick-up and deliver passengers. This means that if a lot of people want to take a ride at the exact same moment and there a not enough vehicles to satisfy this demand, the request has to be denied. With the integration of freight transport, the vehicles are more occupied than before and their spatial distribution might change. Without the acquisition of new vehicles, this could lead to a higher number of denied requests than before, which has negative image and service effects for the supplier.
Similar to this example, the pick-up and delivery of packages might lead to higher service time for passengers - the service time being waiting time and the travel time. Because of a higher number of requests the system has to handle, a passenger might have to wait longer than before and the duration of the trip increases, especially because the pick-up and drop-off of packages can take longer than the same procedure for passengers.
The third KPI is the profit of the system. The main goal for the bus company is to increase revenue while keeping the costs low. The transport of packages might increase the efficiency of the usage of the vehicles and makes it pos- sible to gain more profit with more requests. Of course, the increased fuel consumption for the higher number of trips will diminish the profit and needs to be taken into account in this KPI.
Fuel is another important factor when it comes to the last KPI as well. Cur- rently, there are two sparate systems: The DRT takes care of the passengers while other suppliers deliver the packages. With the integration of freight into the DRT system, a more optimal routing can be developed, which reduces the length of trips and therefore reduces emissions.
The following four hypotheses about the integration of freight and passenger transportation are therefore the basis for this paper
• Number of required busses will increase
• Service time of passengers will increase
• Profit will increase
• Emissions will decrease
A model will be generated to simulate a currently existing DRT system in a rural area with real passenger data. After validating the model comparing its results with the actual outcome, different scenarios will be tested for the in- sertion of packages. This includes on the one hand side the way, in which the package is delivered (e.g. directly to the customer or via a pickup station), and on the other hand how spatial, temporal and other distributions affect the KPIs.
After investigating these results, the status quo and the insertion of the pack- ages will be compared. In the status quo, there is no integration but separation of package and passenger logistics. There are two options, how packages could be transported: The customer drives to the shop using his own car or a separate delivery van financed by shops that picks up the packages and delivers them to the customers. After evaluating those options and calculating the KPIs, a bus with the capability to pick up and deliver packages as well will have to handle the same requests like both options and the KPIs will be compared with the previous ones.
1.3 Scope and limitation
The approach to combine passenger transportation with freight logistics is no new idea. With the upcoming automation of vehicles and the reduced costs due to the omission of drivers, there have been different approaches to im- plement these concepts in modern solutions (more in chapter 2). One of the companies, which are planning to introduce freight transportation in their cur- rent operating system, is the FLEXIBUS KG in rural Bavaria. In the project
"Autobus.Schwaben", which is funded by the Federal Ministry of Food and Agriculture to evaluate mobility solutions to strengthen rural areas, the bus company wants to examine restrictions and opportunities of those concepts.
The company Trafficon - Traffic Consultants, which creates mobility solutions for their customer and is the host company of this thesis, is responsible for the conceptual part of the project. One cooperation partner of this project is the online marketplace atalanda, where people can purchase the products of local shops (like sport article shops, stationery stores, craft shops and so on) via the internet. The customers can either pick up their products at the shop or choose a home-delivery. In this project, the second point would be carried out by FLEXIBUS.
To support this project, the previously described model with its KPIs will be conducted. FLEXIBUS will provide a set of real passenger data for a spe- cific location, which will be the input for the model. The location will be Krumbach, a town with around 12.500 inhabitants, which is denoted as pre- dominantly rural according to the NUTS scale of the EU (EUROSTAT, 2020).
The spatial limitation of the model will be the serving area of the DRT service area of Krumbach. The model will imitate the original FLEXIBUS system and will be implemented in tight cooperation with FLEXIBUS.
Nevertheless, some simplifications have to be made for the model, for example traffic conditions will be neglected. Currently, there is no implementation of package delivery, which means that there is no data, which could be used in the model. Different scenarios will be implemented in the model, which will vary in spatial and temporal distribution and will have different magnitudes to see how the system reacts in different cases. The duration of picking up a package and handing it over to the customer will be assumed because there is no data about it yet.
An important part of the model will be to evaluate the advantages and disad- vantages of the following three scenarios on how to handle the packages:
• The packages could be picked up at the local shop and directly delivered to the customer
• The shops bring the packages to a central hub, where the bus picks them up and delivers them to the customer
• The bus picks up the packages from the local shops and delivers them to a local hub, where the customers can get them
After a review of literature and other relevant sources, the methodology will be explained with a focus on the Adaptive Large Neighborhood Search, a heuris-
tic algorithm to solve routing problems with constraints. Data collection and processing will be discussed afterward, especially looking at the selection of Krumbach as site for the case study. Here, the project "Autobus.Schwaben"
will be evaluated more deeply, where conceptual and legal requirements are discussed as well as cooperation with different stakeholders in the process and their needs (customers, shops, online-platforms). Furthermore, the data col- lection consists of a review of the data set by the FLEXIBUS to understand the status quo. In the section about data processing, the different parameters for the model as well as scenarios and package demand sets will be introduced.
