IN
DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 60 CREDITS
STOCKHOLM SWEDEN 2020 ,
A pragmatic approach to improve the efficiency of the waste
management system in Stockholm through the use of Big Data,
Heuristics and open source VRP solvers.
A real life waste collection problem;
Stockholm’s waste collection system and inherent vehicle routing problem, VRP
RAFAEL SALCEDO VILLANUEVA
TRITA ABE-MBT-19711
For:
Nick, Asad, Anca, Jasna, Hossein, Matteo, Alice, Jorn, Sander, Stephen, Tessa, Johannes, Ali,
all of them were part of my 2 year experience, and shall remain in me forever.
Abstract
In this thesis, we will address a real life waste collection problem; Stockholm’s waste collection system and inherent vehicle routing problem, VRP. To do this we will first delve into some mathematical theory of Combinatorial Optimization and Heuristics to understand the fundamentals of the problem. Following with some pragmatic approaches recommended by experts within the Smart Cities context. Finally, the most important part of the work is the creation of a model of the actual collection system and two optimized versions. After completing the model of the system, we compare the current situation of the system with alternatives in the system's planning phase. To achieve this modelling we have to make use of different GIS and VRP software; CartoDB and Open Door Logistics respectively. CartoDB has a freeware version while Open Door Logistics is an open source software operating with an open source algorithm called JSPRIT.
Finally the results, which are both quantitative and qualitative, based mainly on the modelling phase, plus other cases studies and pragmatic recommendations, give us some hints of what can be achieved in Stockholm’s waste collection system.
The modelling of the system has been simplified to make the comparison less prone of discrepancies with
regards to the control variable. Minimizing the variability of the problem such as disregarding the “time-
windows” and differentiated capacity vehicles, improves the credibility of the final results; these being,
reorganizing the weekly work load, and districting (clustering) the entire municipality depending on the
number of contractors handling each waste type.
Index
Title 1
Abstract 3
Index 4
Chapter 1 Introduction 6
Background 6
Solid waste management and climate change 7
The thesis team 8
Aims and Objectives 8
Chapter 2. Background and Definitions 11
Smart Cities 11
Stockholm’s Waste management 14
Authorities and consumers 16
Limitations of the study: 20
Chapter 3. Methodology - Mathematical problems 21
Characteristics 21
Graph theory 22
The first pragmatic approach; TSP and VRP 23
Combinatorial optimization 25
Heuristics Vs. Metaheuristics 27
Centroid based clustering, or K means clustering 29
Modelling waste collection systems 30
Different variants of the problem 31
Solving the problem 34
Applied software for the GIS analysis 40
Pragmatic approach 42
Chapter 4. Big Data Analysis Process 45
Categories 46
Geocoding 47
Selection of sample weeks (Peak and off peak) 48
Chapter 5. Modelling initial state and optimization scenarios 52
Setting the rules for the model 52
Optimization process (ODL tool) 55
Fat Min week 58
Fat Max week 59
Electronics Min week 60
Electronics Max week 61
Chapter 6 Results 62
Savings 67
Chapter 7 Discussion and Conclusions 71
Chapter 8; Afterword 75
Bibliography 78
Chapter 1 Introduction
Background
Waste management is the administration service provided by both the public and the private sectors regarding: generation, prevention, monitoring, treatment, handling, disposition of solid waste. Solid waste has different categories, explained later in the paper; but regardless of its category all relate to solids and fluids produced by human activity. (Editorial Board/Aims and Scope, 2014)
Waste management systems should be prioritized in both the public and private agendas for all countries, for two main reasons: the environmental implications and the moral obligation that we, as a society, should have towards solid waste handling and disposing. Likewise, all systems composing a city have to become increasingly efficient, for several causes: environmental, social, economical, etc; all of these thriving for a Smart City.
Industrialized countries (such as Sweden) have less economical restrictions and therefore more possibilities to launch many initiatives towards a technological transformation leading to a better overall city system. In this case specifically the waste collection system, thus this research.
During the last 15 years there have been numerous advances and developments in technology and techniques related to the waste collection systems throughout the World. There has even been a synergy between the private and public sector to increase efficiency in their systems, hence making it a profitable activity, while improving the citizen’s standards.
It has been estimated that, from the total amount of money spent on the collection, transportation, and disposal of solid waste, approximately 60-80% is spent on the collection phase alone. Waste management was, until recently, only a public obligation by all governments implying large costs for them and therefore its societies, not to mention the environmental burden. Today this dichotomy is no longer valid, as it involves a third actor, the private sector, and even a fourth actor, the academic sector. (Nikolaos V et all, 2007)
Waste management has been proven to be an interesting market niche and therefore many governments have been privatizing its waste systems (collection, disposal, treatment, etc).
As one would assume, the business model for the private sector relies on dealing with increasing quantities of waste, whereas this would represent an issue for the social/ environmental aspect, hence a paradoxical situation.
Authorities in Sweden tend to implement policies to reduce waste generation as this is beneficial overall for all the actors. For private companies this policy would mean less business and less incentives for them to be part of the game; unless of course having a business model that performs in an efficient manner.
Regardless of who deals with the solid waste (public or private), a sustainable approach has to be
considered. Sustainable waste management is more and more becoming an irreplaceable field to tackle
rate of production of waste, parallel to the population’s growth, while maintaining a level of: reliability, health and environment standards, and cost effectiveness.
According to the world Bank, the World average in solid waste production is: 0.6 kg per person per day, increasing every year. (Kaza et al., 2015)
Solid waste management and climate change
Solid waste is a problem that must be properly managed. It is a matter of health, environment, economy and well being of society. The preservation of natural resources and climate change as stated in the Gaia theory from Lovelock, where everything is interrelated has to be dealt in a responsible way.
The integration of living with non living into a single system.“The Earth is a self regulating complex system involving the biosphere atmosphere, hydrosphere and pedosphere, tightly coupled as an evolving system.” (Robinson, 2009)
Whether the waste is disposed in landfills, or burnt for heat, or recycled, its effects will be of great impact to the environment. For example when a landfill is lacking of management the production of methane (one of the major greenhouse gases) will increase and therefore impact greatly on climate change.
