COMBINING ADVANCED FORECASTING METHODS WITH SYSTEM DYNAMICS – THE CASE OF FINNISH SEAPORTS
Supervisor: Prof. Markku Tuominen Instructor and supervisor: Prof. Olli-Pekka Hilmola
Lappeenranta, September 26, 2008
Lauri Olavi Lättilä Laserkatu 3 BC 232 53850 Lappeenranta
Title: Combining Advanced Forecasting Methods with System Dynamics – the Case of Finnish Seaports
Department: Industrial Engineering and Management
Year: 2008 Paikka: Lappeenranta
Master’s Thesis. Lappeenranta University of Technology.
128 pages, 65 figures, 15 tables and 10 appendices Supervisors: Professor Markku Tuominen
Professor Olli-Pekka Hilmola
Hakusanat: Ennustaminen, systeemidynamiikka, satamat Keywords: Forecasting, System Dynamics, seaports
Seaports play an important part in the wellbeing of a nation. Many nations are highly dependent on foreign trade and most trade is done using sea vessels. This study is part of a larger research project, where a simulation model is required in order to create further analyses on Finnish macro logistical networks. The objective of this study is to create a system dynamic simulation model, which gives an accurate forecast for the development of demand of Finnish seaports up to 2030.
The emphasis on this study is to show how it is possible to create a detailed harbor demand System Dynamic model with the help of statistical methods. The used forecasting methods were ARIMA (autoregressive integrated moving average) and regression models. The created simulation model gives a forecast with confidence intervals and allows studying different scenarios. The building process was found to be a useful one and the built model can be expanded to be more detailed. Required capacity for other parts of the Finnish logistical system could easily be included in the model.
Työn nimi: Edistyneiden ennustemenetelmien yhdistäminen systeemidynamiikan kanssa – esimerkkinä Suomen satamien kysyntä
Osasto: Tuotantotalous
Vuosi: 2008 Paikka: Lappeenranta Diplomityö. Lappeenrannan teknillinen yliopisto.
128 sivua, 65 kuvaa, 15 taulukkoa ja 10 liitettä Tarkastajat: Professori Markku Tuominen
Professori Olli-Pekka Hilmola
Hakusanat: Ennustaminen, systeemidynamiikka, satamat Keywords: Forecasting, System Dynamics, seaports
Satamilla on merkittävä rooli kansakuntien hyvinvoinnin kannalta. Useat valtiot ovat hyvin riippuvaisia kansainvälisestä kaupasta ja suurin osa kaupasta tapahtuu meriteitse. Tämä tutkimus on osa laajempaa tutkimusraporttia, jossa tarvitaan simulointimallia laajempien analyysien luomiseksi Suomen makrologistisista verkostoista. Työn tavoitteena on luoda systeemidynaaminen malli, joka antaa tarkan ennusteen Suomen satamien kysynnän kehittymisestä vuoteen 2030 ulottuvalla ajanjaksolla.
Työn painopisteenä on osoittaa, kuinka systeemidynaaminen satamien ennustemalli on mahdollista rakentaa tilastollisen analyysien avustuksella. Työssä käytetään ennustemenetelminä ARIMA- (autoregressive integrated moving average) sekä regressiomalleja. Luotu malli antaa ennusteen luottamusväleillä ja mahdollistaa eri skenaarioiden tarkastelun. Mallin luomisprosessi havaittiin hyödylliseksi ja rakennettua mallia on mahdollista laajentaa sisältämään yksityiskohtaisempia tietoja Suomen logistisista järjestelmistä.
during the summer of 2008. This thesis is only one part of a larger research project and I have had the possibility to work in an interesting and challenging project.
I would like to express my gratitude to the supervisor of this study, Professor Markku Tuominen, for giving me the opportunity to conduct research at Lappeenranta University of Technology. I would also like to thank my instructor, Professor Olli-Pekka Hilmola, for his advices and guidance during this research. Without his mentoring during my studies I would not have been able to conduct this research.
Finally, I would like to give many thanks to my family and to my fiancée Anja for their support during these years.
September 26, 2008
Lauri Lättilä
1.1 Background ... 1
1.2 Study objectives and research questions .... 2
1.3 The structure of the study ... 3
2 Quantitative Modeling and Forecasting ... 5
2.1 Systems Thinking and System Dynamics ... 5
2.2 Quantitative Forecasting Methods ... 11
2.2.1 Principles of quantitative forecasting and method selection ... 13
2.2.2 Time Series Analysis ... 15
2.2.3 Goodness of fit criteria ... 29
2.2.4 Top-Down and Bottom-up forecasts ... 31
2.3 Other simulations ... 32
3 Forecasting port demand ... 35
3.1 Definition ... 35
3.2 Literature review ... 36
4 Research environment ... 43
4.1 Research approach ... 43
4.2 Background for this research ... 44
4.3 Data collection and analysis ... 44
4.4 Reliability and validity ... 45
5 The system dynamic model ... 48
5.1 Building process ... 48
5.1.1 Gather expert opinions ... 49
5.1.2 Gather data ... 53
5.1.3 Correlation ... 54
5.1.4 Exports ... 57
5.1.5 Imports ... 60
5.1.6 Export transition ... 63
5.1.7 Import transition ... 65
5.2 Building the System Dynamic model using Vensim ... 67
5.2.1 Exports and imports in the system dynamic model ... 67
5.2.2 Transition in the system dynamic model71 5.3 The final model ... 76
5.4 Results from the model ... 79
5.4.1 Total demand ... 80
5.4.2 Liquid bulk ... 84
5.4.3 Dry Bulk ... 86
5.4.4 General goods cargo ... 89
5.4.5 Ports of Kotka and Hamina ... 93
5.4.6 Summary of the model ... 109
model ... 114
7 Conclusions ... 116
7.1 Results of the study ... 116
7.2 Suggestions for further research ... 117 References
Appendices
Figure 2: Forecasting method selection tree... 14
Figure 3: Example of an additive and a multiplicative model... 18
Figure 4: Creating an ARIMA model... 22
Figure 5: The model’s building process... 48
Figure 6: Causal diagram of Imports and Exports.... 50
Figure 7: Causal diagram of transition... 50
Figure 8: From national demand to local demand... 52
Figure 9: Pareto chart from Finnish ports... 53
Figure 10: Linear connection between exports in Euros and exports in tons... 59
Figure 11: Linear connection between imports in Euros and imports in tons... 62
Figure 12: Export transition’s regression model’s confidence limits and real values... 64
Figure 13: Total exports in thousand tons... 67
Figure 14: Total exports in Euros... 68
Figure 15: Exports in individual ports... 69
Figure 16: Total imports in thousand tons... 71
