i

Forecasting Models for Demand of Containers Throughput in Cat Lai Terminal - Saigon New Port, Vietnam

by

Phan Hoang Vu

A project submitted in partial fulfillment of the requirements for the degree of Master of Engineering (Professional) in

Industrial and Manufacturing Engineering

Examination Committee: Dr. Huynh Trung Luong (Chairperson) Prof. Voratas Kachitvichyanukul

Nationality:

Vietnamese

Previous Degree:

Marine Engineering Degree Vietnam Maritime University

Asian Institute of Technology School of Engineering and Technology

Thailand December 2018

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ACKNOWLEDGEMENTS I wish to express my sincere gratitude and appreciation to my advisor, Dr. Huynh Trung Luong for his valuable advice and consultation during my thesis study. I would like to express my truly appreciation to Professor Voratas Kachitvichyanukul for suggestions, comments to finish my thesis study as well. I wish to express my special thanks to all my co-workers, my classmates for supporting on the information, documents and necessary data. Finally, I wish to express my deep gratitude for the constant encouragement from my beloved parents, my family over my studying time at AIT.

iii

ABSTRACT

The paper researches about the forecasting methodologies used to predict container volumes in “Cat Lai Terminal– Sai Gon New Port”. The main purpose of this study is to focus on the quantitative analysis of forecasting techniques and to select an appropriate method to help do forecast of containers of Cat Lai Terminal in 2018.

To achieve the target, in this research, some forecasting models will be built in Excel to do demand forecasting of Cat Lai Terminal. The model is expected to help that company to figure out a suitable demand for each month. In addition, the small programming will be built by MATLAB software to run automatically ARIMA model to figure out the best appropriate for the given demand.

The forecasts are based on the figures of container throughput in TEU unit (TEU definition: abbreviation for twenty-foot equivalent unit) of the Cat Lai Terminal in Ho Chi Minh City, belonging to Saigon Newport Corporation during last 4 years: 2014, 2015, 2016 and 2017 by each month. This paper suggests decision makers and businesses to choose the appropriate forecasting model for port operation in order to avoid unsatisfying the customer demand. Keywords: Simple linear regression, Moving average, Simple exponential smoothing, Static, Holt’s model, Winter’s model, Time series - Arima.

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TABLE OF CONTENTS

CHAPTER TITLE PAGE TITLE PAGE i ACKNOWLEDGEMENTS ii ABSTRACT iii TABLES OF CONTENTS iv LIST OF TABLES v LIST OF FIGURES

LIST OF ABBREVIATIONS vi vii

1 INTRODUCTION 1 1.1 Overview 1 1.2 Problem Statement 1 1.3 Objectives 1 1.4 Scope and Limitation

1.5 Methodology 1 1

2 BACKGROUND ABOUT FORECASTING METHOD

AND LITERATURE REVIEW 3

2.1 Background of Forecasting Techniques 3 2.2 Forecasting Methods 4 2.3 Literature Review of Time Series – ARIMA

2.4 Evaluation of Forecast Error 10 16

3 INTRODUCTION OF THE COMPANY 17 3.1 Background of the Company

3.2 The Important Role of Forecast to the Company 3.3 Data Collection

17 19 20

4 DEVELOPING FORECASTING MODELS

4.1 Simple Linear Regression 4.2 Time Series Decomposition 4.3 Moving Average 4.4 Simple Exponential Smoothing 4.5 Static Method 4.6 Trend – Corrected Exponential Smoothing (Holt’s Model) 4.7 Trend and Seasonality Corrected Exponential Smoothing

(Winter’s Model) 4.8 Auto Regressive Integrated Moving Average (ARIMA)

Model

21 21 24 28 31 34 40 43

47

5 CONCLUSION AND RECOMMENDATION 51 5.1 Selection

5.2 Conclusion 51 52

5.2 Recommendation 52 REFERENCES 53

v

LIST OF FIGURES

FIGURE TITLE PAGE

Figure 2.1 Types of Variations in Time Series Data - Trend 5

Figure 2.2 Types of Variations in Time Series Data – Seasonality 6

Figure 2.3 Types of Variations in Time Series Data – Cycles 6

Figure 2.4 Example of Moving Average 6

Figure 2.5 Example of Simple Exponential Smoothing 7

Figure 2.6 Example of a Time Series ARIMA 10

Figure 2.7 Example of an ACF of a recorded data set - ARIMA 12

Figure 2.8 Example of ACF of AR(1) with negative Phi -ARIMA 13

Figure 2.9 ACF of MA(1) 14

Figure 3.1 Cat Lai Terminal Layout 18

Figure 3.2 Cat Lai Terminal picture 18

Figure 3.3 Cat Lai Terminal market share in 2017 19

Figure 3.4 Container throughput in TEU unit from 2014 to 2017 20

Figure 4.1 Line Chart of Demand in 04 Years 29

Figure 4.2 Data Estimate and Verify the ARIMA Model 47

Figure 4.3 Difference at 12-lags 48

Figure 5.1 Line Chart of Winter’s Forecasts 52

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LIST OF TABLES

TABLE TITLE PAGE

Table 3.1 Container throughput in TEU unit of Cat Lai Port from 2014 to 2017

20

Table 4.1 Estimate parameter a and b 21

Table 4.2 The Forecasting Values of Linear Regression Model 23

Table 4.3 The Forecast Error of Simple Linear Regression Model 23

Table 4.4 Seasonal Index of quarters 1, 2, 3 and 4 24

Table 4.5 Trend Line Estimation 25

Table 4.6 Forecast of Time Series Decomposition Model 27

Table 4.7 Forecast Error of Time Series Decomposition Model 27

Table 4.8 The Forecasting Values of Moving Average 29

Table 4.9 Forecast Error of Moving Average Model 30

Table 4.10 The Forecasting Values of Simple Exponential Smoothing 32

Table 4.11 Pair comparison between Forecast Error and other values of α 32

Table 4.12 Forecast Error of Simple Exponential Smoothing Model 33

Table 4.13 Seasonal Factor S and seasonal index S estimation 37

Table 4.14 The Forecasting Values of Static Method 38

Table 4.15 Forecast Error of Static Method 39

Table 4.16 The Forecasting Value of Holt’s Model 41

Table 4.17 Forecast Error by Changing Values of α and β 41

Table 4.18 Forecast Error of Holt’s model 42

Table 4.19 Forecast Error with Various Values of α, β and γ 45

Table 4.20 Forecast of Winter’s Model 45

Table 4.21 Forecast Error of Winter’s Model 46

Table 4.22 Forecast of ARIMA 49

Table 4.23 Forecast Error of Winter’s Model 49

Table 5.1 Forecast Error of All Models 51

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LIST OF ABBREVIATIONS

MSE: Mean Squared Error

AE: Absolute Error

MAD: Mean Absolute Deviation

MAPE: Mean Absolute Percentage Error

STD: Standard Deviation

TS: Tracking Signal

1

CHAPTER 1 INTRODUCTION

1.1 Overview The forecasting techniques have been regarded as one of the most important elements in the operation of the port. This is because of its direct effect on the whole function including strategy, expansion decision, management. Therefore, the need of a well-adapted forecasting model is crucial. As well as the model has been constructed, the forecasting data give more confidential information which can be used as indicator for all related department of the port such as human and equipment planning, scheduling, accounting, in order to accomplish the forecasting demand. However, the building of the forecasting model is one challenging task, especially in the port activities. One reason of this is the fluctuation of the data, causing by various factors including the changing weather, new governmental policies, business activities of the port’s customer, the rising amount of circulation vehicles, while the port expansion capacity is limited. In this research, two forecasting models are built then compared in order to have the more accurate forecasting data. 1.2 Problem Statement As seen in the Overview section, with the potential inaccuracy of any forecasting model in determining the realistic demand, managers often struggle to create an accurate production plan that can help their port processing enough products/containers to satisfy their customer demand. The first problem is the inaccuracy of the forecasting models leading to error in comparison with the actual demand. This problem cannot be solved completely because we cannot know the real solution until the time comes and gives an actual data. However, it is possible to minimize such error by finding the relationship within the errors itself in order to compute. 1.3 Objectives The objective of this thesis is to determine a forecasting technique suitable to Cat Lai terminal by applying various quantitative forecasting models. 1.4 Scope and Limitation This research will focus on some basic forecasting methods such as Simple Linear Regression (SLR), Moving Average Model, Simple Exponential Smoothing (SES), Static model, Holt’s Model, Winter’s Model and Time Series ARIMA. The creation of forecasts value will be based on the collected data in last four years. 1.5 Methodology The research process will focus on the steps of how to do some basic forecasting methods and using the output of the model to predict containers volumes in port industry. In

2

addition, the small programing that is used to compute and calculate the corresponding parameters of the Time series - ARIMA models. The details of the research process are written as follows:

Start

Specify problem

Research and literature review

Some Basic forecasting methodsAnd

Model for Time Series - ARIMA

Data collection

Run forecasting models

Validation of models

Output of Model Forecasted Demand

End

Yes

No

- Specify Problem: Investigate the problem that is happening in port operation. Define the problem in the problem statement and explain the scope & limitations of the thesis.

- Research and Literature Review: Research about the problem and examine prior writings to help assist in solving the problem.

- Some basic forecasting methods and Model for Time series ARIMA: Develop or

modify some basic forecasting models and the Time Series model that are best fitted for the problem used to forecast future data.

- Validation of models: Justify and validate the model if it is best suited to the model

and given data. - Forecasted Demand: The forecasted demand (output) computed from forecasting

models

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CHAPTER 2 BACKGROUND ABOUT FORECASTING METHODS AND LITERATURE

REVIEW In this chapter, the background of forecasting techniques which are the tools used to help operator determine the proper distribution of the number of containers throughout their port for future time intervals will be discussed. The literature review of these tools will also be mentioned to incorporate and strengthen the idea behind this application 2.1 Background of Forecasting Techniques There are a lot of different forecasting techniques that have been researched and used for predicting the customer demand. In this thesis, the Simple Linear Regression Model, Moving Average, Simple Exponential Smoothing, Static, Holt’s Model, Winter’s Model and Auto-regressive Integrated Moving Average (ARIMA) will be mentioned in order to compare how the forecasted data will be different between one another.

• Conception and Role of Forecasting

Forecasting process is an essential activity in many business areas. It eases the determination and adaptation to future demands, allowing a company to reach sustainable solution and growth opportunities. Forecasting is a planning tool that helps management in its attempts to cope with the uncertainty of the future, relying mainly on data from the past and present and analysis of trends. To archive this, collection and processing data in the past and present is critical to analyze the trend, in the past then in future, via mathematical models. As the market becomes more and more concurrent, forecast becomes more and more important. Thanks to forecasting data, can be done plans for production, investment, saving, policies. Therefore, the accuracy of forecast is crucial.

• Method to Forecast

In this thesis, the collected data is done first within a specific time period in the past. Many forecasting techniques will be applied such as Static, Regression Analysis, Moving Average, Exponential Smoothing, Holt’s and Winter's, Time series. The next step is the forecast error evaluation in order to ranking and choosing the forecast result. Steps in the forecasting process are shown as follows: Step 1: Understand the objective what needs to be forecast: level of detail, units of analysis and time horizon required. Step 2: Evaluate and analyze data: identify necessary data and whether it’s available. Step 3: Identify the main factors that influence the forecast. Step 4: Select and test the forecasting via forecasting error comparison Step 5: Forecast value generation Step 6: Monitor the forecast accuracy over time to determine whether it is performing in a satisfactory manner.

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2.2 Forecasting Methods Various forecasting methods can be classified in 02 following types:

• Qualitative methods: where there is no formal mathematical model, often because the data available is not thought to be representative of the future (long-term forecasting).

• Quantitative methods: where historical data on variables of interest are available. These methods are based on an analysis of historical data concerning the time series and also examine the cause-and-effect relationships of the variable with other relevant variables.