Waste generation increases with population growth as well as with the industrialization and economic level; therefore one as an engineer has to state the following question: does it has to be this way? Do we have to generate more waste as societies evolve economically and technologically?
As this paradigm is challenged one has to ask if the way waste is managed currently is the most efficient and beneficial/ or least aggressive to the environment.
Solid waste should be managed through different activities such as prevention, recycling, composting, incinerating and landfilling. According to the EPA (USA) this is referred as integrated solid waste management, ISWM. (US EPA, 2019)
ISWM evaluates local needs and conditions, as well as selecting the most appropriate waste management activities for those conditions.
According to the waste strategy in Sweden, there is a hierarchy of activities that should be followed to achieve a more efficient plan, where prevention is the top priority and disposal at landfills is the least. In Sweden waste is incinerated with a process that recuperates heat energy and therefore is located in the second to last level of the hierarchy. (Naturvårdsverket, 2015)
The concept of integrated sustainable waste management (ISWM) was defined in 2001 by Klundert &
Anschütz. They came up with a tool to comprehend waste management systems in a rather holistic manner. Their assessment follows the structure: 1) Stakeholders, 2) elements of the system, 3) the aspects
Fig. 1.1 (US EPA, 2019)
of the local context. This approach suggests that a model of an efficient waste collection system can be
“generic” and iterated in any city context. (Guhr, 2014)
The stakeholders are all the involved in the waste management system.
All actors or entities have a roll in the process and have an importance level designated. E.g collection companies, treatment plants, authorities, citizens, etc.
Authorities of a region or city design a plan in which the waste will be collected and will be moved amongst the different actors and entities of the system.
The local context are the different “lenses through which the existing waste system can be assessed and with which a new or expanded system can be planned” (van de Klundert & Anschütz, 2001). This aids the decision makers to know all the different stakeholders in context and prioritize among the different options (Guhr, 2014).
The thesis team
After completing a successful Smart Cities course project a thesis topic with the same background arose;
my course professor Hossein Shahrokni invited me to continue with it. The project started as an analysis to find possible benefits (from an intuitive perspective) from organizing Big Data produced by the waste collection operators over a long period of time.
The general idea was that by reducing the energy consumption inherent to the waste collection and handling, the operation costs would also be reduced, hence the system would be optimized. Professor Hossein had all the background and knowledge of the problem in Sweden, as well as the notion of where the project should lead to.
The topic was indeed interesting from an Energy- Engineering point of view. At this point a particular problem arose in front of me; a potential ‘dead end’ situation full of uncertainties and therefore a difficult decision for me to take. I knew beforehand the optimization problem for the Vehicle Routing Problem (explained later) is a very complex one; subject for many academic researchers since the late 50’s. This would require lots of computer programming, an aptitude and/or abilities that I don’t really posses.
Therefore we needed to find a team mate that would fill this void while being enthusiastic about the topic as well.
Sander Claeys apart from being an achiever engineer and an expert in whatever computer language he has in front of him, will also understand the problems and manage to solve them no matter what. He is the definition of dexterity and versatility, and also very important, he posses the ability of understanding things in a holistic mathematical way. That’s exactly what you need to solve this type of hard optimization problems.
Aims and Objectives
The present work intends to give a clear picture to the stakeholders involved in Stockholm’s waste management system (Stockholm Vatten och Avfall), as well as interested readers in the topic, to show how efficient the collection system operates in Stockholm municipality and what could be done to improve it.
In order to do this, first it is necessary to understand fully how the system operates, by taking a look into
Agency (Natur Vardsverdket) as well as the statistics regarding waste handled in the recent years and the operation by all the implied actors.
Then it is necessary to comprehend the system in terms of a vehicle routing problem and see how this can be approached and solved by means of a heuristic methods. A brief explanation on the mathematical approach will be given in the following chapters.
This thesis however, does not attempt to solve the problem in a fully mathematical rigor. Instead it propose to generate new strategies for Stockholm’s collection system by making use of all available information and tools:
- Modelling different scenarios with the Big Data provided by the city; make recommendations with the results.
- Case studies in other cities,
- pragmatic recommendations given by experts on the field,
For the modelling phase we were provided with Big Data of waste collected in a period of over 5 years.
This information package had to be processed and organized (curated) in such a way that would allow us to know the real situation of the collection system; understanding which information could be used and which had to be discarded for being unreliable.
In this middle stage we had to decide both the software and language we were to use in order to model the system.
Once organized and curated we proceeded to the modelling stage; first we modeled the initial state, and then compared it to two different scenarios. An initial state called state 0, versus a weekly reorganization (scenario 1) and finally a clustering model + weekly reorganization or Planning week (scenario 2), of the waste generation points throughout Stockholm. (see table)
The results of these comparisons gave us hints of where the system can be improved and how.
The final conclusions should be regarded in an intuitive manner as realistically it would imply a lot of time and effort for both the Government and society to push for these transformations in the system to take effect.
Table. 1.1
Table 1-1
Scenario 0 Scenario 1 Scenario 2
Initial state Weekly planning /reorganization K-means clusters + weekly planning
Model of the system as it is today (2015)
By setting all the points generated in a week, the companies can reorganize in order to reduce distances, the pick up frequencies and reduce operation costs.
By using the K means algorithm
different districts of Stockholm
would serve to reorganize the
influence of the waste collection
companies.
The system reorganization seems complicated as stated before by my colleague Adrian Guhr in his Thesis project: “The potentials of information and communication technology to improve waste management in Stockholm” (Guhr, 2014), as there are many inconsistencies and flaws in the official reports. (See Chapter 6)
In the final chapter a discussion around the different intuitive solutions regarding the waste collection system will be addressed. Eg: reorganizing the waste collection into different districts, or re scheduling the waste collection for all the companies involved.
The thesis will therefore intend to respond the following question:
What is the actual state of waste management in Stockholm?, specifically the collection phase.
In order to do this, first a few notions on general definitions of waste management will be explained.
Following a linkage between this problem and the concept of Smart Cities. Why is it important to know the new paradigms of modern cities and how to cope with the current changes, specifically in the fields of solid waste management.