Figure 17: Export transition in Finland... 72
Figure 18: Individual ports’ shares from export transition... 73
Figure 19: Import transition in the system dynamic model... 74
Figure 20: The export transition shares... 75
Figure 21: The development of industrial production in Finland... 76
Figure 22: Russian oil exports during years 1997 to 2007... 78
Figure 23: Total demand in the first scenario... 80
Figure 24: Total demand in the second scenario... 81
Figure 25: Total demand in the third scenario... 82
Figure 26: Total demand in the fourth scenario... 83
Figure 27: Total liquid bulk demand in the first scenario... 84
Figure 28: Total liquid bulk demand in the second scenario... 85
Figure 29: Total liquid bulk demand in the third scenario... 85
Figure 30: Total liquid bulk demand in the fourth scenario... 86
Figure 31: Dry bulk demand in the first scenario.... 87
Figure 32: Dry bulk demand in the second scenario... 88
Figure 33: Dry bulk demand in the third scenario.... 88
Figure 34: Dry bulk demand in the fourth scenario... 89
Figure 37: General goods cargo demand in the third scenario... 91 Figure 38: General goods cargo demand in the fourth scenario... 92 Figure 39: Liquid bulk demand at Hamina according to the first scenario... 93 Figure 40: Liquid bulk demand at Kotka according to the first scenario... 94 Figure 41: Liquid bulk demand at Hamina according to the second scenario... 95 Figure 42: Liquid bulk demand at Kotka according to the second scenario... 95 Figure 43: Liquid bulk demand at Hamina according to the third scenario... 96 Figure 44: Liquid bulk demand at Kotka according to the third scenario... 96 Figure 45: Liquid bulk demand at Hamina according to the fourth scenario... 97 Figure 46: Liquid bulk demand at Kotka according to the fourth scenario... 97 Figure 47: Dry bulk demand at Hamina according to the first scenario... 98 Figure 48: Dry bulk demand at Kotka according to the first scenario... 99 Figure 49: Dry bulk demand at Hamina according to the second scenario... 100 Figure 50: Dry bulk demand at Kotka according to the second scenario... 100 Figure 51: Dry bulk demand at Hamina according to the third scenario... 101 Figure 52: Dry bulk demand at Kotka according to the third scenario... 101 Figure 53: Dry bulk demand at Hamina according to the fourth scenario... 102 Figure 54: Dry bulk demand at Kotka according to the fourth scenario... 103 Figure 55: General goods cargo demand at Hamina according to the first scenario... 104 Figure 56: General goods cargo demand at Kotka according to the first scenario... 104 Figure 57: General goods cargo demand at Hamina according to the second scenario... 105 Figure 58: General goods cargo demand at Kotka according to the second scenario... 105
Figure 61: General goods cargo demand at Hamina
according to the fourth scenario... 108
Figure 62: General goods cargo demand at Kotka according to the fourth scenario... 108
Figure 63: Total demand for all Finnish ports... 110
Figure 64: Industrial production index... 111
Figure 65: The historical prices of crude oil... 113
TABLE OF TABLES Table 1: The Major principles behind System Dynamics 6 Table 2: The basic elements of system dynamics ... 8
Table 3: Autocorrelation and partial autocorrelation patterns ... 23
Table 4: Developing an econometric model ... 25
Table 5: Goodness of fit criteria for forecasts .... 29
Table 6: Methodological frameworks ... 43
Table 7: Correlations between variables in the import and export models ... 55
Table 8: Correlations between variables in the transition models ... 56
Table 9: The shares of export transition for liquid bulk, dry bulk, and general goods cargo ... 74
Table 10: The regression models for industrial production ... 77
Table 11: The regression models for Russian oil exports ... 78
Table 12: The simulated scenarios ... 79
Table 13: The simulated, aggregate total demand in Finnish ports in different scenarios ... 83
Table 14: The simulated general goods cargo demand in Finnish ports in different scenarios ... 92
Table 15: Ports impacted by transition ... 115
2
ˆa
σ maximum likelihood estimate of standard deviation at forecast
bt adjustment factor b0 constant
b1 coefficient for variable X C consumption
Ct cyclicality component at time t ei error during time period i
Fi amount of error during time period i G governmental consumption
I investments
It irregular component at time t k amount of observations used M imports
Mt moving average
'
Mt second moving average n amount of observations
p amount of time periods to forecast r number of parameters in the model St seasonal component at time t
Tt trend component at time t X exports
Xi actual observation of variable X during time period i
Y national production
Yi dependent variable Y in observation i Yt value of observation at time t
p t
^
Y + forecast during time period t + p
AIC Akaike Information Criteria
ARIMA Autoregressive Integrated Moving Average BIC Bayesian Information Criteria
GDP Gross Domestic Product
IMF International Monetary Foundation PACF Partial Autocorrelation Function TEU Twenty-foot equivalent unit
1 INTRODUCTION
1.1 Background
Seaports play an important part in the Finnish foreign trade flows as over 75 percent of trade (in tons) happens through seaports (National Board of Customs, Statistics Unit, 2007, 270). On a global scale the amount of trade through sea is enormous and trade using containers has increased to 142.9 million TEU a year (Drewry Shipping Consultants, 2007, 6). As the world becomes even more connected through globalization, this trend will most likely continue to grow (IMF, 2007, 3).
As seaports usually require significant investment from companies or governments (in Finland most ports are owned by municipalities), estimating their development plays an important part. They also play an important part in the competitiveness of the national infrastructure and thus have an indirect impact on the competitiveness of companies. In addition to competitiveness of a nation, seaports play an important part in the overall wellbeing of a nation as most countries are heavily dependent on trade (for instance, in Finland the amount of exports and imports are 44.5 percent and 39.3 percent, respectively, from the Finnish GDP) (SF, Economic Statistics: National Accounts, 2007, 322).