This project will present a brief overview of some of quantitative methods which are more appropriate. List of forecasting methods apply in this project:

• Time series method: simple exponential smoothing, moving average, static, Holt’s model, Winter’s model and ARIMA

• Explanatory method: simple linear regression. 2.2.1 Simple Linear Regression Model The simple linear regression model seeks to fit a line through various data over time.

bXaYt += Yt is the regressed forecast value or dependent variable in the model, a is the intercept value of the regression line, and b is similar to the slope of the regression line. However, since it is calculated with the variability of the data in mind, its formulation is not as straight forward as our usual notion of slope.

One approach in estimating the trend in the data is regression analysis. Let’s consider a situation where Y is the observed Response Variable; X is the Independent Variable and E is the Random Error. For a linear trend, the variables can be expressed as the following equation

Yi = a + b Xi + ei Where a and b are estimated from the data. In order to obtain the expression for a

and b, consider the error for each observation:

ei = Yi − a − b Xi For n observations, the sum of square error is:

( )∑ ∑= =

−−=n

i

n

iiii bXaYe

1 1

22

The method of least square seeks to minimize the sum of square error, i.e.,

5

( )

∑ ∑∑

∑ ∑

∑

= ==

= =

=

+=

+=

−−

n

i

n

ii

n

iiii

n

i

n

iii

n

iii

XbXaYX

XbnaYts

bXaYMinimize

1 1

2

1

1 1

1

:.

So, solving for a and b yield:

[2.1]

[2.2] 2.2.2 Time Series Decomposition Time-ordered sequence of observations taken at regular intervals over a period of time. Future values of the series can be estimated from past values Types of Variations in Time Series Data

• Trend - long-term movement in data

• Seasonality - short-term regular variations in data

• Cycles – wavelike variations of long-term

• Irregular variations - caused by unusual circumstances

• Random variations - caused by chance

Figure 2.1 Types of Variations in Time Series Data - Trend

n

XbYa

n

ii

n

ii ∑∑

==

−= 11

∑ ∑

∑∑∑

= =

===

−

−

=n

i

n

iii

n

ii

n

ii

n

iii

nXX

nYXYXb

1

2

1

2

111

6

Figure 2.2 Types of Variations in Time Series Data - Seasonality

Figure 2.3 Types of Variations in Time Series Data - Cycles

Application of this model needs to follow the steps below:

• Step 1: Determine the index of seasonality • Step 2: De-seasonalize data: compute the ratio between actual demand and

corresponding index of seasonality • Step 3: Compute trend using regression [2.1]; [2.2]. • Step 4: Estimate forecast • Step 5: Calculate forecast error

2.2.3 Moving Average Averaging techniques are used to smooth variations in the data. This method is used when demand has no observable trend or seasonality.

[2.3]

Where: MAt,n : MA forecast made in period t-1 using n actual observations

Figure 2.4 Example of Moving Average

1

, n

AMAF

t

ntii

ntt

∑−

−===

7

2.2.4 Simple Exponential Smoothing Simple Exponential Smoothing (SES) is a forecasting method that involves a smoothing constant that helps smoothen the slope of a given data set. Systematic component of demand equal level.

Initial calculation of level, oL , the average of all past data:

[2.4] Existing forecast for all future periods is equal to the existing calculation of the level and is shown as follows:

[2.5]

After observing demand 1tD + , reconsider the calculation of the level:

[2.6]

α is the smoothing constant that ranges in: 0 1α< < . With this, we need to find an appropriate smoothing constant and the forecast value at t = 1 is normally the same as the demand at t = 1. From t = 2 onwards, we can then compute a new forecasting table, Ft, and we can use this to compute the next value at t+1. However, we can only normally predict for certain the next value after the given demand data before the future time intervals is based entirely on forecast value which could lead to huge margins of error. This is one of the biggest weakness of using this method for forecasting.

Figure 2.5 Example of Simple Exponential Smoothing

10 n

DL

n

ii∑

==

;1 tt LF =+ tnt LF =+

ttt LDL )1(11 αα −+= ++

8

2.2.5 Static Method In the Static method, a model with mixing systematic components of demand is considered. For more details, Systematic component = (level + trend) * (factor of seasonality) Where:

L: estimate of level for period t= 0 T = estimate of trend

tS = estimate of seasonal factor for period t

tD = actual demand in period t

tF = forecast of demand in period t Then the forecast in period t for demand in period t + l is given by:

( )t l t lF L t l T S+ + = + + [2.7] 2.2.6 Trend –Corrected Exponential Smoothing (Holt’s Model) In this Holt’s model, we assume the demand is to have a level and trend but no seasonality. Obtain initial estimate of level and trend by running a linear regression between demand

tD and time period t of the following form:

tD at b= + [2.8] where:

0

0

T aL b

==

In period t , the forecast for future periods is shown as follows:

1t t tF L T+ = + and t n t tF L nT+ = + [2.9]

After observing demand for period t, revise the estimates for level and trend as follows:

( )( )1 1 1t t t tL D L Tα α+ += + − + [2.10]

( ) ( )1 1 1t t t tT L L Tβ β+ += − + − [2.11] where: α : smoothing constant for level, where 0<α <1 β : smoothing constant for trend, where 0< β <1 2.2.7 Trend and Seasonality –Corrected Exponential Smoothing (Winter’s Model)

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In this method, the demand is assumed to have a level, trend, and seasonal factor. Systematic component = (level + trend) x (seasonal factor) We assume that to have periodicity P Obtain initial estimates of level ( )0L , trend ( )0T , seasonal factors ( )1,..., pS S

using the

same procedure in static forecasting. In period t , the forecast for future periods is given by:

( )( ) ( )1 1 and t t t t t l t t t lF L T S F L lT S+ + + += + = + [2.12]

After observing demand for period 1t + , revise estimates for level, trend, and seasonal factors as follows:

( ) ( )( )1 1 1/ 1t t t t tL D S L Tα α+ + += + − + [2.13] ( ) ( )1 1 1t t t tT L L Tβ β+ += − + − [2.14] ( ) ( )1 1 1 1/ 1t p t t tS D L Sγ γ+ + + + += + − [2.15] where:

α : smoothing constant for level, where 0<α <1 β : smoothing constant for trend, where 0< β <1 γ : smoothing constant for seasonal factor, where 0<γ <1 2.2.8 Auto-regressive Integrated Moving Average (ARIMA) Notations

Indices

t: time intervals, 0,1, 2,3,...t ∈ Parameters

:tz the available demand known at time t Decision Variables

p: the time lag of the AR section of ARIMA, 1,2,3,...p ∈ q: the time lag of the MA section of ARIMA, q 1,2,3,...∈ d: the difference taken based on integration of equation [10], d 1,2,3,...∈

:tω the forecasted data for period t computed from equation, [10] a :t the random shock, or error, computed by taking t tz z− B: the backward shift operator after computing the corresponding p to expand the autoregressive part of the model.

Mathematical Model

10

[2.16]

where: 2.3 Literature Review of Time Series – ARIMA In the past, people in the production industries has always been struggling to determine the number of products that their factories should produce for their customers because the risk of not having enough products or having too much inventory can cause detrimental problems because it involves multiple cost that really hurt the profitability of the company. This problem exists because it is very difficult and almost always unpredictable for the demand and interest of the customers since there is no telling what the customers can think. Therefore, industrialists have been trying to develop multiple forecasting techniques in order to assist and potentially reduce the amount of cost for backorders or the cost for inventory. Techniques, such as Moving Average, Exponentially Smoothing, Holt’s and Winter’s Models (Chopra 2013), Time Series Analysis, are examples of models that are used to help predict customer’s demand and give the factory managers an idea of how much production they should schedule their factories to produce.

Figure 2.6 Example of a Time Series ARIMA

An example of a time series can be seen if Figure 2.6. As we can see, the x-axis of the data is always representing the time interval that the data is recorded. As each time interval is graphed, we can look at the connection of the data and see if there is any relationship of the demand throughout time. If such a model fit, we will be able to forecast the next data point. As time goes on, industrialists and mathematicians continued to improve the accuracy in order to correctly predict the future values of the demand in order to avoid overproduction or underproduction. Time-series analysis has becoming more popular especially the basic model, Auto-regressive (AR), first determined the relationship between the past data values

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together. It uses the regression techniques in order to find the coefficients between the past time data together. This model and the Moving Average (MA) model will be investigated further into this thesis. The baseline of an Auto Regressive (AR) model is shown in equation [1]:

[1]

tz represents the forecasted point at time t and it is computed using the past data points

1 2, ,...,t t t pz z z− − − with coefficients 1 2, ,..., pφ φ φ correspondingly and a random shock, at, which is the error value of the the data point at time t. The random shock cannot be computed as shown for the forecasted point because it has not happen in reality. However, we can use this equation to compute the relationship between the past data points in the same equation to compute the error. If all of the coefficients of the AR model are less than 1, the time series is said to be stationary because the data points are not fluctuating between each other which indicates that the demand is stable through out time. However, if one coefficient is greater than 1, then the time series is considered to be non-stationary because the past data points have shown a trend, whether increase or decrease, at that specific time lag.

On the other hand, the Moving Average (MA) model is shown in equation:

tz once again represents the forecasted point at time t and in this case only the random

shock, or the error, is taken into consideration instead of the past data points. This model is often used to determine whether the time series has a relationship between the errors because the coefficients 1 2, ,..., qθ θ θ would be large in case of a large difference. If all of the coefficients in the MA model are less than 1, then the model does not show a huge margin of errors between the data points. However, similar to the AR model, if one of the coefficients is greater than 1, this indicates that there is potentially that the forecasted data might give a big error due to the potential fluctuations. We can combine both models to create the “Mixed Autoregressive – Moving Average Model” which is grouping the AR and MA model together as shown in equation:

In this model, we can see that this model represents the combined methodologies of both the basic models. With this ARMA model, we can find the next forecasting point using the given data The simplified version of the AR, MA, and ARMA models are shown in equations [4], [5], [6] using the backshift operator B in order to shorten the economically form. Equation [4] represents a stationary AR model.

[4]

[5]

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[6] However, in reality, most time series are nonstationary because not only of the nonpredictable fluctuations between the data, but also there normally is a trend or season within a given data set. If such cases we need to look how the data series would look if we take difference levels between the data points. The difference level of the generalized autoregressive operator, ( )Bϕ , can be shown in equation [7].

[7] With this, we create a homogenous nonstationary of the form in equation [8] and an expanded form in equation [9]:

[8]

[9] Where tω is computed shown in equation [10]:

[10] Equations [9] and [10] represents the ARIMA process which is the baseline for computing the forecasted demand in this thesis. The difference of such would indicate if the data has a season. However, in order to achieve such information or even to have an initial idea of what specific ARIMA model a given set of data would be best fit, we need to compute the auto-correlation function (ACF) of the data set to find how the data is responding at increasing time lag. A point of the ACF, denoted as kρ , is used as a tool to identify the ARIMA model of a data set with k representing the lag in the data series. The general equation to solve kρ is the following:

( , )( )t t k

kt

Cov Z ZVar Z

ρ −= [11]

Having multiple calculations of kρ , we are able to graph a ACF graph similar as to Figure

Figure 2.7 Example of an ACF of a recorded data set - ARIMA

As we can see in the figure, there is a certain pattern that this time series’ ACF is falling into and this helps identify the best fit ARIMA model for the recorded time series. What

13

needs to be done is compute sample ACF of the baseline ARIMA function starting with the AR function.

Figure 2.8 ACF of AR (1) with negative Phi - ARIMA

Figure 2.3 and 2.4 represents basic ACF of an AR (1) with corresponding positive and negative φ -values. We can see that a similarity between the two ACF is that the value of

kρ decreases exponentially ask increases. An apparent difference is that the negative φ -value ACF’s kρ fluctuates between positive and negative values ask increases. Using this sole information, we can predict that the ACF of Figure 2-2 does have AR properties for values of k from 1 through 7 because the values of kρ does show a decrease but not exponentially. The ACF of the MA (1) process is different from the AR process. Because the error of MA (1) only appears twice in a recorded time at t = 0 and t = 1, the ACF is computed theoretically in Figure 2.5 below.