Waste&
collec*on&
system&
op*mized&
BIG&data&
acquisi*on&
Informa*on&
proccesing&
So;ware:&GIS&
and&VRP&
solvers&
Theory:&
&VRP&and&
Heuris*cs&
Topic&Scholar:&
Pragma*c&
approaches&
Clustering&
techniques&
Fig. 1.2 The concept of the entire system
Chapter 2. Background and Definitions
Smart Cities
Smart Cities: a concept that has been proven resilient and iterative throughout the most recent decades. There are countless books, articles, papers that tackle the subject;
but ,what exactly is a Smart City?
Before tackling the definition it’s important to understand the reason why Smart Cities have become a core subject; with great relevance to many disciplines; all in favor of a more sustainable future.
A city as we know is a large human settlement, as vain as this definition may sound. Cities as opposed to rural settlements (villages, towns, townships, etc).
In 2008 for the first time the urban population surpassed the rural one. To have an understanding of the hasty rate at which this change took over, imagine back in 1900 a urban population representing only 1/8 (200 million people) of the world’s population at the time. Just over a hundred years later the proportion is balanced. By 2100 the World population could grow up to 10 billion, and 8 billion would be living in cities; from one eighth to eight times in 200 years. (Townsend, 2014) (WHO | Urban population growth, 2015)
Then along with the humans, came the technology that nowadays assimilate symbiotic appendices;
smartphones, smart cars, smart devices and everything that encompasses the world of IoT (Internet of things). Also, it was in 2008 the year when apparently IoT devices surpassed the human population. In 2010 the ratio was 1.84 (devices per capita), and in 2020 it is estimated it will be 6.58. (SafeAtLast.co, 2019)
As well as with human growth rate, technology growth rate in terms of devices connected to the internet, is increasing at intimidating speeds.
The third inflection point happened also near 2008, but more precisely on 2014, when the CO2 ppm levels surpassed the 400 ppm threshold in a definitive manner.
"Our forecast supports the suggestion that the Mauna Loa record will never again show CO2 concentrations below the symbolic 400 ppm within our lifetimes," the researchers wrote. The 400 ppm levels are part of a steady increase in carbon dioxide levels since the industrial era, compared to the planet's pre-industrial CO2 concentration of 280 ppm.” (McCarthy, 2016)
It is the opinion of the author that this last point is the most significant, and the main reason Cities have to evolve and therefore be conceived in a more responsible sustainable way, hence the concept of Smart Cities.
Returning to the definition of a City, at least from the classical definition perspective, where the services
offered such as: Health, Education, Communication, Sanitation, etc, would be an inherent part of the
definition; currently this is rendered insufficient, under this new scope. A Smart Cities is a paradigm rather
than a defined concept, and this opens a whole new way for studying cities; From the point of view of all disciplines.
As stated before, there are numerous articles, books and papers trying to tackle the paradigm of Smart Cities. There is one main consensus on the things that are intrinsic for a City to become Smart.
After a brief revision on the definition of Smart Cities we find the following 3 ‘dimensions’ that several authors agree upon the general definition of Smart Cities.
1) Human dimension 2) Technological dimension 3) Institutional dimension
First, Citizens are essential for a Smart City to even be considered one. Through participation, both in an active or passive manner, but more often though the use of technology.
Second, the technological dimension refers to the use of technology such as ICT’s. A new wave of ubiquitous technology has been developed and evolving since the 2000’s, in such a hasty manner. As mentioned before, currently there are 3.5 IoT devices for each human being.
Thirdly, the interaction between the government and the institutions (including the academic sector) pushing for smart initiatives.
But why has it become a trend or even a mandate (in some regions of the World) to generate these Smart Initiatives?
Cities have experienced a massive city growth in terms of its population, and so does the problems inherent to these.
E.g Urban Sprawl, insecurity, lack of infrastructure regarding sanitation, health, mobility problems, etc.
Also, very important, the Cities is where the main concentration of humans and resources will be in a near future, therefore they are essential in reversing climate change through responsible sustainable strategies.
Also lets recall the United Nations Sustainable Development goals (SDG). (Un.org, 2015)
Sprouting from the Kyoto Protocol in 1997, the first World effort to gather the most of the countries with the main purpose of limiting CO
2emissions and safeguard the environment all over the World.
Then in 2005 when it entered in force, many countries had to launch smart initiatives to cope with the Protocol mandate. Then came the Covenant of Mayors (in Europe) implemented in 2008, and it was an initiative for many European cities to reduce their CO
2emissions more than 20% by the year 2020. Later in 2010, the European Union launched the 2020 plan, also called the 20/20/20 plan, and it was based on the Covenant of mayors. The main objective was an overall 20% reduction of CO
2equivalent, while a 20%
increase in energy efficiency, and a 20% minimum usage of renewable energy sources in the whole European Union.
Summarizing, there have been Smart Cities initiatives since then (2005).
Hence a Smart City is arguably a collection of smart implementations. Some cities have been adopting
projects of diverse nature, several times with a bottom up strategy; meaning that the strategies or
government. A very common examples is the shared bicycle systems, that has been spreading throughout the World mostly as a Top-down approach. The first shared bicycle system was probably a Bottom-up strategy. This first project (perhaps in Europe) probably wasn’t a successful project, financially speaking, but the initiative was the spark that ignited a revolution of “smart” ideas that as a whole improve city conditions. (Renata Paola Dameri and Rosenthal-Sabroux, 2012)
Cities with a greater maturity in the field of Smart Cities have been pursuing policies that promote smart initiatives, hence a top down approach.
The smart city paradigm tackles several domains, not just the urban design but social, ecological and technology as a platform to thrive for better quality in all the aspects that conform a city, any city in the World. There is a strong motivation by academic institutions, organizations, technological firms, governments who without knowing precisely how, they want to contribute into the “smartness" of their cities. Individually or as a whole.
Recently more and more massive efforts has been taking place throughout the world. Eg. Masterplans in the field of Transport, Energy, Solid Waste management, drinkable water, social health, etc.
With regards to the solid waste management, there have been several initiatives across the world, that help to make the systems more efficient, hence less costly for society and more environmentally friendly.