The results of the simulation will be analyzed in the next chapter, starting with a validation of the model, then taking a look at the different scenarios, where the KPIs will be examined, as well as an analysis of the impact of the demand set. The last part of the analysis will be a comparison between the separation of freight and passenger transportation and their integration. In the last chapter, the results will be discussed taking care of the hypotheses and the background of the simulation.
Review of literature
The literature used in this thesis focuses on three different parts: The concep- tual analysis for the integration of freight in a DRT system, different categories of vehicle routing problems and finding appropriate optimisation algorithms to create a model, which is able to forecast the impact on the DRT system.
Therefore, the literature for all three topics will be discussed separately in the following sections.
2.1 DRT systems and freight transportation
DRT systems have been around for a couple of centuries now. Although they share the basic idea of serving different passengers at the same time without regular schedules and with a relatively small fee compared to taxis, it is in- teresting to see how they are used for different aims in different scenarios. In Europe, the following four systems of routes have been implemented and inves- tigated (Mageean and Nelson, 2003): Fixed route, Semi-Fixed Route, Flexible Route and Virtual Flexible Route.
While regular bus services serve fixed routes with regular stops or semi-fixed routes, in which some stops need to be pre-ordered (for example by pushing a button), DRT systems are more flexible. Services can be either corridor wise, where a bus traverses from one terminal to another and stops at non-predefined stop points (often door-to-door) or area-wise, where a bus leaves the depot, fol- lows a route along requested stops and returns later to the same depot without any necessary intermediate stops. The FLEXIBUS follows an area-wise ap- proach.
Similar to varying route services, the method of booking and the usage of
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telemetrics vary throughout different systems. It is interesting to see that DRT system are not necessarily used in only one specific NUTs but range from sparsely populated regions in Finland to bigger cities like Florence or Gothen- burg (ibid).
Therefore, DRT systems can be used in various environments with different goals (see for example Ryley et al., 2014). The authors investigated differ- ent use cases for DRTs by creating Mixed Logit models from stated prefer- ences experiments. Those cases included DRT for shopping services to malls in deposited areas, service to hospitals, employment shuttles, a "rural hop- per" bringing people from sparsely populated areas to more urban regions and DRTs specializing in transporting passengers to train stations. They showed that services bringing people to stations or airports are able to generate eco- nomic benefits and a rather high market share, while other cases were rather difficult to finance. On the other hand, use cases including "rural hopper" were able to meet social needs and benefited the society.
In Germany, projects around DRT systems were introduced in the last couple of years, mainly encouraged by the new opportunities of automated driving vehicles. One of the main sites for experiments was the city of Schorndorf in Baden-Württemberg, where system requirements, operation and vehicle con- cepts were established in a group consisting of scientists, local citizens, oper- ators and politicians and tested in a case study (Brost et al., 2018).
Similar to this approach, a concept for the "MultiBus" in northern Germany was introduced in the early 2000s, where other current systems were evaluated to establish a viable service (Dalkman et al., 2004). The difference compared to the project in Schorndorf is that part of the concept was the integration of a parcel delivery service. While not modeling the impact of this idea, the concept evaluated legal and operational requirements, marketing concepts and explained the whole process from the order of the customer until the final de- livery (HHS-Ingenieure, 2004). The key difference to the concept discussed in this paper is that the parcels will be solely provided from bigger logistic companies like DHL, GLS or Hermes and not local shops. Unfortunately, this part of the MultiBus was never implemented.
A project, which was successfully carried out in a pilot, is Cargo Hitching in the Netherlands (van Duin et al., 2019). The idea is that people with dif- ficulties to find regular jobs take parcels from a logistic hub near the center of Nijmengen, store them as private luggage in trolleys or containers inside a regular bus and take care of them until they reach the "Cargo Hitching service desk" near a bus stop. For the final delivery to the customer different ideas have been proposed, for example using bikes as a mode for last-mile delivery
from the service desk or permitting pick up by the customers at the desk only.
According to their survey, respondents consider the possibility to offer peo- ple with poor job prospects work the most beneficial objective of this project while lower emissions come second.
Not only busses can be used as a transportation vehicle for freight but other public transport modes as well (see Cochrane et al., 2016). The authors eval- uated the challenges and opportunities of different examples of "freight on transit" (FOT) concepts using a three-round Delphi study asking experts on freight / logistics, public transport, policy / planning, finance and traffic flow about their assessments. They claimed that the benefits of FOT might not be substantial and that society and transit agencies are more likely to benefit than freight operators. One important finding was that the current public transport infrastructure should be able to support additional movements, which was not the case for their site Toronto.
On the other hand, Krumbach as rural area shows different properties than cities like Toronto, which makes a deeper investigation of advantages and dis- advantages necessary for insights how the implementation of freight trans- portation could look like and what obstacles need to be tackled.
2.2 Vehicle Routing Problems
In current research many different sets of problem formulations have been pro- posed, which fit this concept. The most common one might be the Travelling Salesman Problem (TSP). The task is to find a route for a salesman to its cus- tomers, which is as short as possible, where every customer is only visited once and where the first node and the last node are the same. Of course, this does not suit the DRT because it needs to be distinguished between origin and destination, which makes more sophisticated problem formulations necessary.