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Figure 2.9 ACF of MA (1)

There are only two values recorded for the theoretical ACF of MA (1) because 0kρ ≠ is computed at k = 0 and k = 1. What this shows is that for a data set to follow an MA process, the ACF of the data set must show steep decrease towards 0 or within the sigma zones and show no further values higher than sigma zone base on the corresponding MA(q) process. For every q defined in the MA process, only the q values are allowed to exceed the sigma zone in order for the MA process. With such a high potential background about how we can examine the relationship closely between the data points. This method of Time Series Analysis is a strong candidate for a forecasting method different from others like the list mentioned above. The information about time series above can be found in the textbook written by Box et al. (1994). ARIMA analysis has been researched before especially in forecasting the supply chain demand done by Ali and Boylan (2012). In the paper, the authors applied the basic models, AR(1), MA(1), ARIMA(1,1,1), ARIMA(1,1,2), and compared the flexibility of the models when trying to forecast the demand. However, the data of such comparison assumed that the time series is stationary hence as mentioned in 2.1, the time series does not fluctuate or season. Ali and Boylan, however, mentioned that using the ARIMA process, the bullwhip effect of the demand of the supply chain was reduced and this was a very strong claim. The authors were then able to compute the forecast the demand of the supply chain using simpler methods such as the Simple Moving Average (SMA) and Simple Exponential Smoothing (SES) in order to forecast a next data set for their upstream and downstream of the supply chain. After forecasting the using the SMA and SES, Ali and Boylan went further and verify the forecast data using the ARIMA process using the simple ARIMA models listed above, AR(1), MA(1), ARIMA(1,1,1), ARIMA(1,1,2). From here, they were able to compare how the results by showing using the 4 models after computing the inventory cost reduction using the Forecast Information Strategy (FIS) using a calculation using FIS and No Information Sharing (NIS) shown in Figure 2.6. In Figure 2.6, we can see that the AR (1) model had the highest inventory cost reduction between the time series model. Ali and Boylan then claimed in their paper that it is possible for businesses to use these forecasting techniques of time series to reduce the stock keeping units (SKUs).

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Figure. Inventory cost reduction by using FIS instead of NIS: effect of lead time (L)

Another paper done by Syntetos et al. (2015) summarized the demand and how it is computed using the ARIMA processes and specifically mentioned about Ali’s achievement in his paper. However, Syntetos believed that it is not a practical method applied into supply chain, stating: “…optimal forecasting methods are not always employed in supply chain. Often, simpler methods such as SMA and SES are used instead.” This is because often times due to the lack of time and requirement to complete forecasting the demands. However, they mentioned that there are two limitations into this computation using the ARIMA model which is:

1. There is only one member at each stage of the supply chain hence it makes it a basic foundation of the forecasting. However, the supply chains are generally complex and has many members at each stage hence it makes the forecasting model potentially more complex.

2. The model is applied on an Order-Up-To (OUT) inventory system. This means that it has not been tested upon other inventory hence it lacks the analysis on other systems.

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2.4 Evaluation of Forecast Error Forecast error evaluation is a step to consider to know that the forecasting method is suitable or not. In case of, the observed error is inside past error calculations, the existing method can be used. Otherwise, if the observed error is outside past calculations then that method is not suitable. Also, if all used forecasts to be consistently over or under calculation demand then the forecasting method should also consider to be changed. Forecast error can be calculated by using formulas as follows:

• Forecast error for period t is given by tE :

t t tE F D= − [2.17] • One measure of forecast error is the mean squared error (MSE):

2

1

1 n

n tt

MSE En =

= ∑ [2.18]

• Absolute error (AE) in period t , tA :

t tA E= [2.19] • Mean absolute deviation (MAD) to be the average of the absolute deviation over

all periods:

1

1 n

n tt

MAD An =

= ∑ [2.20]

• Standard deviation (STD) of the random component N(0,σ):

1.25MADσ = [2.21] • Mean absolute percentage error (MAPE):

1

1 100n

tn

t t

EMAPEn D=

= ∗∑ [2.22]

• Bias: indicates whether the forecast regularly under – or overestimates demand; it

should fluctuate around 0: 1

n

n tt

Bias E=

= ∑ [2.23]

Tracking signal: tTS should be inside the range of ± 6. If not, possibly use a new

forecasting method: tt

t

BiasTSMAD

= [2.24]

17

CHAPTER 3 INTRODUCTION OF COMPANY

3.1 Background of the Company Tan Cang Port, which is the cradle where Saigon New Port (SNP) Corporation develops and grows, sits on the land which is still classified as the one for military purpose and belongs directly to the Ministry of Defense. The rear admiral of Vietnam Navy is at the same time general director of SNP Corporation. In 2016, SNP Corporation handled 5,692,200 TEUs throughout their terminals in Vietnam and held about 68% market share in Ho Chi Minh City area and 50% market share nationwide in 2015 (Saigon New Port 2016; VPA 2017). Although the overall terminal utilization in Ho Chi Minh City was about 70% in 2015, there is a substantial difference between individual terminals. Cat Lai Terminal where is managed by Saigon New Port Corporation and is the biggest container terminal in Vietnam for the time being in terms of capacity has already been utilizing full of its capacity and congestion has been recorded in 2016 and early 2017 due to a huge amount of container backlog (Vietnam Customs News 2017). Cat Lai terminal is located on district 2, Ho Chi Minh City, Viet Nam. It is a feeder – port with a total area of 160 ha, the total length is 2,040m, equipped with 30 modern quay cranes, TOP-X's modern container terminal management system RBS. It has the ICD system with total warehouse area is nearly 500.000 m2, includes CFS warehouse, cool warehouse etc. to international standards. Cat Lai port is the first choice for customers who want to deliver goods in southern provinces. Cat Lai Newport now has 13 main areas, which are: • Gates area: 4 gates, control the flow of traffic inside and just outside the terminal

• Container yard: includes areas to store containers, RTG crane, using top lift & side lift

trucks, internal trucks. • Berths’ bridge system: include STS Gantry Cranes, work effectively to handle the

number of ships that come in and out of the terminal.

• Barge area 125: receive goods for exporting/importing locally, using single or dual conveyor, combined with crawler cranes.

• Scanner area: owns 3 of the 5 scanners of Ho Chi Minh City, including Gantry CXG6-I.3 (sponsored by Japan), HCVP 6030 Smiths and HCVM 3528L Smiths (sponsored by Vietnam’s General Department of Customs).

• Manual inspection area: for containers that have to be 100% inspected.

• Cold storage area: for containers with goods that have to be stored in cold condition,

area equipped with huge number of power outlets.

18

Figure 3.1 Cat Lai Terminal Layout

• IMDG goods’ area: for handling of dangerous goods or hazardous materials, including

explosives, liquified gas, oxidizer, radioactive substance, corrosive substance, etc.

• Control tower: direct every single thing that happens inside the port - the registration of containers that are stored in the port, how long will they be in there before shipment, where to put them, how and when to handle ships that come in, optimize the amount of time for them to load/unload goods before getting them out for other ships to come in.

• Port’s business area: for payment procedures, can be done online or offline.

Figure 3.2 Cat Lai Terminal picture

• Customs’ supervision board: supervise the goods/ships/barges/etc. that are under

management of the customs, for both exporting and importing.

19

• Specialized examination centers: includes 6 centers to test the professional ability of employees according to plan.

Figure 3.3 Cat Lai Terminal market share in 2017

3.2 The Important Role of Forecast to the Company In the case of Cat Lai Terminal Port, the container throughput is one determining factor affecting the whole operation of the port, especially in the condition of the raising industrialization in Ho Chi Minh City and the surrounding provinces. It plays the important role from the planning of manpower and equipment for handling container from ship to the depot and vice versa. It also effects on the layout of the container on the port and then the decision on investment and future development. Therefore, the forecasting of the container throughput is critical to the port. The Cat Lai Terminal is already congested several times in 2018, so the need of accurate forecasting data is crucial to the future operation and decision for expansion.

20

3.3 Data Collection

Below is the container throughput in TEU unit (TEU definition: abbreviation for twenty-foot equivalent unit) of the Newport Cat Lai Terminal in Ho Chi Minh City, belonging to Saigon Newport Corporation during last 4 years: 2014, 2015, 2016 and 2017 by each year’s quarter. The figure is shown in table 3.1 below:

Table 3.1 Container throughput in TEU unit of Cat Lai Port from 2014 to 2017

Year 2017 2016 2015 2014

Jan 345,599 335,026 333,847 293,384

Feb 266,963 224,198 241,575 198,795

Mar 384,390 328,695 300,323 310,517

Apr 360,766 331,842 309,610 301,455

May 393,300 338,423 312,565 287,826

Jun 383,967 329,712 328,146 310,172

Jul 384,713 373,571 321,889 319,709

Aug 390,308 352,868 313,357 316,187

Sep 384,713 317,679 312,578 304,058

Oct 386,652 332,744 322,813 305,951

Nov 394,721 359,524 334,208 313,642

Dec 399,275 412,975 344,719 352,906

Average 372,947 336,438 314,636 301,217

The main objective of this thesis is to forecasting the demand of containers volume in 2018 through calculating forecasts from January to December in year 2018 (period t = 49 to 60) by using various models of quantitative methods.

Figure 3.4 Container throughput in TEU unit from 2014 to 2017

0100,000200,000300,000400,000500,000

1 2 3 4 5 6 7 8 9 10 11 12

TEU

Monthly

The container throughput in TEU unit during last 4 years

2017 2016 2015 2014

21

CHAPTER 4 DEVELOPING FORECASTING MODELS

4.1 Simple Linear Regression First step: Estimate the parameter a and b: We have to calculate P*P, P*D, the average of P and D, sum of P*P and calculate P*D, the result is showed in the table 4.1 below:

Table 4.1 Estimate parameter a and b

Year Periods Month Demand P*P P*D

2014

1 Jan 293,384 1 293,384 2 Feb 198,795 4 397,590 3 Mar 310,517 9 931,551 4 Apr 301,455 16 1,205,820 5 May 287,826 25 1,439,130 6 Jun 310,172 36 1,861,032 7 Jul 319,709 49 2,237,963 8 Aug 316,187 64 2,529,496 9 Sep 304,058 81 2,736,522 10 Oct 305,951 100 3,059,510 11 Nov 313,642 121 3,450,062 12 Dec 352,906 144 4,234,872

2015

13 Jan 333,847 169 4,340,011 14 Feb 241,575 196 3,382,050 15 Mar 300,323 225 4,504,845 16 Apr 309,610 256 4,953,760 17 May 312,565 289 5,313,605 18 Jun 328,146 324 5,906,628 19 Jul 321,889 361 6,115,891 20 Aug 313,357 400 6,267,140 21 Sep 312,578 441 6,564,138 22 Oct 322,813 484 7,101,886 23 Nov 334,208 529 7,686,784 24 Dec 344,719 576 8,273,256

2016

25 Jan 335,026 625 8,375,650 26 Feb 224,198 676 5,829,148 27 Mar 328,695 729 8,874,765 28 Apr 331,842 784 9,291,576 29 May 338,423 841 9,814,267 30 Jun 329,712 900 9,891,360 31 Jul 373,571 961 11,580,701 32 Aug 352,868 1,024 11,291,776 33 Sep 317,679 1,089 10,483,407

22

34 Oct 332,744 1,156 11,313,296 35 Nov 359,524 1,225 12,583,340 36 Dec 412,975 1,296 14,867,100

2017

37 Jan 345,599 1,369 12,787,163 38 Feb 266,963 1,444 10,144,594 39 Mar 384,390 1,521 14,991,210 40 Apr 360,766 1,600 14,430,640 41 May 393,300 1,681 16,125,300 42 Jun 383,967 1,764 16,126,614 43 Jul 384,713 1,849 16,542,659 44 Aug 390,308 1,936 17,173,552 45 Sep 384,713 2,025 17,312,085 46 Oct 386,652 2,116 17,785,992 47 Nov 394,721 2,209 18,551,887 48 Dec 399,275 2,304 19,165,200

Average Average Sum Sum 24.5 331,309.5 38,024 410,120,208

Base on the equations [2.1] and [2.2], parameter a and b are calculated:

∑ ∑

∑∑∑

= =

===

−

−

=n

i

n

iii

n

ii

n

ii

n

iii

nXX

nYXYXb

1

2

1

2

111

𝑏𝑏 = ∑𝑥𝑥𝑥𝑥 − 𝑛𝑛(𝑥𝑥�)(�̅�𝑥) ∑𝑥𝑥2 − 𝑛𝑛(�̅�𝑥)2 =

410120208 − (48 × 331309.5 × 24.5)38024 − (48 × 24.5 × 24.5) = 2225.384

𝑎𝑎 = �∑ 𝑌𝑌𝑖𝑖 − 𝑏𝑏 ∑ 𝑋𝑋𝑖𝑖 𝑛𝑛

𝑖𝑖=1𝑛𝑛𝑖𝑖=1

𝑛𝑛� = (𝑥𝑥� − 𝑏𝑏�̅�𝑥) = 331309.5 − (2225.384 × 24.5) = 276787.6

Second step: Estimate forecast value

Following the regression model as xY a bx= + , The result of model is 𝑌𝑌𝑥𝑥 = 276787.6 +2225.384 𝑥𝑥

Then the forecast for periods 49 is: 𝐹𝐹49 = 276787.6 + 2225.384 ∗ 49 = 385831

Next, the forecast for each period from t = 49 to 60 is showed in table 4.2 below:

23

Table 4.2 The Forecasting Values of Linear Regression Model

Year Period Month Forecast

2018

49 Jan 385,831 50 Feb 388,057 51 Mar 390,282 52 Apr 392,508 53 May 394,733 54 Jun 396,958 55 Jul 399,184 56 Aug 401,409 57 Sep 403,634 58 Oct 405,860 59 Nov 408,085 60 Dec 410,311

Third step: Estimate forecast error Base on the equations form [2.17] to [2.24], forecast error is calculated and showed in table below (table 4.3):

Table 4.3 The Forecast Error of Simple Linear Regression Model

Periods Demand Forecast Error AE MSE MAD %Error MAPE TS

1 293,384 279,013 -14,371 14,371 206,526,228 14,371 4.90 4.90 -1.00

2 198,795 281,238 82,443 82,443 3,501,717,201 48,407 41.47 23.18 1.41

3 310,517 283,464 -27,053 27,053 2,578,437,628 41,289 8.71 18.36 0.99

4 301,455 285,689 -15,766 15,766 1,995,968,877 34,908 5.23 15.08 0.72

5 287,826 287,915 89 89 1,596,776,668 27,944 0.03 12.07 0.91

6 310,172 290,140 -20,032 20,032 1,397,528,070 26,626 6.46 11.13 0.20

7 319,709 292,365 -27,344 27,344 1,304,692,471 26,728 8.55 10.76 -0.82

8 316,187 294,591 -21,596 21,596 1,199,906,114 26,087 6.83 10.27 -1.67

9 304,058 296,816 -7,242 7,242 1,072,410,528 23,993 2.38 9.40 -2.12

10 305,951 299,041 -6,910 6,910 969,943,685 22,285 2.26 8.68 -2.59

11 313,642 301,267 -12,375 12,375 895,689,271 21,384 3.95 8.25 -3.28

12 352,906 303,492 -49,414 49,414 1,024,525,452 23,720 14.00 8.73 -5.04

13 333,847 305,718 -28,129 28,129 1,006,582,259 24,059 8.43 8.71 -6.14

14 241,575 307,943 66,368 66,368 1,249,305,482 27,081 27.47 10.05 -3.00

15 300,323 310,168 9,845 9,845 1,172,480,516 25,932 3.28 9.60 -2.76

16 309,610 312,394 2,784 2,784 1,099,684,808 24,485 0.90 9.05 -2.81

17 312,565 314,619 2,054 2,054 1,035,245,667 23,166 0.66 8.56 -2.88

18 328,146 316,845 -11,301 11,301 984,827,785 22,506 3.44 8.27 -3.46

19 321,889 319,070 -2,819 2,819 933,413,028 21,470 0.88 7.89 -3.76

20 313,357 321,295 7,938 7,938 889,893,185 20,794 2.53 7.62 -3.50

21 312,578 323,521 10,943 10,943 853,219,306 20,325 3.50 7.42 -3.05

24

22 322,813 325,746 2,933 2,933 814,827,643 19,534 0.91 7.13 -3.02

23 334,208 327,971 -6,237 6,237 781,091,436 18,956 1.87 6.90 -3.44

24 344,719 330,197 -14,522 14,522 757,333,212 18,771 4.21 6.79 -4.25

25 335,026 332,422 -2,604 2,604 727,311,076 18,124 0.78 6.54 -4.54

26 224,198 334,648 110,450 110,450 1,168,534,065 21,675 49.26 8.19 1.30

27 328,695 336,873 8,178 8,178 1,127,732,027 21,176 2.49 7.98 1.71

28 331,842 339,098 7,256 7,256 1,089,336,401 20,678 2.19 7.77 2.11

29 338,423 341,324 2,901 2,901 1,052,063,223 20,065 0.86 7.53 2.32

30 329,712 343,549 13,837 13,837 1,023,376,637 19,858 4.20 7.42 3.04

31 373,571 345,774 -27,797 27,797 1,015,288,542 20,114 7.44 7.42 1.62

32 352,868 348,000 -4,868 4,868 984,301,356 19,637 1.38 7.23 1.41

33 317,679 350,225 32,546 32,546 986,572,806 20,029 10.25 7.32 3.00

34 332,744 352,451 19,707 19,707 968,978,074 20,019 5.92 7.28 3.99

35 359,524 354,676 -4,848 4,848 941,964,495 19,586 1.35 7.11 3.83

36 412,975 356,901 -56,074 56,074 1,003,139,010 20,599 13.58 7.29 0.92

37 345,599 359,127 13,528 13,528 980,973,126 20,408 3.91 7.20 1.59

38 266,963 361,352 94,389 94,389 1,189,613,772 22,355 35.36 7.94 5.68

39 384,390 363,578 -20,812 20,812 1,170,217,455 22,315 5.41 7.88 4.75

40 360,766 365,803 5,037 5,037 1,141,596,291 21,883 1.40 7.72 5.08

41 393,300 368,028 -25,272 25,272 1,129,329,482 21,966 6.43 7.68 3.91

42 383,967 370,254 -13,713 13,713 1,106,918,164 21,770 3.57 7.59 3.31

43 384,713 372,479 -12,234 12,234 1,084,656,539 21,548 3.18 7.48 2.78

44 390,308 374,704 -15,604 15,604 1,065,538,655 21,413 4.00 7.40 2.07

45 384,713 376,930 -7,783 7,783 1,043,206,177 21,110 2.02 7.28 1.73

46 386,652 379,155 -7,497 7,497 1,021,749,548 20,814 1.94 7.17 1.39

47 394,721 381,381 -13,340 13,340 1,003,796,691 20,655 3.38 7.09 0.76

48 399,275 383,606 -15,669 15,669 987,999,196 20,551 3.92 7.02 0.00

4.2 Time Series Decomposition

First step: Calculating seasonal index We have to calculate the sum of each quarter in each year first, and take the average value of quarter 1 in 4 years The value of seasonal index (quarter 1, 2, 3 and 4) as below:

S1 = 890828 / 993929 = 0.896 S2 = 1.003, S3 = 1.029, S4 = 1.072

Seasonal index of quarters 1, 2, 3 and 4 are calculated and showed in table 4.4

Table 4.4 Seasonal Index of quarters 1, 2, 3 and 4

Quarter Demand

Average Seasonal Index 2014 2015 2016 2017

Q1 802,696 875,745 887,919 996,952 890,828 0.896 Q2 899,453 950,321 999,977 1,138,033 996,946 1.003

25

Q3 939,954 947,824 1,044,118 1,159,734 1,022,908 1.029 Q4 972,499 1,001,740 1,105,243 1,180,648 1,065,033 1.072 Average 903,651 943,908 1,009,314 1,118,842 993,929

Second step: Calculating de-seasonalize demand De-seasonalize demand is calculated by dividing demand with seasonal index. We calculate de-seasonalize demand of period 1 = 293384/0.896 = 327438, for example. The de-seasonalize demand form period 2 to 48 is determined by using the same method. Third step: Trend line Estimation We use equation Yx = a + bx (regression) to estimate the trend, the estimating parameter a and b by using equations [2.1] and [2.2]: Firstly, we have to calculate data in order to determine parameter a and b, for detail calculating that is showed in table 4.5 below:

Table 4.5 Trend Line Estimation

Periods (Pi)

Demand (Di)

Seasonal Index

Deseasonal Demand

(Yi) P*P Yi * Yi P*Yi

1 293,384 0.896 327,438 1 107,215,316,406 293,384 2 198,795 0.896 221,869 4 49,226,039,373 397,590 3 310,517 0.896 346,559 9 120,103,245,686 931,551 4 301,455 1.003 300,553 16 90,332,310,173 1,205,820 5 287,826 1.003 286,965 25 82,348,971,307 1,439,130 6 310,172 1.003 309,244 36 95,632,016,795 1,861,032 7 319,709 1.029 310,699 49 96,533,704,948 2,237,963 8 316,187 1.029 307,276 64 94,418,537,787 2,529,496 9 304,058 1.029 295,489 81 87,313,645,169 2,736,522 10 305,951 1.072 285,402 100 81,454,331,422 3,059,510 11 313,642 1.072 292,576 121 85,601,003,985 3,450,062 12 352,906 1.072 329,203 144 108,374,851,056 4,234,872 13 333,847 0.896 372,597 169 138,828,597,598 4,340,011 14 241,575 0.896 269,615 196 72,692,224,152 3,382,050 15 300,323 0.896 335,182 225 112,346,919,255 4,504,845 16 309,610 1.003 308,684 256 95,285,779,849 4,953,760 17 312,565 1.003 311,630 289 97,113,325,254 5,313,605 18 328,146 1.003 327,165 324 107,036,614,301 5,906,628 19 321,889 1.029 312,817 361 97,854,662,146 6,115,891 20 313,357 1.029 304,526 400 92,735,934,337 6,267,140 21 312,578 1.029 303,769 441 92,275,427,646 6,564,138 22 322,813 1.072 301,132 484 90,680,198,270 7,101,886

26

23 334,208 1.072 311,761 529 97,195,042,103 7,686,784 24 344,719 1.072 321,566 576 103,404,841,140 8,273,256 25 335,026 0.896 373,913 625 139,810,891,507 8,375,650 26 224,198 0.896 250,221 676 62,610,539,905 5,829,148 27 328,695 0.896 366,847 729 134,576,793,468 8,874,765 28 331,842 1.003 330,849 784 109,461,359,654 9,291,576 29 338,423 1.003 337,411 841 113,846,026,158 9,814,267 30 329,712 1.003 328,726 900 108,060,666,400 9,891,360 31 373,571 1.029 363,043 961 131,800,045,560 11,580,701 32 352,868 1.029 342,923 1,024 117,596,339,228 11,291,776 33 317,679 1.029 308,726 1,089 95,311,710,673 10,483,407 34 332,744 1.072 310,396 1,156 96,345,380,319 11,313,296 35 359,524 1.072 335,377 1,225 112,477,642,028 12,583,340 36 412,975 1.072 385,238 1,296 148,408,218,897 14,867,100 37 345,599 0.896 385,713 1,369 148,774,649,236 12,787,163 38 266,963 0.896 297,950 1,444 88,774,069,487 10,144,594 39 384,390 0.896 429,007 1,521 184,046,745,581 14,991,210 40 360,766 1.003 359,687 1,600 129,374,694,218 14,430,640 41 393,300 1.003 392,124 1,681 153,760,940,508 16,125,300 42 383,967 1.003 382,819 1,764 146,550,037,911 16,126,614 43 384,713 1.029 373,871 1,849 139,779,336,434 16,542,659 44 390,308 1.029 379,308 1,936 143,874,608,996 17,173,552 45 384,713 1.029 373,871 2,025 139,779,336,434 17,312,085 46 386,652 1.072 360,683 2,116 130,092,108,056 17,785,992 47 394,721 1.072 368,210 2,209 135,578,521,665 18,551,887 48 399,275 1.072 372,458 2,304 138,724,978,441 19,165,200 P Average N Y PP YY PY 1176 331,310 48 15,903,086 38,024 5,345,419,180,921 410,120,208