Information collection is essential to start proposing initiatives or plans.
Innovative new ways to gather information are being used nowadays in the City of Barcelona.
Collection bins with sensors and communication layers informs the dispatch centre on when to deploy the recollection units.
In Stockholm, the way the information was collected over a long period of time was through filling surveys by hand. Nevertheless this could be the first step for Stockholm and other cities in Sweden and Europe to gather information in more
innovative ways. The relevance in data acquisition will trigger new ways of doing
things. Collecting or harvesting information, not just for the utilitarian reason but for actually improving the Citizen’s life quality.
Following with the Barcelona example; since 2003 Barcelona’s Waste management has been collecting real time information regarding waste collection points throughout the city. Electro-buses are deployed during the night to the waste collection points, also through a VRP (explained later) implementation to reduce its time and distance covered, making the system even more efficient. No noise is generated because the buses are electric, and no traffic problems due to the deployment during nighttime. Apart from that, the waste collection points work as WI-FI hot spots for the city dwellers and are integrated to a network that shows where public parking spaces are vacant or occupied, making daily parking though the city an easier task, and saving time and money for the citizens. Many instances are tackled under the same scope and infrastructure.
Fig. 2.1
This is one example of many that have been sprouting throughout the world.
This is what can be achieved with Big data analysis and analytics.
In our particular case we have the collection system of an important city, such as the Capital of Scandinavia, Stockholm; but the question is: how efficient is the waste collection system?
Of course this is not an easy question to answer, but with the help of Big data we can help stakeholders unveil a complex system in
order for them to take the next steps in actions to improve amongst other things the citizen’s life.
To close on the Smart Cities topic I would like to add what my definition of a Smart City is:
A smart city is a city that combines the use of technologies to help the monitoring of the city, to help improve all the systems composing the city; while having a population with the same opportunities and participation possibilities, with an ecological vision of the city and its resources.
Stockholm’s Waste management
The current operation in Stockholms Waste collection system appears to be inefficient, from a practical and intuitive point of view. After a thorough analysis of the Environmental codes, where the interactions amongst the different actors (households and businesses) are described, it remains a bit confusing from the operations/ logistics point of view.
Thanks to my colleagues work (Guhr, 2014) this situation has been clarified as he provided a more comprehensive picture of the system, describing a SWOT analysis of the system to point out areas of potential improvement, for present and future projects.
Classification
It is relevant to explain, prior to the analysis, the classification of waste to define the different types of waste and to explain which will be comprised in our analysis.
Waste according to the Swedish government is any object or substance that the holder discards, intends to or is obliged to discard. (Regeringskansliet, 2000)
Firstly, there should be a clear distinction between the concept of waste and by-product. By-product should be considered all objects that were produced in a manufacturing process of another object or substance. Also if the object can be continuously used it is considered by-product.
Waste ceases of being considered waste once it has been treated (landfilled, incinerated) or recycled.
Fig. 2.2
manufacturing). It is important to take into account that household and businesses waste can be considered, but is not necessarily the same thing.
The following figure portrays the situation of the different types of waste in Stockholm and is interesting to note the sources and the magnitude of each type of waste. Note that there is no classification for business waste as this can be part of households and other types, such as bulky.
The following chart portrays the waste categories in Stockholm (2013):
Household waste
Waste leftovers that cannot be recycled and are therefore incinerated. According to the environmental code, “household waste” is all matter, object or substance generated by households and comparable waste from other sources, such as businesses. (Regeringskansliet, 2000, 1998, chapter 15)
So, in reality this means waste generated in shops, offices, restaurants, institutions and businesses with mixed waste in bags or bins is considered “household waste”. In this sense household waste can in fact be anything and this creates an ambiguity in the classification of it.
The term “bulky household waste” is also a name given to the same category, whereas “Bulk waste” is referred to all objects that are too big to be disposed in bags (explained below).
Household waste can be paper, cardboard kitchen waste, packaging, glass, textiles, metal, wooden and plastic objects, electronic waste, garden waste, bulk waste, hazardous waste, latrine, sludge from septic tanks. However the sludge and latrine are not included in the statistics since these are treated separately in treatment plants (A Strategy for Sustainable Waste Management Sweden’s Waste Plan ISBN 91-620-1249-5, 2006)
Households waste that is not subject to producer responsibility is collected by the municipalities or their contractors. Bulk, electronic, and hazardous waste is taken personally to a recycling centre or left in a bulk waste room for future collection.
Packaging waste: Paper and cardboard, plastic, metal and glass packaging and newspaper that are material recycled. All handled and collected by the responsible producer of each material (explained below).
Fig. 2.3
Packaging waste Common waste
Bulky waste
All the waste that is too big to be disposed in the same manner as household waste is considered Bulky Waste. It is generally collected by private companies hired by the businesses or building owners. These companies usually take the waste to the nearest recycling facility to avoid expensive travelling distances.
(Ribbing, 2013). All waste that cannot be sorted as recycling material e.g. paper, some type of plastics and wood turn into burnable material contributing to the energy system, as mentioned previously.
Some will be recycled, other incinerated, and landfills. Source: household and businesses.
Food waste
Organic leftovers from food.
In 2012, 8,849 tons of food waste were registered by the city’s collection system (Guhr Adrian, 2014) Large quantities come from businesses such as restaurants that produce organic waste.
This type of waste requires a separate bags and bins system. All food waste is treated in Uppsala Vatten and SYVAB, with which they produce biogas. (Guhr Adrian, 2014)
Commercial waste
The responsibility for waste generated by commercial establishments is for the businesses themselves.
They have to ensure that the waste generated there has to be collected in the correct manner complying with the environmental standards.
The exception is when the waste generated is not comparable to the one of a household in terms of amount or if its extra bulky. In this case the business just have to contract a specialised contractor for the remaining waste. The businessman can also take the waste personally to the municipal recycling centre if that was the case, where there is a charge upon the quantity of the waste delivered. It’s important to note the difference between a small and big commercial establishment. The big ones will have to establish an agreement with a collection contractor for picking up their waste.
This type of waste was the one composing the Big data, hence the one we worked with.