1.2 Study objectives and research questions
The objective of this study is to examine the development of Finnish ports during the next twenty years. The research question can be presented as:
How will the demand for major Finnish seaports evolve up to year 2030?
Ports have four types of demand: Imports, exports, import transition, and export transition. In Finland the presence of Russia has a major impact on import and export transition. Hence, in order to study the main research question it has to be further divided to smaller questions:
How will the individual sub-demands develop up to year 2030?
What are the driving factors behind the individual sub- demands and how will they develop?
The research question and the sub-questions are analytical by nature as the purpose is to find the driving factors behind Finnish ports’ demand and estimate their development. This study focuses only in the most important Finnish sea ports as there are at least 29 ports in Finland (Finnish Port Association, 2008). In Finland it is assumed that the national demand will concentrate on fewer ports and thus it is only relevant to study the most important ports.
Also, as the handling of different kinds of cargo (liquid bulk, dry bulk, and general goods cargo) differs greatly, the forecast of each port should also be divided to different kinds of cargo and hence, the third sub-question is:
How will the demand regarding individual cargo types (liquid bulk, dry bulk, and general goods cargo) develop at each port up to year 2030?
This study is only interested in the actual demand at the seaports. Hinterland logistics is assumed to be sufficient and it will not impose any constraints for the development of ports. The data for this study has been collected from numerous different public sources.
All of the data is second hand data as there is an abundance of it and the sources are reliable. The data collected and their sources are presented in Appendix 1.
1.3 The structure of the study
Chapter 2 explains the principles of quantitative forecasting and modeling. System Dynamics and different quantitative forecasting methods are presented briefly as well as some goodness of fit criteria and the difference between top-down and bottom-up forecasts. A literature review of publications regarding system dynamics with Monte Carlo simulations is also presented in this chapter.
In Chapter 3 the role of ports is discussed. A literature review about the forecasting or simulations of port demand is also presented in this chapter. This literature review also shows, which kind of demand has been studied earlier (liquid bulk, dry bulk, or general goods cargo).
Chapter 4 explains how the empirical part of this study has been conducted. Also, the research approach of this study is presented. The data collection process is also reviewed and reliability as well as validity of the study is discussed.
In Chapter 5 the actual construction process of the simulation model is presented. This chapter also shows the results from the model on a national level and also in two important Finnish ports. Chapter 6 presents the discussion about the model and chapter 7 the conclusions of this study among future research directions.
2 QUANTITATIVE MODELING AND FORECASTING
2.1 Systems Thinking and System Dynamics
Systems Thinking sees everything being connected to everything else. It gives a holistic view about the systems we live in and encourages taking action, which serves the long-term best interest for the whole. It helps to identify the leverage points for the system and helps to avoid policy constraints. Systems Thinking can be seen as a method to enhance learning. One very popular book about Systems Thinking is Senge’s “The Fifth Discipline”. It examines Systems Thinking in the light of a learning organization and links it with four other, basic disciplines. (Sterman, 2000, 4; Senge 1990; Maani & Maharaj, 2004, 22)
Systems Thinking concentrates on dynamic complexity. It is different from detailed complexity, where the complexity arises from the wide array of possibilities, while in dynamic complexity the nonlinear and multiloop feedbacks create the complexity. (Sterman, 2000, 4 – 5;
Maani & Maharaj, 2004, 24)
System Dynamics has been developed by Jay Forrester in the late 1950s. The first book, “Industrial Dynamics”, was published during the year 1961. It presented the philosophy and methodology of System Dynamics.
“Industrial Dynamics” was later expanded to Urban and World Dynamics. The famous “Limits of Growth” –book based its findings on a system dynamic model called
World3, developed by Forrester. (Forrester, 1991, 11 - 20)
System Dynamics take systems thinking into modelling and use programs to calculate the outcomes. The programs have a graphical view, but the basic principles are based on mathematics. According to Sterman (2000, 79 – 81) there are 12 principles for successful use of System Dynamics. These are presented in Table 1.
Table 1: The Major principles behind System Dynamics. This table shows the most important principles behind system dynamics. (Sterman, 2000, 79 – 81)
Principle
Develop a model to solve a particular problem, not to model the system
Modelling should be integrated into a project from the beginning
Be sceptical about the value of modelling and force the
“why do we need it” discussion at the start of the project
System Dynamics does not stand alone. Use other tools and methods as appropriate
Focus on implementation from the start of the project Modelling works best as an iterative process of joint inquiry between client and consultant
Avoid black box modeling
Validation is a continuous process of testing and building confidence in the model
Get a preliminary model working as soon as possible. Add detail only as necessary
A broad model boundary is more important than a great deal of detail
Use expert modelers, not novices
Implementation does not end with a single project.
There are 6 basic types of elements in system dynamic models and they are presented in Table 2 and Figure 1.
By combining these elements it is possible to simulate more complex elements such as delays. Elements have their own kind of mathematical formulaes underneath and they will be presented later. (Sterman, 2000, 137 - 147, 191 - 197)
Stock
Inflow Outflow
Variable
Source Sink
Feedback loops
Figure 1: A simple system dynamic model. This figure shows the basic elements of system dynamic models. The elements are explained in Table 2 (Adapted from Sterman, 2000, 137 - 147, 191 – 197)
Figure 1 shows a simple system. The inflow could be Production and outflow Sales. The stock would then indicate Finished Goods Inventory. The variable would be the desired amount of finished goods which the company wants to hold. The feedback loops from the variable and stock to the valve would tell the inflow how much of products should be produced. Sales would take goods from the stock, which would then send a signal to production. Production would then produce the desired amount.
Table 2: The basic elements of system dynamics.This table shows the basic variables in System Dynamics. The pictures are presented in Figure 2. (Adapted from Sterman, 2000, 137 - 147, 191 – 197)
Name Description
Stocks Stock can be visualized as a bath tube where the water flows from a valve. If only the valve is open water will keep accumulating in the stock. So stocks can be said to be accumulations.
Flows There are two kinds of flows: Inflows and Outflows. Inflows flow into a stock while outflows flows out of them. A flow may be both an inflow and outflow if it flows from a stock to a stock.
Otherwise the other end will be a sink or source.
Causal loops Causal loops indicate an information flow from an element to another element. They might have a positive or negative polarity. A positive causal loop indicates that the target variable increases due to the causal loop. A negative loop does the vice-versa. A causal loop might also be called a feedback loop.