The first one is the so-called Vehicle Routing Problem (VRP). The Vehicle Routing Problem consists of a set of entities requiring trips between their ori- gin and some destinations in a network using a fleet of vehicles, respecting constraints on the vehicles, customers and drivers (Shaw, 1998). Constraints for the vehicles can be for example capacity or the equipment (for example to carry a wheel-chair). A more general problem formulation is the Pickup and Delivery Problem with Time-Windows (PDPTW). In this case, it is not nec- essarily customers, who are picked up, but more generally some entity. The focus of PDPTW is to adhere the time windows of the request, which define when an entity needs to be picked up and when it needs to be delivered, and
its service-time, which indicates how much time is between the delivery and the pick-up (Ropke and Pisinger, 2006).
Indeed, the PDPTW is able to include many features of the DRT system but does not feature its unique trait of being flexible through time. Therefore, the Dial-A-Ride-Problem (DARP) was introduced, where trips are not known be- forehand. The DARP aims for designing routes and fitting schedules to trans- port as many passengers, who request a trip throughout the day with origin and destinations, as possible (Cordeau and Laporte, 2003). This problem for- mulation was used by (Li et al., 2014) to introduce the Share-a-ride Problem (SARP) when creating a model, which investigated the possibilities for taxis to pick-up and deliver packages in an urban area. The SARP differentiates from the DARP because it widens the transported entities from only one good to several ones with different attributes and requirements, for example passen- gers and parcels. In their paper, they also proposed a static Freight Insertion Problem (FIP), where requests for parcels are put inside an already developed route and no new optimization process over the whole route is conducted.
Summarizing the different approaches, the problem of integration of freight transportation in a DRT system can be categorized as SARP problem with con- sideration of the time-window constraints of the PDPTW. Although the focus of those problem formulations varies to a certain amount, all of them aim for an optimisation of the usage of some vehicles carrying entities in predefined constraints.
2.3 Optimization Algorithms
As there is no data about the impact of freight logistic in DRT systems avail- able, a model needs to be implemented to be able to estimate effects on travel- time and waiting time of the passengers as well as emissions. An important part is the distribution of routes on a set of vehicles in a way that all constraints (capacity of busses, time-windows of passengers and parcels) are taken into consideration as discussed in the previous chapter.
Held (2008) presented various different algorithms to solve routing problems and stated that optimal solutions are not suitable for a high number of requests due to the high complexity of these problems. Therefore, he proposes heuris- tic approaches as appropriate because - while not finding the best solution - very good results can be achieved. In his paper he discussed the following four heuristics.
• Ant Colony Optimization (ACO)
• Agent-based Algorithms
• Generic Algorithms
• Large Neighborhood Search / Adaptive Large Neighborhood Search The main idea of the ACO is that "ants" traverse a network consisting of arcs and nodes (origins and destinations). An ant is placed on every origin and vis- its all nodes in the network. All ants spread pheromone on their visited edges, which increases the probability that a later ant chooses this edge if it has dif- ferent options. The ACO generates a minimum-distance path, which is called a journey. ACO was used for the DRT system in Schorndorf to analyze walked distance, trip duration and the number of required vehicles and compare the results with a conventional public transport line (Barrilero et al., 2017).
Contrary to optimizations of ACO, agent-based modeling has the approach that entities are able to make decisions and act according to a set of rules and constraints. An example is the investigation of a Dynamic Vehicle Routing Problem (DARP) for an urban freight transport service at Yogyakarta city in Indonesia (Sopha et al., 2016). Retailers with the attributes location, lateness tolerance and demand as well as trucks with the attributes optimal route and new demand were implemented. The authors stated that the biggest advantage of agent-based algorithms is that the heterogeneity can be captured very well.
Another example is the use of agent-based modeling to investigate the impli- cations of shared autonomous vehicles (Fagnant and Kockelman, 2014).
Generic algorithms try to imitate the idea of evolution theory (Held, 2008).
Generic algorithms aim for creating a high number of possible solutions, which are generated from parts of previous solutions. The sum of all solutions is called population with single solutions of a population called a chromosome, which is encoded by genes. The number of all genes can be seen as key for the encoding of the chromosome. Chromosomes from previous iterations are selected in an iterative process, where those with better results are used with higher probability. Afterward they are attached again to create new solutions.
A cellular Genetric Algorithm was proposed by (Alba and Dorronsoro, 2006) to solve the capacitated VRP. The authors were able to show promising results for benchmark data sets.
Large Neighborhood Search (LNS) and Adaptive Large Neighborhood Search (ALNS) are optimization algorithms with the idea of destroying nodes in a set of routes and repairing it afterward with the aim of finding better solu- tions according to an objective function consisting of values for waiting time, operational costs and other selectable attributes. The LNS was invented by
(Shaw, 1997) and expanded by (Ropke and Pisinger, 2006) into the ALNS, which found high usage in the last decade for Vehicle Routing Problems.
An idea to integrate passenger and freight transportation using public trans- port and develop an optimized model was proposed by (Masson et al., 2017).
According to their idea, busses take packages from sub-urbs to the core of a city, where city freighters take it and deliver it to the final customer. For their two-tier optimization modeling the city of La Rochelle in France, they pro- posed the ALNS as the fitting algorithm.