Special Waste
Additionally to the previously types of waste there is a producer responsibility for: pharmaceuticals, radioactive, electronic, tires, cars, batteries, etc.
Authorities and consumers
Stockholm City, specifically the Traffic Agency (Trafikkontoret) is responsible for the collection and treatment of waste (household, bulky and food types).
FTI AB
(Förpacknings- och Tidningsinsamlingen) represents the companies in the producer responsibility program
FTI is owned by the four “material companies” Plastkretsen, RK Returkatong, Svenska MetallKretsen and Pressretur, and furthermore collaborates with Svensk Glasåtervinning. Each organization is responsible for the recycling of the respective material group and financed by the respective packaging industry:
Plastic, metal, newspaper and glass
Building owners
Single house buildings or apartment buildings owners have the same obligations. Single family house are provided with waste disposal equipment by the city.
Building owners have to provide their own infrastructure to their tenants. In the case of packaging waste collection the owner has to hire (like in the case of businesses) their own service of collection. (Guhr, 2014)
Envac is a company that developed a vacuum system that collects waste in different points of Stockholm.
A very interesting actor to analyze but goes beyond the scope of this study.
Treatment plants
As mentioned before, waste is either treated in the recycling plants, treated in an anaerobic process (food waste) or incinerated for hear recuperation (household and some bulky waste). (Guhr, 2014)
Fortum AB; runs the incineration plant Högdalenverket south of Stockholm and the local district heating grid. Högdalenverket receives all household waste from Stockholm to produce energy for the local district heating grid. The facility has a capacity of 700,000 tons of waste per year.
Sydvästra Stockholmsregionens Va-Verksaktiebolag (SYVAB) runs the wastewater treatment plant Himmerfjärdsverket in the south of Stockholm. The plant receives half of the food waste collected in Stockholm to produce biogas via anaerobic digestion.
Uppsala Vatten is a water-, wastewater, and waste management company and operator of a biogas plant north of Stockholm. The facility receives the other half of Stockholm’s food waste.
Söderhalls Renhållningsverk AB (SÖRAB) is a municipality owned waste collection company with responsibilities primarily in the municipalities north of Stockholm. They also run a number of recycling facilities in the area. The largest and most visited of these is Habgy, which also receives all waste types from Stockholm except for household waste.
Söderenergi is a local energy company that incinerates shredded bulky waste from Stockholm in its cogeneration unit at Igelstaverket in Södertälje. (Guhr, 2014)
Recycling stations:
Recycling stations are responsibility of the limited company called Förpacknings- och tidningsinsamlingen (FTI). (Guhr, 2014)
Statistics
In Sweden the production of waste is relatively large compared to the rest of Europe. It lies on the 6th place, with a quantity that is more than twice than the average in Europe. The mining activity in Sweden is the main responsible actor for this number.
Regarding household waste, Sweden produces 500 kg per person per year. The corresponding figures for 2008 were 800 kg/person/year in Ireland, while 300 kg/person/year were produced in the Czech Rep.
In general terms Households produced approximately 5 million tonnes of waste while the service sector
produced 1 million tonnes, in 2008. Household waste disposed as landfill was just 1% (in 2010) as this
method of disposing has been mostly banned in the country. Instead waste is recycled or incinerated for
energy recuperation. (From waste management to resource efficiency Sweden’s Waste Plan 2012–2017,
2013)
Of the 234,518 tons of household waste the majority is produced by households. Most of it is disposed in bins and bags, and collected at the curb-side. There are also buildings that have containers.
Businesses produce around 65,000 tons (Guhr Adrian, 2014). These dispose of their waste in the same manner, either by bins and bags or by containers. There is also a third type of disposal which is the vacuum system. This type accounts for about 24,000 tons.
Reno Norden AB and Liselotte Lööf AB are the two companies that operate the household waste collection. They together have in their inventory a fleet of between 70 - 85 trucks. Bulky waste accounted in 2012, with 130,938 tons collected by the city. 89,241 tons were collected by the city owned recycling centers and 42,375 by collection companies (Guhr Adrian, 2014)
Not relevant for this project but an interesting fact nonetheless is the amount of energy produced by the incineration of this type of waste accounted for 600 GWh (80% district heating, 20% electricity) per year, more less supplying district heating for 80,000 homes and electricity for 200,000 homes. (Stockholm's Stad, 2013d).
After the incineration 15% remains as sludge and 5% as ash. Sludge can then be disposed in landfills. Fly ash can be stabilized with charcoal and cement and then also goes to landfills. (Dalgren, 2013) (Guhr, 2014)
Costs of Waste Management
It is important to know the costs related to waste management since our focus is to generate savings through an optimization process. Knowing this amount would give us a clear hint of the potential savings that driving fewer distances or reducing the traveling time would imply.
The budget set by the government is based on its agenda and its operations fees charged to both users of the system (citizens and businesses) and operators of the system (collection contractors).
Since the service is a public one, it should not (in theory) generate any type of profit margin.
According to the law, any activity conforming the cleaning service can be outsourced to private companies, as mentioned before. The following table shows the budgeting analysis for the service.
Fig. 2.4 (From waste management to resource efficiency Sweden’s Waste Plan 2012–
2017, 2013)
Fees set to building owners or business owners are stablished depending on the specific location of the bins, the size or weight as well as accessibility and comfort for the collection contractor.
Additional fees have been added to increase the citizen awareness of its production of waste. Basically fees upon the additional waste generated. Separated collection of food waste is completely free. Some parts of the city are developing sensors on the containers to weight the waste per household in order to generate the bill. According to Avfall Sverige (2012a) an average single family house pays about 2000 SEK a year in waste fees. (Guhr, 2014)
An analysis of the effects weight fees in Stockholm showed that the number of collection tours for households waste has shifted from weekly to every two weeks or monthly even in the period May 2012 to 2013.
Separate food waste collection has increased substantially since the weigh fee exception started and this has created the food waste collection companies problems, logistically speaking. Demand has surpassed the offer. Economically speaking the system has gone more expensive, as administrative costs have increased significantly as income from fees have been cut down.