Sinks / Sources
Sink and sources are the end “boundaries” of the system. They represent stocks which are outside of the constructed model. A source indicates a stock from which an inflow takes its components. A sink is the stock where an outflow flows. They have infinite capacity and the do not have any kind of constraints.
Valve Valve is the flow regulator. They are a part of a flow and indicate the amount of components flowing through.
Variables Variables are connected with causal loops. Causal links relate the variables and the polarity indicates how the dependent variable changes due to changes in the independent variable.
It is possible to create a rather complex system with these 6 elements. Even thought one would understand how every element operates, the operation of the whole
system might not be that clear. The feedbacks create complexity beyond the individual elements.
The actual simulation happens purely on mathematical functions. In the mathematical sense, the stock variables are integrals as they present the accumulation from different kind of flows. E.g. Stock in Figure 1 is an integral function of “Inflow – Outflow”. The value of Stock during time period X is only an integration of that function with a lower value of 0 and the higher value of X. It should be noted, that the equation inside the stock variable might not be as simple as inflows minus outflows. It is possible to take, for instance, only 50% of the sum of two inflows if one wants to simulate a situation, where to inflow objects are used to create only one object.
Usually the equations of inflows and outflows are more sophisticated than the ones of stocks. As stated earlier, Inflow in Figure 1 uses a variable and the feedback from Stock in order to control the amount of objects to move from Source to Stock. The equation can contain anything from a random distribution to different kinds of mathematical functions. Thus, it is possible to create even highly sophisticated equations in each of the possible variables in the model.
According to Sterman (2000, 191) stocks and flows are one of the most important concepts in system dynamics, but on the other hand, a simulation model can also be constructed without the use of these. It is possible to create a meaningful and useful model only using variables and feedbacks between the variables. The
variables can contain the exactly same functions as the flows, but there is no need to use stocks or sources / sinks. If one is not interested in the aggregation of different flows during the simulation period, it is possible to only use variables and feedbacks.
If a system dynamic model contains equations, which have a random distribution function or seeds, a Monte Carlo simulation should be conducted as one cannot trust the results from one single simulation run. Even though some simulation softwares (such as Vensim and Anylogic) allow the use of Monte Carlo simulations, very few research papers have been published on the subject. “System Dynamics” and “Monte Carlo” were used as search words on the databases of Elsevier, ABI- Inform Global, and Ebscohost. The results: only two papers were found to have a system dynamic model with a Monte Carlo simulation. The first paper (Fiddaman, 2002) was about policy options in a climate-economy model and the second one (Miller & Clarke, 2007) was about air transportation infrastructure. More publications can be found in System Dynamics Society’s yearly conferences. The papers are summarized in Appendix 2.
Only those papers are presented, which contain a system dynamic model simulated using Monte Carlo –experiments.
There were only 13 papers in eight years worth of System Dynamic Society’s conferences and journal publications. Overall it can be said, that the amount of publications with Monte Carlo simulations is relatively low. All expect one (Nircan, 2001) of the publications had a similar way of conducting a Monte
Carlo analysis. Either the seed of a variable with a predefined random distribution was allowed to vary between some values or a variable itself was allowed to vary between some defined levels.
Most Monte Carlo simulations were used to study the amount of uncertainty in the final results of the model. Moxnes & Kråkenes (2005) used Monte Carlo in conjunction with other methods when they tried to find optimal policies concerning fisheries and pricing. As the model had stochastic variables, a Monte Carlo simulation was needed to include the uncertainty. The purpose of the paper was to show how an optimal policy can be obtained, when uncertainty is included. On the other hand, Graham et al. (2002) used Monte Carlo to define a working model, which was compared with historical data. The variables in the model were allowed to vary and the results of the model were compared to historical data. This method is similar to neural network approach, where the model’s actual values are searched and optimized, rather than given.
Nircan (2001) used Non Parametric Monte Carlo Technique in order to feed random curves in a model. In his paper the randomness comes through the whole equations, while in other papers the equations were predefined.
2.2 Quantitative Forecasting Methods
There are different kinds of methods to divide forecasting methods into smaller classes. Armstrong (2004, 9) has divided forecasting methodology into two major areas: judgmental and statistical methods. In
statistical methods the data is objective, while in judgmental methods the data is subjective. Makridakis &
Wheelwright (1989, 13) expand Armstrong’s classification by adding a third method; technological methods. In technological methods long-term issues regarding technological, societal, economic, or political nature, are studied.
According to Pitkänen (2008, 3) it is possible to divide forecasting methods into projective methods, methods generating optional possibilities, and goal- oriented methods. In projective methods the objective is to find out the most probable trend in development.
On the other hand, in methods generating optional possibilities the main objective is to find out how various events impact the behavior of a system. In the goal-oriented methods the main purpose is to find out the possible ways how to reach a desired goal. This kind of classification is based on the objective of the forecasting method.
Pitkänen (2008, 3 - 4) also shows how it is possible to classify forecasting methods according to the used data. In this way forecasting should be divided into statistico-empirical methods, intuitive methods, qualitative-structural methods, and simulations. In statistico-empirical methods statistical methods are used to create estimates about the future. In intuitive methods judgmental data is used to generate the estimates. On the other hand, in qualitative-structural methods the purpose is to gain an understanding of the actual problem and other methods are used to make the actual forecasts. In the final class, simulation
models, the simulations are used to analyze the situation and to create forecasts. There are also other classifications as well (such as micro or macro, long term or short term,) but they will not be presented (Hanke et al., 2001, 3).
2.2.1 Principles of quantitative forecasting and method selection
Armstrong (2004, 7 – 8) has summarized some general forecasting principles, which have long historical foundations. These principles were developed prior of the 1960s (earlier than the whole concept of system dynamics was developed), but still hold true. The principles are: correct for biases in judgmental forecasts, forecasts provided by efficient markets are optimal, use the longest time series available, econometric forecasting models should be fairly simple, do not use judgment to revise predictions from cross- sectional forecasting models that contain relevant information, and theory should precede analysis of data in developing econometric models. (Armstrong, 2004, 7 – 8)
On the other hand, according to Hanke et al. (2001, 8) there are only two major rules, which govern the whole forecasting process: The forecast should be technically correct and produce accurate enough forecasts, and the forecasting procedure and results should be efficiently presented and management should use the information in decision-making.