The ALNS as solution algorithm was proposed for a very similar idea by (Ghilas et al., 2013), where they investigated the integration of passenger and freight transportation. In their model, the bus system was scheduled with fixed frequencies and lines investigating different scenarios for example taxis pick- ing up parcels at specific stops of the bus and deliver it to the customer.
Taxis as possible modes for transporting passengers and freight are investi- gated as well in (Li et al., 2014) in general and improved in (Li et al., 2016b) by implementing time slacks with additional destroy and repair algorithms and in (Li et al., 2016a) by implementing stochastic travel times and delivery loca- tions to resemble real situations more appropriate. For these ALNS models, a taxi could pick up and deliver packages, if there is no passenger in the taxi during this time with a priority of picking up passengers.
It can be seen that all four algorithms are promising approaches. Nevertheless, very similar use cases as the one discussed in this thesis were investigated with the ALNS, where combinations of freight and passenger transportation were evaluated. The results of the ALNS for these models were promising with relatively fast processes and high accuracy. Although interesting approaches using busses as carriers for packages into the center of a city and two-tier sys- tems using carriers for the last mile, there was no implementation, in which a DRT system picks up and delivers packages from door-to-door with the pas- senger still in the bus. This thesis aims for filling this gap by using the well developed ALNS for this concept.
Methodology
3.1 Problem Definition
The integration of freight transportation in a DRT shows some promising virtues for bus companies, shops and customers like a higher service due to same-day delivery. On the other hand, the integration might lead to higher in-vehicle and waiting times for passengers because the driver has to pick up or deliver packages. There is clearly a trade-off between the service quality of the passenger and the increase in profit for the bus company.
For decision-makers, who want to evaluate the impact of the integration of freight transportation into their systems, qualitative measures are necessary, for example how much packages a bus can deliver throughout the day without having to deny passenger requests or increasing the number of busses. Other interesting factors are the effects on in-vehicle time and waiting time for the passenger, which should only increase marginally. Therefore, a model, which reflects the real world appropriately, is necessary to have a reasonable basis for decision-makers, if they want to implement these systems. The distribu- tion of all available busses among the requests needs to be organized in the most fitting way to decrease costs for users as well as for the company. The main problem is to find an optimized route, which has the lowest overall cost - consisting of operational costs (driver, fuel) and user costs (waiting time, in- vehicle time).
These optimized routes need to take care of constraints coming with the re- quest of passengers as well as from packages. First of all, the demand should not be higher than the actual capacity of seats and storage area for the packages respectively. Secondly, the transported entities should not be picked up before they are ready (departure time constraint) or delivered later than their desired
14
latest arrival time (arrival time constraint).
Additionally, natural boundaries need to be taken care of, for example that the origin of a request is served before the destination in the route sequence. It is necessary to calculate in-vehicle times and waiting times of all customers as well as the distance each bus travels along the day. Therefore, parameters need to be implemented to be able to store the results for each bus and calculate the overall value. The output of the model should provide these values as well as the best overall sequence of nodes distributed among a set of vehicles and their calculated schedule.
3.2 Mathematical Model
The problem of distributing a number of vehicles in the the most appropriate way to generate the fewest costs can be implemented in mathematical expres- sion calculating operational as well as user costs. These costs are summarized in an objective function, which consists of cost-terms with different weights.
The following mathematical model aims for the minimization of the objective function while following the previously introduced constraints. The formu- lation adopts key features of the expressions by (Ropke and Pisinger, 2006) and (Li et al., 2014) with respect to the requirements and restrictions in this particular case.
For this formulation, a set of vehicles K has to fulfill n requests in a given time period. The problem is defined on a graph G with pickup nodes P and delivery nodes D. The graph G consists of nodes V and arcs A, where arcs are the connection between all nodes A = V · V . Each vehicle runs on a sub graph GK = (VK, AK).
A request is represented by the origin node i and the destination node j and can be either a request for a package or for a passenger. The route from i to j throughout a combination of arcs in the graph has the non-negative distance dij ≥ 0 and travel time tij ≥ 0.
Requests need to be served within a given time-window. For the arrival time, the earliest possible arrival is ai with the latest arrival time being bi. If the vehicle arrives earlier than expected to the origin node, the vehicle has to wait and the request is still accepted. On the other hand, it is denied and put inside the request bank zi if the node cannot be reached before the latest arrival time bi. The destination node has the time-windows gj and hj in which the passen- ger or package needs to be delivered. While a passenger delivery that is too early does not get penalized, a package delivery before the given time-window
can be denied depending on the scenario (see chapter 4.3.3). Similar to the arrival time, a request will be denied and put inside the request bank zi if the delivery of the request is too late.
Each node has a specific service time sifor boarding or delivery. The service time for passengers is smaller than the one for packages in the origin node and 0 for the destination node, while the delivery time for a package at the desti- nation will be added to the overall time.