𝑏𝑏 = 410120208 − (1176 ∗ 15903086

48 )

15903086 − (1176 ∗ 117648 )

= 1.29

a = (15,903,086 – 1.29*1176) / 48 = 331283

Then the result of regression is Y = 331283 + 1.29x We have: Trend for period t=1 = 331283 + 1.29*1 = 331284 Trend for period t=2 = 331283 + 1.29*2 = 331285 Trend for period t=3 = 331283 + 1.29*3 = 331287 Trend of other periods is estimating by using the same way. Fourth step: Estimating forecast value

27

Forecast for period i is calculated by trend value multiply with seasonal index value, it shows as below: Fi = Ti * Si F1 = T1 * S1 = 331284 * 0.896 = 296830 Continue, the forecast of period 2 to 48 is estimating by using the same way Forecast of Time Series Decomposition for period t = 49 to 60 is showed in table 4.6

Table 4.6 Forecast of Time Series Decomposition Model

Year Period Month Seasonal

index Forecast

2018

49 Jan 0.896 296,886 50 Feb 0.896 296,887 51 Mar 0.896 296,888 52 Apr 1.003 332,344 53 May 1.003 332,345 54 Jun 1.003 332,346 55 Jul 1.029 340,963 56 Aug 1.029 340,964 57 Sep 1.029 340,966 58 Oct 1.072 355,215 59 Nov 1.072 355,217 60 Dec 1.072 355,218

Fifth step: Estimate forecast error Base on the equations form [2.17] to [2.24], forecast error is calculated and showed in table below (table 4.7)

Table 4.7 Forecast Error of Time Series Decomposition Model

Periods Demand Seasonal Index Forecast Error AE MSE MAD %Error MAPE TS

1 293384 0.896 296830 3446.42 3446.42 11877793.71 3446.42 1.17 1.17 1.00

2 198795 0.896 296832 98036.57 98036.57 4811523847.65 50741.50 49.32 25.25 2.00

3 310517 0.896 296833 -13684.27 13684.27 3270102303.60 38389.09 4.41 18.30 2.29

4 301455 1.003 332282 30826.68 30826.68 2690147851.02 36498.49 10.23 16.28 3.25

5 287826 1.003 332283 44456.98 44456.98 2547402889.47 38090.19 15.45 16.11 4.28

6 310172 1.003 332284 22112.27 22112.27 2204327856.05 35427.20 7.13 14.62 5.23

7 319709 1.029 340899 21190.15 21190.15 1953569963.75 33393.34 6.63 13.48 6.18

8 316187 1.029 340900 24713.48 24713.48 1785718243.02 32308.35 7.82 12.77 7.15

9 304058 1.029 340902 36843.81 36843.81 1738134702.68 32812.29 12.12 12.70 8.17

10 305951 1.072 355149 49197.85 49197.85 1806364062.25 34450.85 16.08 13.03 9.21

11 313642 1.072 355150 41508.23 41508.23 1798779453.64 35092.43 13.23 13.05 10.22

12 352906 1.072 355152 2245.62 2245.62 1649301398.64 32355.20 0.64 12.02 11.15

28

13 333847 0.896 296844 -37002.70 37002.70 1627755128.24 32712.70 11.08 11.95 9.90

14 241575 0.896 296845 55270.46 55270.46 1729688567.64 34323.96 22.88 12.73 11.05

15 300323 0.896 296847 -3476.39 3476.39 1615181681.11 32267.46 1.16 11.96 11.64

16 309610 1.003 332297 22687.22 22687.22 1546402209.15 31668.69 7.33 11.67 12.58

17 312565 1.003 332299 19733.52 19733.52 1478343947.83 30966.63 6.31 11.35 13.50

18 328146 1.003 332300 4153.81 4153.81 1397172293.45 29477.02 1.27 10.79 14.33

19 321889 1.029 340915 19026.10 19026.10 1342689136.61 28926.98 5.91 10.53 15.26

20 313357 1.029 340916 27559.42 27559.42 1313530772.58 28858.60 8.79 10.45 16.25

21 312578 1.029 340918 28339.75 28339.75 1289226525.16 28833.89 9.07 10.38 17.24

22 322813 1.072 355165 32352.46 32352.46 1278201749.17 28993.83 10.02 10.37 18.26

23 334208 1.072 355167 20958.84 20958.84 1241726586.31 28644.48 6.27 10.19 19.22

24 344719 1.072 355168 10449.22 10449.22 1194537407.59 27886.34 3.03 9.89 20.12

25 335026 0.896 296858 -38167.82 38167.82 1205027209.33 28297.60 11.39 9.95 18.47

26 224198 0.896 296859 72661.34 72661.34 1361744236.87 30003.90 32.41 10.81 19.85

27 328695 0.896 296860 -31834.51 31834.51 1348843923.37 30071.70 9.69 10.77 18.74

28 331842 1.003 332313 470.76 470.76 1300678841.03 29014.52 0.14 10.39 19.44

29 338423 1.003 332314 -6108.94 6108.94 1257114714.51 28224.68 1.81 10.10 19.77

30 329712 1.003 332315 2603.35 2603.35 1215436805.58 27370.63 0.79 9.79 20.48

31 373571 1.029 340931 -32639.96 32639.96 1210595848.86 27540.61 8.74 9.75 19.17

32 352868 1.029 340932 -11935.63 11935.63 1177216583.50 27052.95 3.38 9.55 19.07

33 317679 1.029 340934 23254.69 23254.69 1157930651.26 26937.86 7.32 9.48 20.02

34 332744 1.072 355182 22438.06 22438.06 1138681713.11 26805.51 6.74 9.40 20.95

35 359524 1.072 355183 -4340.55 4340.55 1106686246.57 26163.65 1.21 9.17 21.30

36 412975 1.072 355185 -57790.17 57790.17 1168714501.28 27042.17 13.99 9.30 18.47

37 345599 0.896 296872 -48726.94 48726.94 1201298284.99 27628.24 14.10 9.43 16.32

38 266963 0.896 296873 29910.22 29910.22 1193227834.88 27688.29 11.20 9.48 17.36

39 384390 0.896 296874 -87515.62 87515.62 1359016468.33 29222.33 22.77 9.82 13.46

40 360766 1.003 332328 -28437.70 28437.70 1345258622.92 29202.71 7.88 9.77 12.49

41 393300 1.003 332330 -60970.40 60970.40 1403115486.18 29977.53 15.50 9.91 10.13

42 383967 1.003 332331 -51636.11 51636.11 1433191013.54 30493.21 13.45 10.00 8.27

43 384713 1.029 340947 -43766.02 43766.02 1444406677.08 30801.88 11.38 10.03 6.77

44 390308 1.029 340948 -49359.69 49359.69 1466951506.89 31223.65 12.65 10.09 5.09

45 384713 1.029 340950 -43763.36 43763.36 1476913295.19 31502.31 11.38 10.12 3.66

46 386652 1.072 355199 -31453.33 31453.33 1466313262.22 31501.25 8.13 10.07 2.66

47 394721 1.072 355200 -39520.94 39520.94 1468347127.56 31671.88 10.01 10.07 1.40

48 399275 1.072 355201 -44073.56 44073.56 1478224866.54 31930.25 11.04 10.09 0.01

4.3 Moving Average

First step: Estimate periodicity value “p”

Following the figure 4.1 below, we see that, there is an observation data in plot chart that seems to be repeated its pattern every 12 periods. So, we will consider p = 12 in this case.

29

Figure 4.1 Line chart of demand in 04 Years

Second step: Estimate forecast value Following equation (2.3):

,12

147

124712,4747

1

,

∑∑−

−=

−

−= ===>== ii

t

ntii

ntt

AMAF

n

AMAF

F47 = MA47,12 = (A35 + A36 + A37 + A38 + A39 + A40 + A41 + A42 + A43 + A44 + A45 + A46) / 12 = (359524 + 412975 + 345599 + 266963 + 384390 + 360766 + 393300 + 383967 + 384713 + 390308 + 384713 + 386652) / 12 = 317156

F48 = MA48,12 = 374089 F49 = MA55,12 = 372947 Continue, the forecast for each period from t = 49 to 60 is showed in table 4.8 below: F49 = F50 = F51 = F52 …. = F60

Table 4.8 The Forecasting Values of Moving Average

Year Period Month Forecast

2018

49 Jan 372,947 50 Feb 372,947 51 Mar 372,947 52 Apr 372,947 53 May 372,947 54 Jun 372,947 55 Jul 372,947 56 Aug 372,947 57 Sep 372,947 58 Oct 372,947

0

100000

200000

300000

400000

500000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47

Actual Data

Periods Actual

30

59 Nov 372,947 60 Dec 372,947

Third step: Estimate forecast error Base on the equations form [2.17] to [2.24], forecast error is calculated and showed in table below (table 4.9)

Table 4.9 Forecast Error of Moving Average Model

Periods Demand Forecast Error AE MSE MAD %Error MAPE TS

1 293,384

2 198,795

3 310,517

4 301,455

5 287,826

6 310,172

7 319,709

8 316,187

9 304,058

10 305,951

11 313,642

12 352,906

13 333,847 301,217 -32,630 32,630 81,902,137 2,510 9.77 9.77 -13.00

14 241,575 304,589 63,014 63,014 359,675,748 6,832 26.08 17.93 4.45

15 300,323 308,154 7,831 7,831 339,785,407 6,898 2.61 12.82 5.54

16 309,610 307,304 -2,306 2,306 318,881,100 6,611 0.74 9.80 5.43

17 312,565 307,984 -4,581 4,581 301,357,922 6,492 1.47 8.14 4.83

18 328,146 310,045 -18,101 18,101 302,817,544 7,137 5.52 7.70 1.85

19 321,889 311,543 -10,346 10,346 292,513,176 7,306 3.21 7.06 0.39

20 313,357 311,725 -1,632 1,632 278,020,702 7,022 0.52 6.24 0.18

21 312,578 311,489 -1,089 1,089 264,838,085 6,739 0.35 5.59 0.02

22 322,813 312,199 -10,614 10,614 257,920,682 6,916 3.29 5.36 -1.51

23 334,208 313,604 -20,604 20,604 265,163,892 7,511 6.16 5.43 -4.14

24 344,719 315,318 -29,401 29,401 290,132,642 8,423 8.53 5.69 -7.18

25 335,026 314,636 -20,390 20,390 295,157,693 8,902 6.09 5.72 -9.08

26 224,198 314,734 90,536 90,536 599,066,335 12,041 40.38 8.19 0.80

27 328,695 313,286 -15,409 15,409 585,672,666 12,166 4.69 7.96 -0.47

28 331,842 315,650 -16,192 16,192 574,119,002 12,310 4.88 7.77 -1.78

29 338,423 317,503 -20,920 20,920 569,413,050 12,607 6.18 7.67 -3.40

30 329,712 319,658 -10,054 10,054 553,802,157 12,522 3.05 7.42 -4.22

31 373,571 319,788 -53,783 53,783 629,246,450 13,853 14.40 7.79 -7.70

32 352,868 324,095 -28,773 28,773 635,453,622 14,319 8.15 7.80 -9.46

33 317,679 327,388 9,709 9,709 619,053,810 14,179 3.06 7.58 -8.87

34 332,744 327,813 -4,931 4,931 601,561,533 13,907 1.48 7.30 -9.40

31

35 359,524 328,640 -30,884 30,884 611,625,367 14,392 8.59 7.36 -11.22

36 412,975 330,750 -82,225 82,225 782,439,577 16,276 19.91 7.88 -14.98

37 345,599 336,438 -9,161 9,161 763,560,734 16,084 2.65 7.67 -15.73

38 266,963 337,319 70,356 70,356 873,729,930 17,512 26.35 8.39 -10.43

39 384,390 340,883 -43,507 43,507 899,861,632 18,179 11.32 8.50 -12.44

40 360,766 345,524 -15,242 15,242 883,172,928 18,105 4.22 8.35 -13.33

41 393,300 347,935 -45,366 45,366 911,827,944 18,770 11.53 8.46 -15.27

42 383,967 352,508 -31,459 31,459 913,681,919 19,072 8.19 8.45 -16.68

43 384,713 357,029 -27,684 27,684 910,257,063 19,273 7.20 8.41 -17.94

44 390,308 357,957 -32,351 32,351 913,354,985 19,570 8.29 8.40 -19.32

45 384,713 361,077 -23,636 23,636 905,472,535 19,660 6.14 8.33 -20.44

46 386,652 366,664 -19,989 19,989 894,474,004 19,667 5.17 8.24 -21.45

47 394,721 371,156 -23,565 23,565 887,257,900 19,750 5.97 8.18 -22.55

48 399,275 374,089 -25,186 25,186 881,988,752 19,864 6.31 8.12 -23.69

4.4 Simple Exponential Smoothing In this method, we start with α = 0.85 to determine the forecast value (F) First step: Determine the level (L) Base on the formula [2.4], the initial level (Lo) is estimated as:

𝐿𝐿0 =1𝑛𝑛�𝐷𝐷𝑖𝑖

𝑛𝑛

𝑖𝑖=1

=1

48�𝐷𝐷𝑖𝑖 = 33131048

𝑖𝑖=1

Apply equation (2.6) then we have:

ttt LDL )1(11 αα −+= ++

2138373299073*)85.01(198795*85.0)1(299073331310*)85.01(293384*85.0)1(

122

011

=−+=−+==−+=−+=

LDLLDL

αααα

Continue, the Level for each period from t = 3 to 48 is calculating in the same way Second step: Estimate forecast value Base on equation [2.5], we calculate:

398406......