Armstrong (2004, 376) has divided forecasting methods to two major branches, judgmental and statistical forecasts. He also presents this in a tree fashion, so it is possible to choose the right forecasting method.
This is presented in Figure 2.
Figure 2: Forecasting method selection tree. This figure helps at choosing the right forecasting method. (Armstrong, 2004, 376)
Hanke et al. (2001, 440), on the other hand, divide forecasting models into two classes, causal forecasting models and time series forecasting methods. In causal forecasting it is assumed that there is sufficient causality between the inputs and the outputs of the system. This is a similar assumption in econometric models so they can be seen to be the same thing. Time series forecasting models (Hanke et al.,2001, 440) can be seen to be a part of extrapolation methods so Hanke et al. only provide a more detailed view about two branches in Armstrong’s (2004, 376) selection tree.
2.2.2 Time Series Analysis
According to Box et al. (2008, 1) time series’
observations are dependent and time series analysis uses different techniques to study this dependence, and in order to analyze these dependencies, it is required to develop stochastic and dynamic models. Box et al.
(2008, 1 – 2) continue by saying that there are five different applications for these models: forecasting future values, determining transfer functions, determining the effects of interventions, creating multivariate models using many variables, and creating control schemes.
The first application, forecasting future values, is the most explicit one. In this application the previous values of the time series will be used to forecast the future values of the time series (Box et al., 2008, 2 – 3. There are a lot of different methods, which can be used to create the forecasts. Hanke et al. (2001, 440) have divided time series forecasting methods to Seasonal Decomposition, Moving Averages and Exponential smoothing, ARIMA, and Neural Networks.
A transfer function uses the values from time series X to explain the values in time series Y. There will always exist noise in addition with the input variable X, so the transfer function might not be that easily estimated. If the variable Y to be forecasted is also an output for a transfer function with input variable X, it is possible to make a better forecast as error in the model tends to decrease. (Box et al., 2008, 3 – 4)
Intervention analysis is somewhat similar to transfer functions, but the input variable is a binary value (either 0 or 1) indicating either presence or absence of an event. The purpose might be to analyze the impact of an intervention or remove the effect of an intervention from time series analysis. (Box et al., 2008, 4 – 5)
In multivariate time series analysis the dynamic relationship between many variables will be studied simultaneously. As different time series are studied jointly, the dynamic relationships give additional information and the forecasts will be more accurate.
(Box et al., 2008, 5)
In the final application, discrete control systems are created. Control systems are used to monitor a process and make corrections in order to control the output. It is possible to create either a feedforward control, where the input variables are also monitored, or create a feedback control were corrections are made to the input variables according to the changes in output variables. (Box et al., 2008, 5 - 7)
2.2.2.1 Classical Time Series Analysis
In classical time series analysis the time series is assumed to be consisted of four components: trend, cyclical fluctuation, seasonal fluctuation, and irregular changes. The trend represents the long term development, while the cyclicality represents systematic fluctuations. The seasonal component impacts
the time series according to the periodicity of the time series. The irregular component is basically an error term and it is assumed to be homoscedastically normally distributed around zero. (Hanke et al., 2001, 143 – 167)
The models can be either additive or multiplicative. In an additive model the variation does not increase as time passes by, but in a multiplicative model it does.
In multiplicative models the seasonal spikes get even higher, while the valleys rise relatively slower. These are presented in Figure 3. The top figure has additive seasonality, while the bottom one has multiplicative seasonality. (Hanke et al., 2001, 145 – 146)
Multiplicative model’s equation is
t t t t
t T C S I
Y = × × × (1)
and additive model’s is
t t t t
t T C S I
Y = + + + (2)
Where Yt = value of observation at time t Tt = trend component at time t
Ct = cyclicality component at time t St = seasonal component at time t It = irregular component at time t
0 10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 10 20 30 40 50 60 70 80 90 100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Figure 3: Example of an additive and a multiplicative model. This figure shows the difference between an additive and a multiplicative time series. The top figure shows an additive model while the lower one shows a multiplicative model.
The analysis starts by taking away the seasonal pattern from the time series. This is done by calculating the average shares during the seasons (e.g. each month in a monthly data, each quarter in a quarterly data etc.) compared to the 12 month moving average. Each month thus gains an own seasonal index. Then the original data is multiplied by the seasonal indexes and one gets the seasonally adjusted time-series. (Hanke et al., 2001, 153 - 157)
When seasonality is removed, only the trend, cyclical, and irregular components are present. As in most cases, it is impossible to calculate the cyclical component and it will be combined with the trend component. After
this the trend component is fitted with some ideal functions (such as a linear, quadratic, or S-shaped trend) and the best fitting function is used to represent the trend component. The forecasts can then be calculated by multiplying or adding the parts together (depending on the chosen model). (Hanke et al., 2001, 147 – 153 & 158)
2.2.2.2 Exponential Smoothing and Moving Averages
Moving averages are used to smooth a time series. The fluctuations from the smoothened time series are assumed to be random fluctuations. The smoothened curve can then be used to create the forecast. Moving averages can be constructed with many different ways.
These include simple averages, moving averages, double moving averages, and exponential smoothing methods.
(Hanke et al., 2001, 99 - 108)
In simple averages the mean value of the relevant historical values is used as a forecast and thus is actually only the mean value of the time series. In the case of moving averages, only k amount of the most recent values are used to create the moving average.
Again the actual forecast is only a mean of the most recent values and it is presented in equation 3. (Hanke et al., 2001, 99 – 108)
k
) Y Y
Y Y Y (
Mt = t+1 = t + t−1+ t−2+L+ t−k+1
(3) Where Mt = moving average
Yt = value of time series at time t
k = amount of observations used
In double moving average, k amount of moving averages are used to create a forecast. When the moving average has been calculated, it is possible to calculate the second moving average. The equation for calculating the second moving average is presented in equation 4.
k
) M M
M M
Mt' =( t + t−1 + t−2 +L+ t−k+1
(4) Where M't = second moving average
The moving average and the second moving average are used to calculate the forecast a and an additional adjustment factor b. Equations 5 and 6 show this.