Requests can have different loads, which are put inside the vehicle. Passengers are denoted as li while the load of goods is defined as mi. For an origin node, the loads are li ≥ 0 and mi ≥ 0 respectively, while they are 0 or negative at the destination nodes. The overall amount of passengers Likand packages in a vehicle Mikafter serving node i are not allowed to be bigger than its capacities Ckand Qk. The start and end of the model will not be the start and end of the actual service time of the FLEXIBUS but rather a snapshot of a specific time during the day, where the insertion of packages seems to be suitable (10:00 to 17:00). Therefore, there are no terminals in a sense that the bus leaves its depot. Still, there will be no passenger or packages in the bus at the starting point θkor ending point θk′ of the model and the upcoming request will be the first and last respectively.
Furthermore, the model uses the following five different decision variables similar to the ones in (Ropke and Pisinger, 2006). The variable xijk, i, j ∈ V, k ∈ K is a binary parameter being 1 if a vehicle drives between the origin node i and the destination node j and 0 otherwise. Sik, i ∈ V, k ∈ K shows the time when a vehicle starts its route at a specific node. If a request is denied because it does not comply with one of the constraints, it is put inside the re- quest bank. In this case, the binary variable zi, i∈ P is set to 1 for this request and otherwise 0. The variables Likand Mik have been introduced earlier.
The mathematical model aims for the minimization of the objective function 3.1 with the following constraints.
min α[(X
k∈K
X
(i,j)∈A
dijxijkf) + kw] + β X
k∈K
(tw+ tt) + γX
i∈P
zi (3.1)
Subject to: X
k∈K
X
j∈Nk
xijk+ zi = 1 ∀ i ∈ P (3.2)
X
j∈VK
xijk− X
j∈VK
xj,n+i,k = 0 ∀ k ∈ K, ∀i ∈ Pk (3.3) xijk = 1 ⇒ Sik+ si+ tij ≤ Sjk ∀k ∈ K, ∀(i, j) ∈ Ak (3.4) ai ≤ Sik ≤ bi ∀k ∈ K, ∀i ∈ Vk (3.5)
gj ≤ Sjk ≤ hj ∀k ∈ K, ∀j ∈ Vk (3.6)
Sik ≤ Sn+i,k ∀k ∈ K, ∀i ∈ Pk (3.7)
xijk = 1 ⇒ Lik+ lj ≤ Ljk ∀k ∈ K, ∀(i, j) ∈ Ak (3.8)
Lik ≤ Ck ∀k ∈ K, ∀i ∈ Vk (3.9)
Lθkk= Lθ′kk= 0 ∀k ∈ K (3.10) xijk = 1 ⇒ Mik+ lj ≤ Mjk ∀k ∈ K, ∀(i, j) ∈ Ak (3.11)
Mik ≤ Qk ∀k ∈ K, ∀i ∈ Vk (3.12)
Mθkk= Mθ′kk= 0 ∀k ∈ K (3.13) xijk ∈ 0, 1 ∀k ∈ K, ∀(i, j) ∈ Ak (3.14)
zi ∈ 0, 1 ∀i ∈ P (3.15)
Sik ≥ 0 ∀k ∈ K, ∀i ∈ Vk (3.16)
Lik ≥ 0 ∀k ∈ K, ∀i ∈ Vk (3.17)
Mik ≥ 0 ∀k ∈ K, ∀i ∈ Vk (3.18)
The objective function consists of three weighed terms: The operational costs, the user costs and the request bank all having different weighs α, β and γ. The operational costs consist of costs for fuel f for the travelled distance dij and for the cost for the driver w summed over the number of vehicles k, while the waiting time twof passengers and their travel time ttare in the user costs. The number of denied requests zi in the last term has a high weigh to avoid the situation that customers are not permitted to travel.
With equation 3.2, a node is either served by a vehicle and part of the route or put inside the request bank if it does not fit anywhere. Because there is no interchange between vehicles, a request consisting of origin and destina- tion is served by a single vehicle, which is provided by constraint 3.3. Correct scheduling for Sikalong the route and between nodes consisting of travel time tij and service time si is guaranteed by equation 3.4. Equations 3.5 and 3.6 ensure that the pickup and delivery of the request are within the given time- periods. The next equation 3.7 prohibits situations, in which the destination node comes before the origin node in one route.
The current number of passengers throughout the route needs to be set cor- rectly for each vehicle, is not allowed to exceed the capacity and is 0 at the start and the end of the route, which is provided by the equations 3.8, 3.9 and 3.10. The same is done for the package with constraints 3.11, 3.12 and 3.13.
The five previously mentioned decision variables are defined in equations 3.14
to 3.18. It needs to be noted that there is no priority between package and pas- senger in this model. The real system follows a first come - first serve approach, meaning that an accepted request will not be rejected afterward if a new trip is requested.
As mentioned in chapter 2 there are different approaches to solve optimisation problems with vehicle distributions like Ant Colony Optimisation or Agent- based heuristics but for this thesis, the ALNS fits best due to its high adaptabil- ity, fast computation and well-investigated usages in similar cases. Therefore, the mathematical model is implemented as ALNS, which is introduced in the next section. The code can be investigated as well in a public Github reposi- tory1.
3.3 Adaptive Large Neighborhood Search
3.3.1 Basic ideas
The foundation of the ALNS was built by (Shaw, 1997), who was investigat- ing algorithms to solve vehicle routing problems. He recognized that many algorithms, which were used during that time, own the problem of being stuck in local minima after some iterations and are not able to find global best so- lutions. Therefore, he created the Large Neighborhood Search, which uses a large neighborhood based upon rescheduling specific requests with the help of constraint programming techniques.