Costs per producers
The total costs of the packaging waste collection and recycling system is about 1 billion SEK per year in Sweden. Since the value of the collected material does not cover these expenses the producers also pay a fee depending on the material type and the purpose of the packaging (FTI, 2014). Data regarding the costs on a local level is unavailable and the same goes for the cost breakdown.
The only thing that we can derive is that the contractor and FTI have a contract that generates a bill in function of its driven kilometres and emptied bins f ( kg, km). (Nilsson, 2013)
Producers get charged via a fixed or flexible fee (FTI, 2013).
Problems related to the existing waste management system
Transport and traffic; Inner city traffic caused by the collection trucks can be, according to Linse, one of the main concerns to the private companies. (Linse, 2013) Stockholm has a very peculiar road system, due to its topology and hydrology , slopes and water all around, and in general due to the way the city has evolved.
Traffic in the city always cause utilitarian vehicles to get stuck, affecting the operations in general, making the time windows for businesses who need their waste to be picked up more constraint.
This has a direct impact on customer satisfaction.
Increasing travelling times translates into extra costs. Someone will pay for them. As Stockholm has congestion fees these increase the collection cost (collection companies are not exempted of paying
Fig. 2.5
regulations. This could perhaps be overcome with the use of electro trucks, as the Government in Barcelona has achieved. (Linse, 2013)
According to the Swedish waste management document, collection and transport in the waste management process is accounted for 8% of all emissions of greenhouse gases. This could be partially due to the small quantities collected at every point.
Limitations of the study:
Geographical boundary: the Stockholm municipality
In an overall geographical analysis we verified that the waste generation points were inside the delimitations of Stockholm municipality. The same for all the depot collection point, disposal site vectors we revised in the model. The idea was to know precisely the spatial scope of the problem. It is important to state that some disposal sites are in reality outside this delimitation, nevertheless this didn’t affect the modelling and optimization process.
The Big Data acquired gave us the possibility to know not just spacial conditions of the problem but also temporal and dimensional. Imagine a set of a million points containing type of waste, amount, time of its collection and direction for final disposal. This basic information could be used to obtain lots of other statistics by inference analysis.
Temporal boundaries: The Big Data included the information for 5 years, from 2009 until 2014.
We selected what according to the analysis was the “cleanest” most reliable information from March 2013
until March 2014. More details on The Big Data will be explained in detail in Chapter 3.
Chapter 3. Methodology - Mathematical problems
In this chapter the main problem is presented in its mathematical abstract expression.
The Vehicle Routing Problem, VRP is a paradigm that describes the problematic in logistics science, in other words, it’s the “mother problem” for an entire world of sub problems that derive from it and each propose a different optimization instance. It is also conceived as a combinatorial optimization and integer programming paradigm, designed to choose the: optimal fleet for utilitarian vehicles, in several types of situations. From this problem definition a whole set of algorithms have sprawled, all with a specific optimization objective (explained later in this chapter).
Defined by Dantzig and Ramler in 1959, specifically for the logistics field; transportation and goods distribution mainly. The Waste collection problem is just a different approach to the same paradigmatic problem. Instead of delivering goods we are collecting waste. (Dantzig and Ramser, 1959)
VRP, as stated above, can be disaggregated into many variants of the “mother problem”, all with different characteristics, for instance: number of depots, time constraints, different types of goods, etc.
Considering the transportation costs and its relevance to any industry or country’s production level and therefore economy , i.e the country’s GDP; any small saving in time and/or distance could have huge positive implications in the respective economies. (Geir Hasle et al., 2007)
NEO is composed of both young and experienced members with the global target of solving multidisciplinary Real-World Problems of interest for our Society and Computer Science
Characteristics
The essence of the VRP is to deliver (or collect) a set goods to a group of customers with known or unknown demand, in such a way that the route covered has the minimal distance and time travelled.
VRP in waste management has been evolving parallel to the development of computers. As will be explained later in this chapter sophisticated Geographic Information Systems (GIS) have been developed and these have also contributed to many algorithmic solutions to the problem. All routing problems have a measurement called a metric (path length) that determine the optimal route to a specific destination.
Fig. 3.1 (Lcc.uma.es, 2016)
Optimal routes are determined by comparing metrics, and these metrics can differ depending on the design of the routing algorithm used. (CHAPTER 2 ROUTING PROTOCOLS, n.d.)
In the present day many algorithms have been tested and benchmarked for planners to choose the best according to any specific situation. The great majority of the routing algorithms include the use of heuristic algorithms, and as we will explain later this type doesn’t guarantee the optimal solution, however near optimal solutions are found within a reasonable amount of time, therefore proving its potential in these type of problems.
It has been explained in several academic papers as well as real cases, the functionality of these methodologies. (Dantzig and Ramser, 1959)
In order to go in depth and comprehend the VRP one has to understand, at least in a general manner, some concepts mentioned already in the introductory paragraph. Concepts such as:
• Graph theory to understand the formulation of the problem
• The genesis of the problem: Travelling salesman problem TSP and Vehicle routing problem VRP
• Combinatorial optimization
• Integer programming problem
• VRP and its many variants
• Heuristics and Metaheuristics approaches to solve the problem
• Clustering methods (Lcc.uma.es, 2016)
Graph theory
The study of graphs as mathematical structures used to model pairwise relations between objects is called graph theory. A graph is composed by vertices or nodes and the edges that connect these.
Graphs can be directed or undirected. Directed means that its set of vertices (nodes) are connected by its edges, hence the nodes having a direction associated with it, e.i arrows or vectors. Undirected meaning that there is no distinction between the two nodes associated with each edge. e.i the absence of an arrow between two nodes means it is undirected. (Educative: Interactive Courses for Software Developers, 2019)
A graph is a pair of sets satisfying
Where: V= Vertices (nodes) E= Edges (links)
Thus the elements of E are 2 element subsets of V.