' t t
t 2 M M
a = × − (5)
Where at = forecast
) M M 1 ( k
bt 2 × t − 't
= − (6)
Where bt = adjustment factor
The actual forecast is calculated using a and b. The forecast for period p is presented in equation 7.
p b a Yt p t t
^ + = + × (7)
Where t p
^
Y + = forecast during time period t + p p = amount of time periods to forecast
In exponential smoothing, the time series’ previous values are weighted with the help of a geometric series and the most recent observations have higher weights.
There can be as many as four variables, which are used as weights and they depend on the type of the series.
The trend in the time series can be linear, exponential, damped, or non-existing and the seasonal component can be multiplicative, additive, or non- existing. The first weighting variable is alpha, which is the general weight for previous observations. Gamma variable impacts the amount of weight in trend while Phi is used with Gamma, if the series is damped. The final variable Delta impacts the seasonal component of the time series. (Hanke et al., 2001, 107 – 123; SPSS, 2008)
2.2.2.3 ARIMA
In ARIMA the previous values are used to estimate a value in the future with the help of autoregressive and moving average variables. These variables have a certain weight, which is calculated from the historical data. ARIMA models can also have seasonal variables.
These variables are used when there is a seasonal pattern in the time series. In seasonal ARIMA model there are also seasonal moving average and autoregressive variables. Constructing an ARIMA model follows an iterative method. This is shown in Figure 4.
(Hanke et al., 2001, 351 – 354; Box et al., 2008, 18 &
367 – 373)
Figure 4: Creating an ARIMA model.This figure shows how an ARIMA model should be constructed. It is an iterative model until the model cannot be further made better.
(Adapted from Box et al., 2008, 18)
First the seasonal part of the model should be constructed. ARIMA uses autocorrelation functions (ACF) and partial autocorrelation functions (PACF) in order to identify the autoregressive and moving average variables. Statistically significant values at periodicity intervals are a clear sign for the need of a seasonal ARIMA part. The seasonal ARIMA variables are then estimated and the seasonal part is validated by studying the ACF and PACF of the estimated model’s error term. (Hanke et al., 2001, 347 – 350 & 379)
After the construction of the seasonal model it is possible to create the regular ARIMA model. The
creation of the regular ARIMA model differs a little bit from the creation of the seasonal part. In the non- seasonal part one is interested in all of the lags of ACF and PACF plots. Table 3 shows how the variables should be chosen. (Hanke et al., 2001, 347 – 350; Box et al., 2008, 335 – 338)
Table 3: Autocorrelation and partial autocorrelation patterns. This table shows what kind of behavior is expected in the hypothetical ARIMA models. Comparing the plots with the hypothetical situations gives an insight what terms should be included in the model.
(Adapted from Hanke et al. 2001, 354)
Autocorrelations Partial
autocorrelations Ma(q) Cut off after the
order q of the process
Die out
AR(p) Die out Cut off after the
order p of the process
ARMA(p,q) Die out Die out
ACF and PACF plots are used to identify the moving average and the autoregressive variables. These variables are then chosen and estimated. When both parts of the ARIMA model have been estimated, diagnostic checking is conducted. If the diagnostic do not show the need for additional variables, the model can be used for forecasting. (Hanke et al., 2001, 347 – 350; Box et al., 2008, 335 – 338)
2.2.2.4 Regression analysis
Regression models are usually linear, but it is possible to use also different regression models. In linear regression one dependent variable is explained using one or more independent variables. When these independent variables have been chosen, there are a lot of different methods how to do the actual estimation.
The most frequently used is OSL (ordinary least squares). The equation to be constructed is (Hanke et al., 2001, 193 – 202)
i 1
0
i b b X
Y = + × +ε (8)
Where Yi = dependent variable Y in observation i
b0 = constant
b1 = coefficient for variable X
Xi = value of independent variable in observation i
i = error at time i
The regression model can also have no independent variables and time is used as an independent variable.
In this situation, the observations are either divided to values between 0 and 1 or time can be stated in particular time units, such as years etc. If the latter is used, it is easier to understand the regression model. For instance, in a model with years as an independent variable, the values of the estimated variable increase for the amount of the coefficient of years during each year. (Hanke et al., 2001, 294)
2.2.2.5 Econometric models
If the single equation regressions gives poor results or the equation is strongly dependent on other parts of a system, econometric models should be considered.
Econometric models are constructed with many different equations and they are jointly determined (Hanke et al., 2001, 319). Econometric models are also usually based on economic data from which the name also derives from (Hanke et al., 2001, 319). Allen & Fildes (2004, 306 – 308) have created a strategy, which should be used when one creates an econometric model. It consists from eight phases and it is presented in Table 4. The phases are followed consecutively.
Table 4: Developing an econometric model. This table shows how an econometric model should be constructed. Each phase will be done one at a time and they will be followed consecutively. (Adapted from Allen & Fildes, 2004, 306 - 308)
Action
1. Define the objectives of the modeling effort
2. Determine the set of variables to use based on economic theory and previous work
3. Collect data, generally as long a time series as possible 4. Form an initial specification of the model
5. Estimate the model
6. Access model adequacy by conducting misspecification tests 7. Simplify the model as much as possible by employing
specification tests
8. Compare the out-of-sample performance of the final model or models against the performance of a benchmark model
In the first phase the purpose of the modeling effort should clearly be defined in order to make sure that econometric models are the best solution. Allen &
Fildes (2004, 309 - 310) point out, that if the purpose of an econometric model is a pure forecast, one must be able to forecast the explanatory variables well enough in order to create a meaningful model. This is where time series forecasting becomes useful. If it is not possible to create meaningful forecasting models for the explanatory variables, the model should be refined.
In the second phase the set of variables are chosen.
All the important causal variables should be included in the beginning so no important variable is left out.
Theory and earlier empirical studies should give guidance in this process. There should also be only one variable for each conceptual variable. (Allen & Fildes, 2004, 310 - 311)
In the third phase there is only one key principle:
collect the longest data series possible. This phase does not require any additional information but the fourth phase does. In the fourth phase an initial specification is chosen and all previous work should be taken in account when specifying the preliminary model.