This idea was the basis for (Ropke and Pisinger, 2006) to develop the ALNS. In contrast to the LNS, this heuristic has a whole set of sub-heuristics for insert- ing and removing requests in the route. Therefore, the ALNS can be defined as a destroy-repair algorithm. Their hypothesis was that heuristics have different strengths, which may or may not suit the current problem. Using a weighted roulette wheel, one removal and one insertion algorithm is selected per iter- ation, which generates a solution. By keeping a score of how well each of the heuristics fared in recent steps, the weight is adjusted over time in a way that effective algorithms, which find better or at least new solutions, are used more frequently than other ones. The aim of the algorithm is to find the so- lution with the smallest objective cost function, which consists of different by the developer selected attributes (for example waiting time, operational costs, penalties for denied requests).
1https://github.com/DominikFuchs27/IntegrationFreightTransportationDRT_public
The following pseudo-code shows the removal of requests i depending on the number of requests N and the chosen percentage of destroyed requests p, stor- age in a set U and insertion in a set of routes Rcurrentfor one iteration using the ALNS algorithm while holding the constraints discussed in the mathematical model.
Data: Number of requests N, share of removed nodes p, current best routes Rbest, current routes Rcurrent, current best cost cbest
Result: current best routes Rbest, current best cost cbest 1 select removal heuristic according to random wheel;
2 whileU < N p do
3 U ← U + i ;
4 end
5 select insertion heuristic according to random wheel;
6 whileU > 0 do
7 for i in U do
8 ifai < S < bi &Lik < Cik &Sik < Sn+i,k then
9 insert i at best-cost position of Rcurrent;
10 else
11 z ← i;
12 end
13 end
14 end
15 Calculate new overall cost c;
16 if c <cbestthen
17 cbest ← c;
18 Rbest← Rcurrent;
19 end
20 Calculate new score;
Algorithm 1:Pseudo-Code for the ALNS
In the following sections, the heuristics for removal and insertion of re- quests will be discussed more deeply.
3.3.2 Removal of requests
The first step in each iteration is the removal of requests. Each heuristic takes as an input the previous solution consisting of busses and their affiliated routes and a percentage of nodes to be deleted, which is in this case 15 %. Requests, which are currently in the request bank, are not part of the removal process but
added in the insertion heuristic later.
Shaw Removal Heuristic
The first heuristic is the removal heuristic proposed by (Shaw, 1998), which was adapted to fit the current problem. Shaws idea was to remove nodes with similar properties and insert them later together because their combination might fit well and it reduces the change of creating better solutions to break them apart. Having them removed together makes it possible to change their position inside routes to assign them together in another vehicle.
The implementation of a so-called Relatedness measure R(i, j) is defined for this particular heuristic, which indicates how similar the requests i and j are. If R gets lower, the difference between the requests decreases, which makes them more related.
For this thesis, the relatedness measure is calculated using a distance term and a time term. Ropke and Pisinger added a demand term and a term, which shows, if this particular vehicle is able to serve special requests (e.g. the trans- portation of wheelchairs). Because the data set consists of requests with only one passenger at a time because every passenger has to book their own re- quest (which leads to for example three requests with the exact same proper- ties but different customer IDs), a demand term is not suitable. A factor iden- tifying specific attributes of the vehicle (for example the capability to carry wheelchairs or certain products) is not necessary because all busses in the later model are the same.
The terms are weighed using φ and ξ and normalized to ensure their values are between 0 and 1 to make them comparable. The measure is defined in equation 3.19.
R(i, j) = φ(dA(i),A(j)+dB(i),B(j))+ξ(|TA(i)−TA(j)|+|TB(i)−TB(j)|) (3.19) The first term relates to the distance and is the sum of the distance between the pickup locations A of requests i and j and the distance between their deliv- ery locations Biand Bj. The second term consists of the differences between the time-windows for pick-up and delivery. The value for the origin refers to the earliest departure while the value for the destination is the latest arrival in minutes.
In the implementation, a random node, which is currently served by a vehicle and not in the request bank, is chosen with its partner node. The relatedness factor of this request to all other requests is calculated and the resulting values are sorted in an ascending list with the most related ones. To prevent com- bining the same requests over and over again, a determinism parameter p ≥ 1
is introduced to generate randomness in the selection. Afterwards a random number y ∈ [0, 1] is generated and the request with the corresponding related- ness factor at position ypis removed along with the previously chosen request.
This procedure is repeated with a new request until the number of nodes to be deleted is reached. In the later model, the following values for the parameters are selected
p= 5 (3.20)
φ = 0.6 (3.21)
ξ = 1 (3.22)
Random Removal
This process removes randomly selected nodes in the current solution. Be- cause origin nodes and destination nodes need to be removed together, the overall number of removed nodes varies throughout the process. If only the origin is selected, the destination will be removed as well and vice versa. Of course, it can happen that both origin and destination are selected randomly.