The best way to picture and understand the basics of graph theory is by drawing a point (node or vertex) and joining two of these by a line (edge, link). The way they are drawn is completely irrelevant in the analysis, all that counts is that the information which pairs of vertices with an edge and which do not. e.g:
Fig. 3.2 The graph on V = {1,…..,7} with edge set E = {{1,2} ,{1,5} ,{2,5},{3,4},{5,7}}
E ⊆ V [ ]
2G = (V,E)
Fig. 3.2
Applications
Graphs can be used for many disciplines, such as mathematics, physics, biology, social sciences, etc. In fact, many problems can be modelled by using graph theory. For example, in computer science graphs can be used to represent networks. In design engineering it can be used to draw the scheme of a microprocessor.
The first pragmatic approach; TSP and VRP
Leonhard Euler published on 1736 the “Seven bridges of Köningsberg” and it's considered to be the first document on graph theory, as well as the first treaty on the routing problem. Euler’s formula relating the number of edges, vertices and faces of a convex polyhedron was explained in this document.
The former city of Köningsberg in Prussia now Kalingrad, Russia, was set on both sides of the Pregel river and included two large islands which were connected to each and the mainland by seven bridges.
The problem was to find a walk path that would cross all the bridges only once. Conditions stated that the bridges had to be crossed entirely in order to reach the islands, and the walk path did not need to start and end at the same point. (Assad, 2007)
Euler prove the solution was inexistent. The difficulty of the problem relied on the technique to establish tests and analysis to prove this in a mathematical rigour.
He pointed out that the only relevant feature of the path was the sequence of bridges crossed. He reformulated the problem in abstract terms, replacing path or bridges for edges and vertex or nodes for each land mass.
The result was called “a graph”. (See Fig. 3.3)
Euler showed that the possibility of a walk through a graph, traversing each edge exactly once, depends on the degree of a node (number of edges touching it). He argued that a minimum condition for this walk would need either zero or two nodes of odd degree. This walk is called the Eulerian path or Euler Walk.
(Assad, 2007)
From the same type of problems two variants arose called: The Chinese postman problem CPP, or postman tour and also The travelling Salesman problem, TSP.
These follow the same logic as the Eulerian path.
In the CPP one intends to find the shortest closed path that visits all the edges at least once in an undirected graph. When the graph has an Eulerian path, the circuit is an optimal solution. Otherwise one
Fig.3.3 The problem of the Seven Bridges of Königsberg. Wikipedia
needs to find the optimal solution, the fewest number of edges to add to the graph so that the resulting multigraph does have an Eulerian circuit. (Assad, 2007)
The TSP asks the following: given a set of points and distances between each pair, what is the shortest possible path if you have to visit all the cities (or points) exactly once and then return to the original city. If no path exists between two “cities”, one has to add an arbitrary long edge and thus complete the graph without affecting the optimal tour. (Assad, 2007)
This approach is the mother concept for the “Vehicle routing problem”, VRP and it's exactly what we are intending to solve, at least in an semi empirical manner.
This type of problem is called a NP hard problem (explained below) in combinatorial optimization, and its a specialization for operations research and theoretical computer science.
The applications that TSP/VRP have can vary; from planning, logistics, and even design and manufacturing (microchips). TSP can be extrapolated into whatever the problem requires, translating cities into customers or in the case of biotechnology into DNA fragments. Distance can be interpreted as times or cost. The problems get even more complex as restrictions or constraints appear.
Complexity theory
“Complexity theory is the study of complex and chaotic systems and how order, pattern, and structure can arise from them. Explained differently, the theory that studies how processes having a large number of seemingly independent agents and can spontaneously order themselves into a coherent system.” (Collinsdictionary.com, 2015)
It is also the theory of classifying problems based on how difficult they are to solve.
According to the complexity theory, the VRP is considered a NP Hard problem, meaning that is is a non deterministic polynomial time hard problem; and as its name suggests it is a hard problem both in terms of definition and solution. It is as hard as the hardest NP Problem. An NP problem is a non deterministic polynomial time problem, and is one that allows non deterministic solutions, i.e not exact, solutions.
A problem is said to be NP hard if an algorithm for solving it can be translated into one for solving any other NP-problem.
Example of the concept of NP-problem
The subset sum problem: Given a set of integers, 1,3,-2,-1,5 , is there a non-empty subset whose sum is zero? The answer here is simple and evident: Yes 3,-2,-1 ; and this can also be formulated in the following manner: ω
1,ω
2,…..ω
n;
Although the previous problem appears to be a simple one, it it almost virtually imposible to determine if any solution exists in the first place, hence the hardness of the problem. (Kleinberg and Éva Tardos, 2006) This is a decision problem (NP-problem).
“As mentioned before the VRP is a NP Hard example; the optimization of it means to find the least cost
cyclic route through all nodes of a weighted graph. This is also known as the Traveling Salesman Problem,
TSP. “ (Lawler et al., 1990) (Wolfram.com, 2019)
Solutions can be of the following type:
- Algorithms designed to find a deterministic solution (works for a limited problem size; as the problem grows in size or parameters, the processing time tends to grow until it becomes unreachable).
- Through heuristic algorithms (explained in detail below), that can deliver a fairly good solution but without being able to prove its optimality.
- Finding a special cases of the problem for which exact heuristics are possible. (Hsor.org, 2019)
Operations research
A scientific approach or discipline used for analyzing problems and making decisions. The fundamental idea behind O.R is to understand the problems (complex situations) through rational bases and then make predictions of the system’s behavior, therefore taking better decisions.
Operations research is done mainly by numerical and analytical techniques for manipulating mathematical and computer models of organisational systems, which could be composed of people, machines and or procedures.
This discipline, as many others, was a development from warfare technology in Great Britain, used to improve many military instances, such as: enemy detection, anti submarine detection and counterattack, effectiveness of bombers, just to mention a few.
The process consisted primarily in direct observation, then data collection, mathematical models formulation, recommendations, then feedback on the impact of the applied changes, and finally repeating the cycle. (see Combinatorial optimization below).
The main objective of OR is the development of mathematical models to improve and optimize real world systems. Models include both deterministic and probabilistic solutions.
Combinatorial optimization
Combinatorial optimization is a topic of applied mathematics that consists in finding an optimal object from a finite set of objects. Exhaustive search for many of these problems is not feasible, as stated before.