Model building should be from a general model to a more specific model. Specifications should only be included when diagnostics tests point out to that. (Allen &
Fildes, 2004, 312 - 316)
If the theory points to a functional form, it should be used. Usually linear functions are better and easier to understand than the non-linear versions. Also, there are more possibilities for pure chance to point out to significance between the variables even though none exist. The model should be estimated initially with
fixed parameters and later on changing the fixed parameters to varying-parameters, if there is a need for them. (Allen & Fildes, 2004, 317 - 319)
In the fifth phase the actual estimation is done.
Whenever possible, only one equation should be used to create the forecast. The variables should be in levels and not in differences initially. Only when it is required to take the first difference in order to create a more meaningful model, it should be done. The estimation should also be done using ordinary least squares as it is the simplest method. All of these principles point out to the key principle which was presented earlier: the econometric forecasting models should be fairly simple. (Allen & Fildes, 2004, 319 - 325)
In the sixth phase misspecification tests are conducted in order to find out whether the model works as it should be. If the tests are not passed, it might mean that the model’s results are unreliable. The model’s residuals should be studied delicately and autocorrelation also needs special attention. (Allen &
Fildes, 2004, 325 - 333)
After the misspecification tests one should do specification tests. The purpose of the specification tests is to simplify the model. The specification tests include reducing the lag lengths and testing for unit roots. Also, if possible the initial model should be simplified to an error correction model. (Allen &
Fildes, 2004, 333 - 339)
In the final phase the econometric model should be compared against other forecasting methods. These methods include subjective and extrapolative models.
The last few observations, which were not used to make the model, are substituted into the model and the results are compared with another benchmarking model.
If the other model performs better than the econometric model, the model should be done again. (Allen & Fildes, 2004, 341 - 346)
2.2.2.6 Neural networks
In neural networks, a network imitating the functioning of brain is used to understand relationship between some variables. Neurons gather information and send an impulse forward according to some criteria. It might be a threshold value which is reached or it always sends some information forward. (Bar-Yam, 1997, 296 - 300)
In practice, examples are programmed into the artificial neural network and the program starts to learn about the relationships. When the program understands the relationships, it is able to make a forecast when new inputs are given to it. (Hanke et al., 2001, 427 – 428)
The artificial neural networks are usually constructed using back propagation as the program has to learn what the relationships behind the variables are (Denton, 1995, 17). The network tries out different values until the output of the model corresponds with the observed values. The program usually minimizes the amount of
squared difference in the output compared to the desired output. (Remus & O’Connor, 2004, 252 – 253)
2.2.3 Goodness of fit criteria
There are many different ways to evaluate the goodness of a forecasting model. Table 5 shows some of the possible goodness of fit criteria and their equations.
Table 5: Goodness of fit criteria for forecasts. This table shows some widely used goodness of fit criteria for forecasts. (Box et al., 2008, 211 – 212. Makridakis &
Wheelwright, 1989, 56 – 59)
Name of goodness of fit criteria Equation Mean error
n e
n
1 i
∑
i=
(9)
Mean absolute deviation
n e
n
1 i
∑
i=
(10)
Mean squared error
n e
n
1 i
2
∑
i=
(11)
Standard deviation of errors
1 n
ei2
∑− (12)
Mean percentage error
n X 100
F
n X
1
i i
i
∑
i=
− × (13)
Mean absolute percentage error
n X 100
F
n X
1
i i
i
∑
i=
− × (14)
Akaike information criteria
t tan n cons
r2 ˆ )
ln(σa2 + + (15)
Bayesian information criteria
n ) n rln(
ˆ )
ln(σa2 + (16)
Where ei = error during time period i n = amount of observations
Xi = actual observation during time period i Fi = forecast during time period i
2
ˆa
σ = maximum likelihood estimate of standard deviation
r = number of parameters in the model
Overall it can be said, that whatever criteria used, it is better to have a lower value. In mean error (and mean percentage error) one is interested about the mean error between the estimate and the observation. If the errors are distributed evenly around the observations, mean absolute deviation (and mean absolute percentage error) gives better information as it tells how large the actual average error is. In mean squared errors larger deviations are punished more severely than smaller deviations. Standard deviation of errors gives similar information as it calculates the standard deviation, not the amount of squared errors. In AIC and BIC (used in models which are calculated using maximum likelihood method, such as ARIMA and regression models) the maximum likelihood estimate of standard deviation is used in conjunction with the amount of variables in the model. Even though more variables might give a smaller deviation, the information criteria penalize these and try to maximize the utility of the model with the least amount of variables. (Makridakis &
Wheelwright, 1989, 56 – 59; Box et al., 2008, 211 – 212)
2.2.4 Top-Down and Bottom-up forecasts
General-to-specific approach first creates a forecast for an aggregate data and then divides the aggregate to specific time series. For instance, one first creates a national forecast for toothpaste demand and after that creates a forecast for one brand. The other way to create a forecast is to first create a forecast for each disaggregate time series and then aggregate the disaggregate forecasts. (Allen & Fildes, 2004,314 – 316)
Schwarzkopf et al. (1985, 1834) have summarized some of the claims regarding both forecasting methods from earlier studies. It might be easier to specify an aggregate equation and thus create more accurate forecasts by first creating an aggregate forecast. On the other hand, information will be lost as data is aggregated and this leads to poorer forecasts.
Lapide (1998, 28) points out the various ways how to aggregate or disaggregate data. Possible dimensions for aggregation are business unit dimension, product dimension, geographic dimension, operational dimension, or time dimension. Lapide (1998, 28) continues giving examples how a top-level forecast can be allocated to individual components: an equal share to all components; historical shares for components;
components’ shares come from component level forecasts.
In the last situation there is a need to create forecasts for each individual component.
2.3 Other simulations
There are many other simulation techniques, but in this chapter only methods relevant to simulating complex systems are presented. Simulations regarding, for instance, computational fluid dynamics, and particles are left out of this chapter. The modeling-paradigms of agent-based-modeling and discrete-event-modeling are presented shortly.
In agent-based modeling the simulation is done simulating individual actors’ behavior and how they interact between each other. The dynamics of the system is derived from the interaction between the actors, not from the actors per se. Each agent has its own states and properties, and uses some kind of functions to interact with other agents. (Borshchev & Filippov, 2004, 6 – 7)
In multi agent-based modeling different agents may have different kind of characters. According to Tweedale et al. (2007, 1091) the most important categories are mobility, reasoning model, and other attributes.