Worst Removal
This removal heuristics deletes the request with the highest cost. In this case, the cost is defined similarly to the objective function with weighs for in-vehicle time, waiting time and the operating cost for the travelled distance. The cost for the driver is not included in this function because they are all the same for each vehicle.
After calculating the cost for each request in the current solution, the requests are ordered with descending costs in a list with the highest costs being at the start. Similar to the Shaw Removal, a parameter p ensures randomization of the selection of the request to prevent removing the same requests over and over again. The request at position yp is removed, where y is a random value between 0 and 1.
3.3.3 Insertion of requests
According to (Ropke and Pisinger, 2006), there are two different ways of in- serting requests when it comes to vehicle routing problems: sequential and parallel insertion heuristics. Sequential heuristics can be viewed like cascades, where one route is built after another. If a request does not fit in the first route, then it is evaluated in the second, then the third and so on. On the other hand, parallel heuristics build up several routes at the same time and try to fit the
request to the best-suited vehicle. While sequential heuristics have the ad- vantage that they find solutions easier, in which fewer vehicles are necessary, parallel insertion heuristics perform better when it comes to the distribution of nodes inside a known number of vehicles. Because the number of required vehicles is known or can be estimated, the following insertion heuristics are solely parallel heuristics.
Basic Greedy Heuristic
The Basic Greedy Insertion heuristic inserts nodes at routes and positions, where they increase the cost the least. The cost is in this case the value of the objective function 3.1 and includes the cost for the driver because the algo- rithm tries to reduce the number of busses. Still, the priority of the algorithm is to serve all incoming requests.
The increase of the objective function for one route in a vehicle k due to the in- sertion of request i is denoted as ∆fik. The set of currently unplanned requests Uconsists of the removed requests and the nodes from the request bank, which have not been inserted in the previous iteration. The nodes of the request are put inside all possible positions in all routes and the increase is calculated for each possible combination. If there are no suitable positions due to a viola- tion of one or more constraints, ∆fik is set to a very high number. The cost for inserting a request at its best position is denoted as ci = mink∈K{∆fi,k}.
After running through all routes, the request is inserted in the route with the smallest ci to minimize
mini∈U ci (3.23)
This heuristic is repeated until there are no more requests in U and they are ei- ther inserted in the routes or put inside the request bank if there is no solution, in which the request fits without resulting in a rejection of any request.
Regret Heuristic
The second type of insertion algorithms is the group of regret heuristics, which have been discussed in (Potvin and Rousseau, 1993) for the Vehicle Routing Problem with Time-Windows. Like in the previous heuristic, the input is a set of currently unplanned trips U, where a request can be inserted at different po- sitions. While the first node of this set has the highest number of possibilities, where it fits, the amount decreases for the later ones. Therefore, there might be only very unsuitable solutions left for the remaining nodes. The idea of the authors is to evaluate, which requests need to be inserted as soon as possible because a later insertion would lead to a noticeably increase in overall costs if it is not inserted in the most-fitting route.
An example would be if there are two busses and two requests A and B. The increase in costs for the first request A is 12 units for the first route and 14 units for the second route at their respective best-cost-position. On the other hand, the second request B increases the overall costs for the first route by 15 units and the second one by 23 units at their best-cost-positions. It can happen that if A is inserted in the first route, B cannot be inserted in the same route anymore due to time or capacity constraints. Therefore, the overall increase in costs would be 35 units. It can be seen that the overall costs would be lower if request B is inserted in the first route first and afterwards request B in the second bus leading to an increase of 29 units.
Similar to the previous heuristic, the increased cost due to the insertion of the request ∆fi,k is calculated for each route. Let xik ∈ 1, ..., m with m being the current number of vehicles denote the route, for which a request i has the kth lowest increase in cost, then the lowest cost can be obtained as in equation 3.24.
∆fi,xi,k ≤ ∆fi,xi,k′ f or k ≤ k′ (3.24) This means that the overall minimum cost position is ci = ∆fi,xi1. The next step is to calculate a regret value ci∗, which resembles the difference between inserting the request in the best route in its best position and in the second-best route in its best position, as seen in equation 3.25.
ci∗ = ∆fi,xi2 − ∆fi,xi1 (3.25) The regret value is calculated for each currently unplanned request in the set U. Afterwards, the request is inserted where the regret value is maximized
maxi∈U ci∗ (3.26)
Similar to before, the request is inserted at the position inside the route, where the increase of the objective functions is the smallest. This process is iterated again with new calculations of regret values in each iteration until there are no unplanned requests left.
The previously described algorithm is called the regret-2-heuristic because the best solution is compared to the second-best. With the same idea, the algorithm can be expanded to compare the best solution to the third-best one or other ones. To define a regret − k heuristic, the maximization of the regret value is calculated according to equation 3.27.
maxi∈U{
Xk
j=1
(∆fi,xik− ∆fi,xi1)} (3.27) For the later model, regret-2 and regret-3 heuristics have been implemented because two or three busses are required, in which the nodes could be inserted.
3.3.4 Choosing Heuristics using adaptive weighs
As discussed previously, the main idea behind the ALNS is to use the strengths of a set of different removal and insertion heuristics. Because the incoming data can vary regarding the number of requests, spatial distribution and time- window constraints, the regular change of both removal and insertion heuris- tics can lead to better solutions overall.