One example of a common problem involving combinatorial optimization in indeed, the Vehicle routing problem, VRP. (El-Ghazali Talbi, 2009)
Fig. 3.4 (Hsor.org, 2019)
Today’s world is becoming more and more complex due to competitiveness and the speed information flows, and this obliges the decision making processes in all the fields to improve at a similar pace.
Decision making consists of:
- Formulation of problem
- Model the problem
- Optimize the problem
- Implement a solution
This models are encountered in many fields of science and engineering, but also in social science and business.
For any given problem there may be several global optimal solutions, therefore it is part of the solving to gather all possible global optimal solutions for comparison purposes.
There are many families of optimization models, but the most successful are based in mathematical programming (e.i linear programming) and constraint programming.
Linear programming example:
Non linear problems however deal with mathematical problems where the objective function and/or constraints are nonlinear. This is the reason why in this type of problems one has to minimize the function f The complexity increases in this type of problems as one has to linearize it with distinct methods. It could be by adding more variables and constraints and sometimes some degree of approximation.
Fig. 3.5 (El-Ghazali Talbi, 2009)
Fig. 3.6 (El-Ghazali Talbi, 2009)
“As problems increase in dimensionality, multimodality, epistasis (parameter interaction), and non- differentiability, it render those approaches impotent”. (El-Ghazali Talbi, 2009)
This is where heuristics come into play as they can solve moderate and large problems.
Heuristics Vs. Metaheuristics
There are countless applications for optimization. In theory every process has the potential to be improved through optimization. Every human activity, both profesional and personal has to do with decision making. In the industrial context the decision making has to do with optimization; by reducing resource usage, production times, reducing costs, etc
The most common methods to solve these problems are heuristics and metaheuristics techniques as no exact algorithm can work on a reasonable computing time when one is dealing with “big” problems, such as VRP, recalling the “NP- Hardness” of the problem.
Modern methods can even find solutions for large problems, such as millions of points within a reasonable time while keeping a 2-3% error from the optimal solution.
In the science world, all fields, Engineering, Economics, Business there are always optimization problems with a very high complexity level, hence difficult to solve. Exact ways to solve it are intensive in terms of consuming resources, these being time or money (computing power). Therefore approximate ways to solve these were developed to obtain “reasonable solutions”.
Many problems in several fields only need a “reasonable solution” rather than an exact one.
This methods otherwise called approximation algorithms or heuristics are problem dependent, designed and applied to particular problems. (e.g Google maps directions )
Metaheuristics goes one level up and is independent of a particular problem, therefore acting like a blackbox that potentially could help solve any optimization problem you put in it. (Uslan, 2010)
The word Heuristic comes from greek heuriskein, which means the art of discovering new strategies to
Fig. 3.7 (El-Ghazali Talbi, 2009)
the upper level of general templates that can be used as guidelines strategies in designing underlying heuristics to solve specific optimization problems. (El-Ghazali Talbi, 2009)
Heuristics represent a family of approximate optimization techniques that gained a lot of popularity in the past two decades. These provides “acceptable” solutions in a reasonable time for solving hard and complex problems. Unlike exact optimization algorithm, heuristics do not guarantee the optimality of the obtained solutions.
Heuristics help convert a rather infinitely large space of solutions into a simpler one by making divisions/
groups and reducing it. In this way Heuristics helps to solve larger problems faster, by obtaining robust algorithms, plus being flexible and versatile. (El-Ghazali Talbi, 2009)
Heuristics are a part of optimization in computer science and applied mathematics that are related to algorithms and computational complexity theory.
An interesting feature of some Heuristics is that they somehow mimic natural metaphors to solve complex optimization problems e.g. ant colony (explained later), evolution of species, wasp swarm amongst others.
The evolution in this technique has been incredibly fast and iterative in many fields of science such as artificial intelligence, machine learning, mathematical programming, and operations research. They help solve real life complex optimization problems, e.i. logistics (our particular interest), bioinformatics, engineering design, networking, medicine, etc.
In the following section some of these heuristic methods will be explained to a greater extent.
Cluster analysis
Cluster analysis is a technique that helps classifying a huge amount of information into manageable meaningful piles. The tool creates subgroups that help the analysis of the whole information in a simplified way. It organizes observed data (eg. people, events, things, etc) into meaningful taxonomies, groups, clusters, based on the initial values of the points, maximizing the similarity of the points in each cluster, hence its definition: A cluster, a group of relatively homogeneous cases or observations classified into operational groups. (Burns and Burns, 2008)
The analysis doesn't make distinction between dependent and independent variables and also doesn't require to have any prior knowledge of the the elements belonging to a certain cluster since these are defined in the process.
The most popular types of clustering are the following:
- Hierarchical clustering; builds models based on distance connectivity.
- Centroid models, represents each cluster by a single mean vector, such as in the k-mean algorithm.
- Density models, defines clusters as connected dense regions in the whole exploration space.
There are over 100 different published algorithms for clustering. There is no best algorithm, they all serve
different purposes, so they have to be tested depending on the problem one intends to solve.
Hierarchical clustering
Is the major statistical method for finding relatively homogeneous clusters of cases based on characteristics. Starting with the same number of clusters as cases then it starts reducing it as steps progress. (Burns and Burns, 2008)
A hierarchical tree diagram, called a dendrogram can be produced to show the linkage points.
In general the merges and splits are determined in a greedy manner.
A measure called metric has to be selected in order to give the clusters a specific shape.
The first step is to determine which elements to merge in a cluster. Usually, we want to take the two closest elements, according to the chosen distance.
Centroid based clustering, or K means clustering
Clusters are represented by a central vector, which may or not be a part of the data set. When the number of clusters is defined by a k number, then the k-clustering gives a formal definition as an optimization problem: “find the k cluster centers and assign all the objects to the nearest cluster center, such that the squared distances from the cluster are minimized.”
Therefore, this type of clustering differs from the Hierarchical explained above since we define the cluster number (k number) as an input data.
This method finds a local optimum, and has to be run several times with random initializations.
The algorithm prefers having clusters of approximately the same size as they will always assign an object to the nearest centroid. (Lloyd, 1982)
Fig. 3.8 (Burns and Burns, 2008)
Fig. 3.9 K-means