Tweedale et al. (Ibid.) continue by saying that there are also other ways to classify the agents but due to the large area of use of agents, it is not possible to create one “right” way to classify all of the different kind of agents.
Another important aspect about multi agent-based models is the interaction between different agents. Cabri et al. (2004, 1) have summarized some of the collaboration
and coordination methods and these include Tuple- Spaces, Group Computation, Activity Theory, and Roles.
As different agents have different characteristics and there are many different ways how agents can collaborate with each other, there is loads of different kind of agent interactions possible.
Discrete-event simulation usually uses a “transaction- flow world view”. Discrete units flow inside the system and compete on the resources. Resources offer services to entities, which are the flowing units in the system.
The name for the simulation comes from events, which are imposed on the entities and resources. (Schriber &
Brunner, 2005, 167 – 168)
The entities can have many different states during the simulation. These states include the active state, ready state, time-delayed state, condition-delayed state, and dormant state. These states are needed by the model in order to conduct the simulation. (Schriber
& Brunner, 2005, 169)
The actual simulation has a two-phase loop: in the first phase all of the possible actions are done during the time period and then in the second phase the simulated clock is advanced. The dynamics of the system comes from the interaction, which is imposed on the actors. (Borshchev & Filippov, 2004, 6; Schriber &
Brunner, 2005, 168 - 169)
Agent-based modeling and discrete-event simulations differ from system dynamics on many dimensions. One obvious one is the amount of aggregation in the model.
System Dynamics is interested in a high level of abstraction while agent-based modeling and discrete- event simulations work on a lower level of abstraction.
Agent-based modeling can be used on any level of abstraction and hence is a more general modeling method than system dynamics. On the other hand, discrete-event modeling cannot be done in a high level of abstraction.
Also, agent-based modeling is a bottom-up modeling method, while system dynamics is a top-down method.
System dynamics also functions mostly of differential equations, while agent-based modeling and discrete- event simulations do not. (Borshchev & Filippov, 2004, 3 – 7)
3 FORECASTING PORT DEMAND
3.1 Definition
Winkelmans (2002, 5) has summarized some definitions for ports from numerous sources. One definition for a seaport is: an area of land and water, where reception, loading, and unloading of ships is possible in conjunction with storage of goods, and there is a connection to inland transportation. Other definitions see seaport as a logistical and industrial center which plays an active role in global transport system.
Winkelmans (Winkelmans, 2002, 5) continues by stating that it is difficult to give a definition to seaports as these include different transport chains, equipment required to conduct these logistical operations, and there is a large diversity of different terminals.
As logistics plays an important part in these definitions, it also needs to be defined. According to the Council of Logistics Management, logistics management is “part of supply chain management that plans, implements, and controls the efficient, effective forward and reverse flow and storage of goods, services and related information between the point of origin and the point of consumption in order to meet customers' requirements” (Council of Logistics Management, 2008). According to this definition, logistics also include the flow of information and services, not merely goods. Also, logistics is part of supply chain management. Vafidis (2007) has summarized definitions for supply chain management. According to
Vafidis (2007, 16 – 17) definitions for supply chain management differ greatly between different researchers. It can either be a minor activity or a complex relationship chain. Thus, the definition of logistics would mean a large area of possibilities.
In this study, a port is “a facility, which can receive ships and transfer cargo. The facility includes the container terminal, which is required to conduct the transshipment between ships and land vehicles.” This definition is chosen as this study is concerned about the actual seaports and the container terminals in their immediate vicinity. Also, only the flow of actual goods is in the area of interest, not the flow of information.
Ports can be categorized to belong to a larger group called terminal systems. Seaports are terminal systems with a maritime container terminal. Terminal systems might also include inland ports, which do not have access to water. When one discusses about the demand for a terminal system with a maritime container terminal, it can also be seen as discussing about the demand of a port. As the capacity of the container terminal impacts the rate at which the berths can serve the customers, their demand is also an important factor in the total capacity of the ports.
3.2 Literature review
In the literature review all of the three words (seaport, container terminal, terminal system) were
used to recognize publications regarding forecasting or simulating a port’s demand. Each publication’s method is also categorized according to either an econometric, simulation, judgmental, or analytical method. The econometric publications use some kind of time series analysis in order to reach their conclusions while simulations are pure simulations about the behavior of the system. The judgmental methods are based on some expert’s personal opinions and the analytical models are mathematical models.
Also, each publication has its main area of interest categorized to the following categories: Competition, port infrastructure, operation procedures, national demand, or other. In publications concerning competition, the main purpose is to study the competitive position between some ports. In operation procedures the interest is in the operational rules of the ports while in port infrastructure one is only interested in the actual infrastructure in the port. In the national demand a country’s total demand is forecasted on a national level. If the publication is not about of any of these categories, it will be entered as other.
Each publication also shows which kind of demand is simulated or forecasted. The demand is divided to liquid bulk, dry bulk, and general goods cargo. The literature review can be found in Appendix 3.
From the 22 publications found, 50% (11/22) have only one port. Four publications have few ports, four have many ports, and three do not have any ports at all. The
publications without ports are all concentrated in national demand and do not divide it in manner. All of these publications (regarding national demand) have also been done using a statistical method. The first one (Lehto et al., 2006) studied how overall seaborne transportation of Finland will develop. This study used GDP as the driving factor. The second one (United Nations, 2007) is mostly interested about Asian countries. Like in the study of Lehto et al. (2006), the driving factor is GDP development. Maloni & Jackson (2005) also uses an statistical method (exponential smoothing) to create a forecast for US ports. Only two additional publications were done using a statistical method in addition to these publications. Fung (2002) created a statistical model, which simulated the competition between three Asian ports. The model uses information from costs, tariffs, services supplied etc.
in order to create the dynamics of the competition.
Veldman & Bücmann (2003) also use a statistical method to study competition among few ports. They also use costs and prices as the basis of their model.
About 70% (15/22) of the publications have used simulation as their method, while only one used an analytical method, one used a judgmental method, and five used a statistical one. All publications with only one port were completed using a simulation. Also, the publications with one port are concentrated only on two subjects, operation procedures and port infrastructure;
four publications were about operation procedures and seven about port infrastructure. Chang (2005) studied the impact of different warehousing and transshipment parameters on a terminal system. Hartman (2004) also