Still, it is necessary to recognize the best heuristics for a specific data set to be able to use these more often than such heuristics, which do neither bring better solutions nor new solutions at all. Therefore, a roulette wheel selection is introduced with weighs for both the removal and insertion parts of the algo- rithm. Assuming k heuristics with weighs wi, i∈ {1, 2, ...k}, a heuristic j is chosen with the probability
wj
Pk
i=1wi
(3.28)
The selection of the insertion and removal heuristics are independent of each other so that different pairs are selected every time.
In the beginning, the weighs are equally distributed among all options but they change after each segment. One segment is a number of iterations (in this case 100), in which the current weigh is used and a score is collected, how well each sub-heuristic fares in recent history. Because it is not clear, whether the removal or the insertion heuristic was the reason for a successful iteration, both parts get the same score. At the beginning of each segment, the score is set to 0 for each heuristic. There are three different ways to increase the score as seen in the following table.
Parameter Description
σ1 The last iteration resulted in a new overall best solution σ2 The last iteration resulted in a new solution. It is better
than the previous solution
σ3 The last iteration resulted in a new solution. It is worse than the previous solution
Table 3.1: Score Adjustment Parameters
A removal-insertion pair gets the highest score σ1if a new global best solu- tion was found meaning that the solution has the lowest overall cost calculated by the objective function. The second highest score σ2 belongs to those it- erations, where a solution was found, which is better than the previous one
but not better than the best one, to reward pairs, which were able to improve routes. Solutions, which were not able to find routes with a lower cost than the previous one but at least new ones, get the lowest score. This ensures that algorithms are applied, which do not put the same requests at the same spot over and over again.
After each segment j the score for all heuristics i is summed up and denoted as πi. To calculate the new weighs wi,j+1 the following equation is used.
wi,j+1 = wij(1 − r) + rπi
θi
(3.29) The number of times a heuristic was selected is denoted as θi while the reac- tion factor r ∈ {0, 1} is able to monitor how quickly the weighs are adapted to the current success. A higher reaction factor leads to a faster change of weighs and is chosen to be 0.1 in this case. The new weights are used in the following segment to calculate the probabilities for the selection of each heuristic as in equation 3.28.
3.3.5 Differences to other ALNS Models
While following the ideas of (Ropke and Pisinger, 2006) quite detailed, there are some key differences between their model and the one presented in this thesis.
The most important one is the different approach to code. Most of the authors formulated ALNS as an employed Mixed-Integer Progaming (MIP) problem (for example Li et al., 2014, Naccache et al., 2018). Similarly, Ropke and Pisinger focused more on the mathematical model, while comprehend imple- mentation using Python was the main focus in this thesis. Using lists and the position of the requests in those lists enabled the calculation of schedules and capacities of each route enabling the observance of the constraints of the math- ematical model.
A second difference is the stopping criteria. For their model, Pisinger and Ropke used acceptance criteria from simulated annealing. This means that a solution is accepted with a given probability that decreases over time using a cooling rate. With this approach, solutions, which are worse than the previ- ous outcome, are accepted as well. The acceptance criteria gets more strict towards the end of the algorithm, which is a previously specified number of iterations. In contrast to this approach, the later discussed model has a fixed number of iterations like in (Shaw, 1997) and accepts all suitable outcomes but stores the best outcomes in a separate place because the number of iterations
is rather small.
For their model, Ropke and Pisinger introduce noise to the objective func- tion to further randomize the insertion of requests. This noise N is randomly generated and either added to or subtracted from the cost coming out of the objective function in an interval [−max N, max N]. The noise is adapted throughout the iterations and depends on the distance between the nodes. Be- cause the number of iterations will be rather small in the later model the model dispenses the insertion of noise.
Application
4.1 Case Study - Project "Autobus.Schwaben"
4.1.1 Chances of Integration of freight in rural areas
As discussed before, many rural areas share the common problem of having few people in a widely spread area. From an economic perspective this has negative impacts on both consumers and suppliers in general. Suppliers like book stores, grocery shops or pharmacies depend on a sufficient number of customers to be able to gain profit and grow or at least sustain their business model because of costs for rent, the salary of employees, insurance or purchas- ing products in the first place. In rural areas, it can be difficult for especially niche shops to be able to attract enough customers. On the other hand, cus- tomers are in a difficult situation as well. Due to long travelling times between different shops and only a small variation (because of the lack of niche prod- ucts), the satisfaction with the variety of products may be low and customers are required to travel long distances to the next bigger city.
On the other hand, the situation for customers improved heavily in the last cou- ple of years. With the upcoming e-commerce, customers are not required to visit shops anymore because they can purchase most of their desired products on the internet. In 2014 between 39 Billion e and 43.6 Billion e (depending on the source) have been gained through online-shopping in Germany, which makes up between 8.5 and 9.5 percent of the whole profit of the retail sector (Beckmann and Hangebruch, 2016). Experts are estimating that the share of online-shopping will increase in all sectors and might lead up to 25 percent in 2025 (ibid). This increase in comfort for customers and shift from the analog purchase of goods in local shops towards buying products online on market-
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