213837331310

4860...49

12

01

==

====

LF

LFLF

The result of forecast for periods from t = 49 to 60 to show in the table below:

32

Table 4.10 The Forecasting Values of Simple Exponential Smoothing

Year Period Month Forecast

2018

49 Jan 398,406 50 Feb 398,406 51 Mar 398,406 52 Apr 398,406 53 May 398,406 54 Jun 398,406 55 Jul 398,406 56 Aug 398,406 57 Sep 398,406 58 Oct 398,406 59 Nov 398,406 60 Dec 398,406

Third step: Estimate forecast error Base on the equations form [2.17] to [2.24] to calculate forecast error.

Fourth step: Determine α value

Firstly, the rule to determine α value is how to get tracking signal value (TS) in rank of (±) 6 by changing α value, where 0 < α < 1 By changing α values within 0.05 < α < 0.09, we can get other tracking signal which is in rank of (±) 6 and pair comparison between forecast error value and other values of α. The result is presented in table 4.11 below:

Table 4.11 Pair comparison between Forecast Error and other values of α

α TS Rank MAD MAPE %Error σ Forecast

Min Max 0.99 -2.82 3.83 29129 9.71 1.16 36411.04 394,640 0.95 -2.89 3.86 28729 9.60 1.24 35911.74 394,313 0.9 -2.97 3.90 28252 9.47 1.35 35315.35 393,900 0.85 -3.04 3.90 27879 9.38 1.45 34848.67 393,483 0.8 -3.11 3.91 27476 9.27 1.56 34344.91 393,065 0.75 -3.27 3.93 27022 9.15 1.66 33778.07 392,648 0.7 -3.52 3.94 26713 9.06 1.76 33391.56 392,229 0.65 -3.81 3.97 26400 8.97 1.87 33000.00 391,806 0.6 -4.14 3.99 26058 8.87 1.98 32572.37 391,370 0.55 -4.54 4.04 25696 8.76 2.10 32120.22 390,903 0.5 -4.98 4.07 25505 8.69 2.23 31881.75 390,376 0.4 -6.12 4.20 25232 8.58 2.59 31540.34 388,916 0.3 -7.83 4.54 25019 8.46 3.28 31274.22 386,188 0.2 -10.43 5.52 25280 8.45 4.76 31600.13 380,250

33

0.1 -13.32 9.74 27826 9.07 8.60 34782.18 364,942 0.05 -12.58 14.62 30941 9.92 12.79 38676.57 348,226

Following table 4.11 above, we see that with α = 0.85, the result seems to be well about error observation values. So, we choice α = 0.85 in this case. Forecast error with α =0.85 is calculated and showed in table below (table 4.12)

Table 4.12 Forecast Error of Simple Exponential Smoothing Model

Periods Demand Level Forecast Error AE MSE MAD %Error MAPE TS

331,310

1 293,384 299,073 331,310 37,926 37,926 1,438,343,550 37,926 12.93 12.93 1.00

2 198,795 213,837 299,073 100,278 100,278 5,746,992,868 69,102 50.44 31.68 2.00

3 310,517 296,015 213,837 -96,680 96,680 6,947,023,740 78,295 31.14 31.50 0.53

4 301,455 300,639 296,015 -5,440 5,440 5,217,666,338 60,081 1.80 24.08 0.60

5 287,826 289,748 300,639 12,813 12,813 4,206,967,627 50,627 4.45 20.15 0.97

6 310,172 307,108 289,748 -20,424 20,424 3,575,330,000 45,593 6.58 17.89 0.62

7 319,709 317,819 307,108 -12,601 12,601 3,087,250,759 40,880 3.94 15.90 0.39

8 316,187 316,432 317,819 1,632 1,632 2,701,677,305 35,974 0.52 13.98 0.49

9 304,058 305,914 316,432 12,374 12,374 2,418,503,225 33,352 4.07 12.87 0.90

10 305,951 305,945 305,914 -37 37 2,176,653,039 30,020 0.01 11.59 0.99

11 313,642 312,488 305,945 -7,697 7,697 1,984,160,647 27,991 2.45 10.76 0.79

12 352,906 346,843 312,488 -40,418 40,418 1,954,951,727 29,027 11.45 10.82 -0.63

13 333,847 335,796 346,843 12,996 12,996 1,817,563,281 27,793 3.89 10.28 -0.19

14 241,575 255,708 335,796 94,221 94,221 2,321,857,237 32,538 39.00 12.33 2.73

15 300,323 293,631 255,708 -44,615 44,615 2,299,765,356 33,343 14.86 12.50 1.33

16 309,610 307,213 293,631 -15,979 15,979 2,171,988,484 32,258 5.16 12.04 0.88

17 312,565 311,762 307,213 -5,352 5,352 2,045,909,317 30,675 1.71 11.44 0.75

18 328,146 325,688 311,762 -16,384 16,384 1,947,160,373 29,881 4.99 11.08 0.22

19 321,889 322,459 325,688 3,799 3,799 1,845,438,021 28,509 1.18 10.56 0.37

20 313,357 314,722 322,459 9,102 9,102 1,757,308,363 27,538 2.90 10.17 0.71

21 312,578 312,900 314,722 2,144 2,144 1,673,845,963 26,329 0.69 9.72 0.82

22 322,813 321,326 312,900 -9,913 9,913 1,602,229,085 25,583 3.07 9.42 0.46

23 334,208 332,276 321,326 -12,882 12,882 1,539,781,995 25,031 3.85 9.18 -0.05

24 344,719 342,853 332,276 -12,443 12,443 1,482,075,901 24,506 3.61 8.95 -0.55

25 335,026 336,200 342,853 7,827 7,827 1,425,243,032 23,839 2.34 8.68 -0.24

26 224,198 240,998 336,200 112,002 112,002 1,852,904,553 27,230 49.96 10.27 3.90

27 328,695 315,540 240,998 -87,697 87,697 2,069,119,637 29,469 26.68 10.88 0.63

28 331,842 329,397 315,540 -16,302 16,302 2,004,713,189 28,999 4.91 10.66 0.08

29 338,423 337,069 329,397 -9,026 9,026 1,938,394,553 28,310 2.67 10.39 -0.24

30 329,712 330,816 337,069 7,357 7,357 1,875,585,615 27,612 2.23 10.12 0.02

31 373,571 367,158 330,816 -42,755 42,755 1,874,051,487 28,101 11.45 10.16 -1.50

32 352,868 355,011 367,158 14,290 14,290 1,821,868,474 27,669 4.05 9.97 -1.01

33 317,679 323,279 355,011 37,332 37,332 1,808,894,036 27,962 11.75 10.02 0.34

34 332,744 331,324 323,279 -9,465 9,465 1,758,326,233 27,418 2.84 9.81 0.00

34

35 359,524 355,294 331,324 -28,200 28,200 1,730,809,113 27,440 7.84 9.76 -1.03

36 412,975 404,323 355,294 -57,681 57,681 1,775,150,353 28,280 13.97 9.87 -3.04

37 345,599 354,408 404,323 58,724 58,724 1,820,375,781 29,103 16.99 10.06 -0.93

38 266,963 280,080 354,408 87,445 87,445 1,973,696,267 30,638 32.76 10.66 1.97

39 384,390 368,743 280,080 -104,310 104,310 2,202,079,477 32,527 27.14 11.08 -1.35

40 360,766 361,963 368,743 7,977 7,977 2,148,618,484 31,914 2.21 10.86 -1.13

41 393,300 388,599 361,963 -31,337 31,337 2,120,165,143 31,899 7.97 10.79 -2.11

42 383,967 384,662 388,599 4,632 4,632 2,070,195,951 31,250 1.21 10.56 -2.01

43 384,713 384,705 384,662 -51 51 2,022,051,920 30,525 0.01 10.32 -2.06

44 390,308 389,468 384,705 -5,603 5,603 1,976,809,602 29,958 1.44 10.12 -2.28

45 384,713 385,426 389,468 4,755 4,755 1,933,382,860 29,398 1.24 9.92 -2.17

46 386,652 386,468 385,426 -1,226 1,226 1,891,385,463 28,786 0.32 9.71 -2.25

47 394,721 393,483 386,468 -8,253 8,253 1,852,592,366 28,349 2.09 9.55 -2.58

48 399,275 398,406 393,483 -5,792 5,792 1,814,695,576 27,879 1.45 9.38 -2.83

4.5 Static model

This is mixed model with components: (level + trend) * (seasonal factor value) First step: Level and Trend Estimation

Begin, we do de-seasonalize demand data as equation below:

1 ( /2)

( /2) ( /2)1 ( /2)

( /2)

( /2)

2 / 2 for even

/ for old

t p

t p t p ii t p

tt p

ii t p

D D D p p

D

D p p

− +

− += + −

+

= −

+ +

=

∑

∑

( / 2 trucated to lower interger)p

[4.1]

For this case, the period is repeated after every 4 quarters, so we consider p value for calculate seasonal demand which is 4*3 = 12. Replace p = 12 into equation [4.1] and we just will get de-seasonalize form t = 7 to 42 𝐷𝐷7��� = [ D1 + D13 + 2*(D2 + D3 + D4 + D5 + D6 + D7 + D8 + D9 + D10 + D11 + D12)] / (2*12) = 293384 + 333847 + 2*(198795 + 310517 + 301455 + 287826 + 310172 + 319709 +316187 + 304058 + 305951 + 313642 + 352906) / (2*12) = 302903 De-seasonalized demand from period 8 to 42 is done similarly. Next, running linear regression to determine Level ( )L and Trend ( )T . In Excel sheet, we use data analysis tool to determine L and T value automatically (Excel /Data/ Data Analysis / Regression). In this tool, we chose Input Y Rank: de-seasonalized demand from t = 7 to 42, and Y Rank: with t = 7 to 42, then we can get L = 282360 and T = 1914 automatically.

35

Next, the de-seasonalized demand included trend can be estimated by equation [4.2];

𝐷𝐷𝑡𝑡��� = L + t * T [4.2] With: t = 1 𝐷𝐷1���� = L + 1* T = 282360 + 1*1914 = 284275 t = 2 𝐷𝐷2����� = L + 2* T = 282360 + 2*1914 = 286189 From periods 3 to 48, The result of de-seasonalized demand included trend T are calculated in the same way. Second step: Seasonal Factor 𝑺𝑺� estimation

Seasonal factor of period t equal “demand of period t” divides “de-seasonalize demand included trend of period t”

𝑆𝑆𝑡𝑡� =𝐷𝐷𝑡𝑡𝐷𝐷𝑡𝑡���

𝑆𝑆1� =𝐷𝐷1𝐷𝐷1���

=293384284275

= 1.03

𝑆𝑆2� =𝐷𝐷2𝐷𝐷2���

=198795286189

= 0.69

The seasonal factors of period t=3 to 48 are calculated in the same way. Third step: Seasonal index S estimation

Given period p, if there are r cycles, for all periods of the form pt + i, where 1 <= i <= p, the seasonal factor for season i is given by:

𝑆𝑆𝑖𝑖 =∑ 𝑆𝑆𝑗𝑗𝑗𝑗+𝑖𝑖𝑟𝑟−1𝑗𝑗=0

𝑟𝑟 [4.3]

In this period, there are 16 quarters in 03 years (48 periods): Quarter 1 = periods 1, 2, 3 Quarter 2 = periods 4, 5, 6 Quarter 3 = periods 7, 8, 9 ………………………….. Quarter 14 = periods 40, 41, 42 Quarter 15 = periods 43, 44, 45 Quarter 16 = periods 46, 47, 48 Then, 𝑆𝑆𝑄𝑄1����� = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝑆𝑆1� ,𝑆𝑆2� , 𝑆𝑆3� ) 𝑆𝑆𝑄𝑄2����� = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝑆𝑆4� , 𝑆𝑆5� , 𝑆𝑆6� )

36

… 𝑆𝑆𝑄𝑄9���� = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝑆𝑆25����, 𝑆𝑆26����, 𝑆𝑆27����) 𝑆𝑆𝑄𝑄10������ = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝑆𝑆28����, 𝑆𝑆29����, 𝑆𝑆30����) … 𝑆𝑆𝑄𝑄15������ = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝑆𝑆43����, 𝑆𝑆44����,𝑆𝑆45����) 𝑆𝑆𝑄𝑄16������ = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝑆𝑆46����, 𝑆𝑆47����,𝑆𝑆48����) Because, the period is repeated after every 4 quarter, then p for estimated seasonal cycle = 4, and r = 4, following the equation [4.3], we obtain seasonal index as below:

𝑆𝑆1 =�𝑆𝑆𝑄𝑄1�����+ 𝑆𝑆𝑄𝑄5�����+ 𝑆𝑆𝑄𝑄9���� + 𝑆𝑆𝑄𝑄13������ �

4

𝑆𝑆2 =�𝑆𝑆𝑄𝑄2�����+ 𝑆𝑆𝑄𝑄6�����+ 𝑆𝑆𝑄𝑄10������ + 𝑆𝑆𝑄𝑄14������ �

4

𝑆𝑆3 =�𝑆𝑆𝑄𝑄3�����+ 𝑆𝑆𝑄𝑄7�����+ 𝑆𝑆𝑄𝑄11������ + 𝑆𝑆𝑄𝑄15������ �

4

𝑆𝑆4 =�𝑆𝑆𝑄𝑄4�����+ 𝑆𝑆𝑄𝑄8�����+ 𝑆𝑆𝑄𝑄12������ + 𝑆𝑆𝑄𝑄16������ �

4

We extent the equation 𝑆𝑆1 = 𝐴𝐴𝐴𝐴𝐴𝐴(𝑆𝑆1� , 𝑆𝑆2� , 𝑆𝑆3� ,𝑆𝑆13����, 𝑆𝑆14����, 𝑆𝑆15����,𝑆𝑆25����, 𝑆𝑆26����, 𝑆𝑆27����, 𝑆𝑆37����,𝑆𝑆38����, 𝑆𝑆39����) 𝑆𝑆1 =𝐴𝐴𝐴𝐴𝐴𝐴(1.032, 0.965, 1.078, 1.087, 0.781, 0.965, 1.015, 0.675, 0.984, 0.978, 0.752, 1.077 ) = 0.927

By calculating similarly, 𝑆𝑆2 = 1.018

𝑆𝑆3 = 1.026

𝑆𝑆4 = 1.051

The seasonal index of each future quarters 17, 18, 19 and 20 will be corresponding to 𝑆𝑆1, 𝑆𝑆2, 𝑆𝑆3 𝑎𝑎𝑛𝑛𝑎𝑎 𝑆𝑆4

37

Table 4.13 Seasonal Factor S and seasonal index S estimation

Year Periods Month Demand De-seasonalized Demand

De-seasonalized

Demand

Seasonal Factor

Seasonal Indices

2014

1 Jan 293,384 284,275 1.032 0.927 2 Feb 198,795 286,189 0.695 0.927 3 Mar 310,517 288,104 1.078 0.927 4 Apr 301,455 290,018 1.039 1.018 5 May 287,826 291,933 0.986 1.018 6 Jun 310,172 293,847 1.056 1.018

7 Jul 319,709 302,903 295,762 1.081 1.026

8 Aug 316,187 306,371 297,676 1.062 1.026 9 Sep 304,058 307,729 299,591 1.015 1.026 10 Oct 305,951 307,644 301,505 1.015 1.051 11 Nov 313,642 309,015 303,420 1.034 1.051 12 Dec 352,906 310,794 305,334 1.156 1.051

2015

13 Jan 333,847 311,634 307,249 1.087 0.927

14 Feb 241,575 311,607 309,163 0.781 0.927

15 Mar 300,323 311,844 311,078 0.965 0.927

16 Apr 309,610 312,902 312,992 0.989 1.018 17 May 312,565 314,461 314,907 0.993 1.018 18 Jun 328,146 314,977 316,821 1.036 1.018

19 Jul 321,889 314,685 318,736 1.010 1.026

20 Aug 313,357 314,010 320,650 0.977 1.026

21 Sep 312,578 314,468 322,565 0.969 1.026 22 Oct 322,813 316,577 324,479 0.995 1.051

23 Nov 334,208 318,580 326,394 1.024 1.051

24 Dec 344,719 319,723 328,308 1.050 1.051

2016

25 Jan 335,026 321,942 330,223 1.015 0.927 26 Feb 224,198 325,741 332,137 0.675 0.927 27 Mar 328,695 327,600 334,052 0.984 0.927 28 Apr 331,842 328,227 335,966 0.988 1.018 29 May 338,423 329,695 337,881 1.002 1.018 30 Jun 329,712 333,594 339,795 0.970 1.018 31 Jul 373,571 336,879 341,710 1.093 1.026 32 Aug 352,868 339,101 343,624 1.027 1.026 33 Sep 317,679 343,204 345,539 0.919 1.026 34 Oct 332,744 346,729 347,453 0.958 1.051 35 Nov 359,524 350,221 349,368 1.029 1.051 36 Dec 412,975 354,768 351,282 1.176 1.051

2017

37 Jan 345,599 357,493 353,197 0.978 0.927 38 Feb 266,963 359,517 355,111 0.752 0.927 39 Mar 384,390 363,870 357,026 1.077 0.927 40 Apr 360,766 368,910 358,940 1.005 1.018 41 May 393,300 372,622 360,855 1.090 1.018 42 Jun 383,967 373,518 362,769 1.058 1.018

38

43 Jul 384,713 364,684 1.055 1.026 44 Aug 390,308 366,598 1.065 1.026 45 Sep 384,713 368,512 1.044 1.026 46 Oct 386,652 370,427 1.044 1.051 47 Nov 394,721 372,341 1.060 1.051 48 Dec 399,275 374,256 1.067 1.051

Fourth step: Estimate forecast value We have input seasonal index for each period t, then the forecast value of period t is calculated by following equation [2.7]:

Ft+l = [ L + (t+l) *T] * St+l

F1 = [L + 1* T] * S1 = [ 282360 + 1*1914] *0.927 = 263387 …… F4 = [L + 2* T] * S4 = [ 282360 + 2*1914] *1.018 = 295130 …… F48 = [L + 1* T] * S48 = [ 282360 + 48*1914] *1.051 = 393160 The result of forecast for each period from t = 49 to 60 to show in the table below:

Table 4.14 The Forecasting Values of Static Method

Year Period Month Seasonal

Indices Forecast

2018

49 Jan 0.927 348,531 50 Feb 0.927 350,304 51 Mar 0.927 352,078 52 Apr 1.018 388,646 53 May 1.018 390,594 54 Jun 1.018 392,542 55 Jul 1.026 397,908 56 Aug 1.026 399,874 57 Sep 1.026 401,839 58 Oct 1.051 413,272 59 Nov 1.051 415,283 60 Dec 1.051 417,295

Fifth step: Measuring of Forecast Error Base on the equations form [2.17] to [2.24], forecast error is calculated and showed in table below (table 4.15)

39

Table 4.15 Forecast Error of Static Method

Periods Demand Seasonal Indices Forecast Error AE MSE MAD %Error MAPE TS

1 293,384 0.927 263,387 -29,997 29,997 899,797,856 29,997 10.22 10.22 -1.00

2 198,795 0.927 265,161 66,366 66,366 2,652,134,352 48,181 33.38 21.80 0.75

3 310,517 0.927 266,935 -43,582 43,582 2,401,219,640 46,648 14.04 19.21 -0.15

4 301,455 1.018 295,130 -6,325 6,325 1,810,915,193 36,567 2.10 14.94 -0.37

5 287,826 1.018 297,079 9,253 9,253 1,465,854,023 31,104 3.21 12.59 -0.14

6 310,172 1.018 299,027 -11,145 11,145 1,242,247,729 27,778 3.59 11.09 -0.56

7 319,709 1.026 303,583 -16,126 16,126 1,101,933,609 26,113 5.04 10.23 -1.21

8 316,187 1.026 305,548 -10,639 10,639 978,340,225 24,179 3.36 9.37 -1.75

9 304,058 1.026 307,513 3,455 3,455 870,962,244 21,876 1.14 8.45 -1.77

10 305,951 1.051 316,735 10,784 10,784 795,495,472 20,767 3.52 7.96 -1.35

11 313,642 1.051 318,746 5,104 5,104 725,546,131 19,343 1.63 7.39 -1.18

12 352,906 1.051 320,757 -32,149 32,149 751,211,767 20,410 9.11 7.53 -2.69

13 333,847 0.927 284,673 -49,174 49,174 879,431,149 22,623 14.73 8.08 -4.60

14 241,575 0.927 286,447 44,872 44,872 960,435,852 24,212 18.57 8.83 -2.45

15 300,323 0.927 288,221 -12,102 12,102 906,170,971 23,405 4.03 8.51 -3.05

16 309,610 1.018 318,509 8,899 8,899 854,484,909 22,498 2.87 8.16 -2.78

17 312,565 1.018 320,457 7,892 7,892 807,885,145 21,639 2.53 7.83 -2.52

18 328,146 1.018 322,406 -5,740 5,740 764,833,336 20,756 1.75 7.49 -2.91

19 321,889 1.026 327,164 5,275 5,275 726,043,650 19,941 1.64 7.18 -2.76

20 313,357 1.026 329,129 15,772 15,772 702,179,998 19,733 5.03 7.08 -1.99

21 312,578 1.026 331,095 18,517 18,517 685,069,698 19,675 5.92 7.02 -1.06

22 322,813 1.051 340,869 18,056 18,056 668,749,731 19,601 5.59 6.96 -0.14

23 334,208 1.051 342,881 8,673 8,673 642,943,758 19,126 2.59 6.77 0.31

24 344,719 1.051 344,892 173 173 616,155,678 18,336 0.05 6.49 0.33

25 335,026 0.927 305,959 -29,067 29,067 625,305,052 18,765 8.68 6.57 -1.22

26 224,198 0.927 307,733 83,535 83,535 869,642,057 21,257 37.26 7.75 2.85

27 328,695 0.927 309,507 -19,188 19,188 851,069,869 21,180 5.84 7.68 1.95

28 331,842 1.018 341,888 10,046 10,046 824,278,807 20,782 3.03 7.52 2.48

29 338,423 1.018 343,836 5,413 5,413 796,865,814 20,252 1.60 7.31 2.81

30 329,712 1.018 345,784 16,072 16,072 778,914,321 20,113 4.87 7.23 3.63

31 373,571 1.026 350,746 -22,825 22,825 770,594,278 20,201 6.11 7.20 2.48

32 352,868 1.026 352,711 -157 157 746,513,978 19,574 0.04 6.97 2.55

33 317,679 1.026 354,676 36,997 36,997 765,370,373 20,102 11.65 7.11 4.32

34 332,744 1.051 365,004 32,260 32,260 773,467,827 20,460 9.70 7.19 5.83

35 359,524 1.051 367,015 7,491 7,491 752,971,959 20,089 2.08 7.04 6.31

36 412,975 1.051 369,026 -43,949 43,949 785,709,211 20,752 10.64 7.14 3.99

37 345,599 0.927 327,245 -18,354 18,354 773,578,575 20,687 5.31 7.09 3.11

38 266,963 0.927 329,019 62,056 62,056 854,560,800 21,776 23.25 7.52 5.81

39 384,390 0.927 330,792 -53,598 53,598 906,307,854 22,592 13.94 7.68 3.22

40 360,766 1.018 365,267 4,501 4,501 884,156,565 22,139 1.25 7.52 3.49

41 393,300 1.018 367,215 -26,085 26,085 879,187,639 22,236 6.63 7.50 2.31

42 383,967 1.018 369,163 -14,804 14,804 863,472,538 22,059 3.86 7.41 1.65

40

43 384,713 1.026 374,327 -10,386 10,386 845,900,310 21,787 2.70 7.30 1.20

44 390,308 1.026 376,292 -14,016 14,016 831,139,893 21,611 3.59 7.22 0.56

45 384,713 1.026 378,257 -6,456 6,456 813,596,241 21,274 1.68 7.10 0.26

46 386,652 1.051 389,138 2,486 2,486 796,043,713 20,865 0.64 6.96 0.39

47 394,721 1.051 391,149 -3,572 3,572 779,378,063 20,497 0.90 6.83 0.22

48 399,275 1.051 393,160 -6,115 6,115 763,919,959 20,198 1.53 6.72 -0.08

4.6 Trend – Corrected Exponential Smoothing (Holt’s Model) Step 1: Determine level L and trend T Next, running linear regression between demand Dt and period t to determine level L0 and trend T0. Using Excel, we use data analysis tool to determine L and T value automatically (Excel /Data/ Data Analysis / Regression) with Input X range with period t from 1 to 48 and Input Y range is demand with t from 1 to 48 also. Running linear regression, we the result that L0 = 276788, T0 = 2225. In this model we calculate with α = 0.01 and β = 0.01 Using formula (2.10) to determine the levels for periods t = 1 to 48 Lt+1 = αDt+1 + (1-α) (Lt + Tt) L1 = αD1 + (1-α) (L0 + T0) = 0.01*293384 + (1-0.01) *(276788+2225) = 279157 …………………… L48 = αD48 + (1-α) (L47 + T47) = 0.01*399275 + (1-0.01) *(381205+2224) = 383587 Using formula (2.11) to determine the trends for periods t = 1 to 48 Tt+1 = β (Lt+1 – Lt) + (1 - β) Tt T1 = β (L1 – L0) + (1 - β) T0 = 0.01*(279157 – 276788) + (1 – 0.01) *2225 = 2227 …………………… T48 = β (L48 – L47) + (1 - β) T47 = 0.01*(383587 - 381205) + (1 – 0.01) *2224 = 2225 Second step: Estimate forecast value Base on equation [2.9] to determine forecasts value for periods t = 1 to 48 Ft+1 = Lt + Tt F1 = L0 + T0 = 276788 + 2225 = 279013 F2 = L1 + T1 = 279157 + 2227 = 281384 …………………… F48 = L47 + T47 = 381205 + 2224 = 383429 Continuing, we determine forecasts for periods t = 49 to 60 Ft+n = Lt + n*Tt F48+1 = F49 = L48 + 1*T48 = 383587 + 1*2225 = 385812 F48+2 = F50 = L48 + 2*T48 = 383587 + 2*2225 = 388038

41

…………………… F48+12 = F60 = L48 + 12*T48 = 383587 + 12*2225 = 410292 The result of forecasts for periods t = 49 to 60 is presented in table 4.16:

Table 4.16 The Forecasting Value of Holt’s Model

Year Period Month Forecast

2018

49 Jan 385,813 50 Feb 388,038 51 Mar 390,264 52 Apr 392,489 53 May 394,714 54 Jun 396,940 55 Jul 399,165 56 Aug 401,391 57 Sep 403,616 58 Oct 405,842 59 Nov 408,067 60 Dec 410,292

Third step: α, β value selection and forecast error estimation Base on the equations form [2.17] to [2.24], forecast error is calculated We need to determine α and β value to get tracking signal value (TS) in rank of (±) 6 by changing α and β value. Forecasting result for periods from t = 49 to by finding out the suitable the value of α and β. We should choose the appropriate values of α and β by pair comparison forecast errors. The result is presented in table 4.17 below:

Table 4.17 Forecast Error by Changing Values of α and β

α β TS Rank

MAD MAPE %Error σ Forecast

Min Max 0.01 0.01 -6.09 5.97 20,668 7.06 3.97 25,834.90 383,429 0.01 0.05 -6.09 6.25 20,733 7.08 4.02 25,915.86 383,212 0.01 0.08 -6.09 6.44 20,789 7.10 4.08 25,985.89 382,988 0.02 0.10 -6.04 6.94 21,155 7.20 4.43 26,443.15 381,579 0.04 0.10 -5.91 6.73 21,788 7.37 4.76 27,234.41 380,285 0.05 0.20 -5.82 6.87 23,042 7.71 5.07 28,802.57 379,024 0.08 0.20 -5.79 6.34 22,517 7.57 2.88 28,145.99 387,769 0.06 0.30 -6.80 6.86 23,137 7.73 3.09 28,921.28 386,938 0.10 0.30 -5.06 6.09 22,318 7.57 0.42 27,897.05 400,971 0.10 0.50 -4.97 4.80 23,223 7.90 1.26 29,028.90 404,300

42

0.30 0.50 -2.32 3.72 26,993 9.14 0.76 33,741.15 402,328 0.70 0.50 -2.08 3.72 33,167 11.02 1.15 41,458.79 394,668 0.90 0.20 -2.16 3.90 30,581 10.20 0.40 38,226.18 397,667

Following table 4.17 above, we see that with α =0.01 and β = 0.01, the result seems to be well about error observation values. So, we choice α =0.01 and β = 0.01 as smoothing constant for level and trend, respectively in this case. Forecast error with α =0.01 and β = 0.01 is calculated and showed in table below (table 4.18)

Table 4.18 Forecast Error of Holt’s model

Periods Demand Level Trend Forecast Error AE MSE MAD %Error MAPE TS

276,788 2,225

1 293,384 279,157 2,227 279,013 -14,371 14,371 206,526,228 14,371 4.90 4.90 -1.00

2 198,795 280,558 2,219 281,384 82,589 82,589 3,513,694,167 48,480 41.54 23.22 1.41

3 310,517 283,054 2,221 282,776 -27,741 27,741 2,598,980,333 41,567 8.93 18.46 0.97

4 301,455 285,437 2,223 285,275 -16,180 16,180 2,014,683,900 35,220 5.37 15.19 0.69

5 287,826 287,661 2,223 287,660 -166 166 1,611,752,652 28,209 0.06 12.16 0.86

6 310,172 290,087 2,225 289,884 -20,288 20,288 1,411,725,531 26,889 6.54 11.22 0.14

7 319,709 292,586 2,228 292,312 -27,397 27,397 1,317,276,855 26,962 8.57 10.84 -0.87

8 316,187 295,028 2,230 294,814 -21,373 21,373 1,209,718,400 26,263 6.76 10.33 -1.71

9 304,058 297,326 2,231 297,258 -6,800 6,800 1,080,443,759 24,101 2.24 9.43 -2.15

10 305,951 299,620 2,231 299,556 -6,395 6,395 976,488,892 22,330 2.09 8.70 -2.60

11 313,642 301,969 2,232 301,851 -11,791 11,791 900,355,585 21,372 3.76 8.25 -3.27

12 352,906 304,689 2,237 304,202 -48,704 48,704 1,023,003,297 23,650 13.80 8.71 -5.02

13 333,847 307,195 2,240 306,926 -26,921 26,921 1,000,060,844 23,901 8.06 8.66 -6.09

14 241,575 308,756 2,233 309,435 67,860 67,860 1,257,554,483 27,041 28.09 10.05 -2.87

15 300,323 310,883 2,232 310,989 10,666 10,666 1,181,302,458 25,950 3.55 9.62 -2.58

16 309,610 313,080 2,232 313,115 3,505 3,505 1,108,238,831 24,547 1.13 9.09 -2.59

17 312,565 315,284 2,231 315,312 2,747 2,747 1,043,492,065 23,264 0.88 8.60 -2.61

18 328,146 317,622 2,233 317,516 -10,630 10,630 991,798,369 22,562 3.24 8.31 -3.16

19 321,889 319,875 2,233 319,854 -2,035 2,035 939,816,323 21,482 0.63 7.90 -3.42

20 313,357 322,020 2,232 322,107 8,750 8,750 896,654,064 20,845 2.79 7.65 -3.10

21 312,578 324,135 2,231 324,252 11,674 11,674 860,445,706 20,409 3.73 7.46 -2.60

22 322,813 326,330 2,230 326,366 3,553 3,553 821,908,278 19,643 1.10 7.17 -2.52

23 334,208 328,617 2,231 328,561 -5,647 5,647 787,559,800 19,034 1.69 6.93 -2.89

24 344,719 330,987 2,232 330,848 -13,871 13,871 762,761,721 18,819 4.02 6.81 -3.66

25 335,026 333,237 2,232 333,219 -1,807 1,807 732,381,870 18,138 0.54 6.56 -3.90

26 224,198 334,357 2,221 335,469 111,271 111,271 1,180,418,785 21,721 49.63 8.22 1.86

27 328,695 336,499 2,221 336,578 7,883 7,883 1,139,001,171 21,208 2.40 8.00 2.28

28 331,842 338,651 2,220 338,720 6,878 6,878 1,100,011,997 20,696 2.07 7.79 2.67

29 338,423 340,846 2,220 340,871 2,448 2,448 1,062,287,175 20,067 0.72 7.55 2.88

30 329,712 342,932 2,218 343,066 13,354 13,354 1,032,821,936 19,843 4.05 7.43 3.58

31 373,571 345,435 2,221 345,151 -28,420 28,420 1,025,560,256 20,120 7.61 7.44 2.12

43

32 352,868 347,708 2,222 347,656 -5,212 5,212 994,360,374 19,654 1.48 7.25 1.90

33 317,679 349,607 2,218 349,930 32,251 32,251 995,746,941 20,036 10.15 7.34 3.48

34 332,744 351,635 2,217 351,826 19,082 19,082 977,169,481 20,008 5.73 7.29 4.44

35 359,524 353,908 2,217 353,851 -5,673 5,673 950,169,722 19,598 1.58 7.13 4.24

36 412,975 356,694 2,223 356,125 -56,850 56,850 1,013,550,971 20,633 13.77 7.31 1.27

37 345,599 358,783 2,221 358,917 13,318 13,318 990,951,103 20,435 3.85 7.22 1.94

38 266,963 360,064 2,212 361,005 94,042 94,042 1,197,606,383 22,372 35.23 7.96 5.97

39 384,390 362,497 2,214 362,276 -22,114 22,114 1,179,437,322 22,366 5.75 7.90 4.98

40 360,766 364,672 2,214 364,712 3,946 3,946 1,150,340,609 21,905 1.09 7.73 5.27

41 393,300 367,150 2,216 366,886 -26,414 26,414 1,139,300,428 22,015 6.72 7.70 4.04

42 383,967 369,513 2,218 369,367 -14,600 14,600 1,117,249,648 21,838 3.80 7.61 3.41

43 384,713 371,861 2,219 371,731 -12,982 12,982 1,095,186,645 21,633 3.37 7.51 2.84

44 390,308 374,242 2,221 374,080 -16,228 16,228 1,076,281,407 21,510 4.16 7.44 2.10

45 384,713 376,545 2,222 376,463 -8,250 8,250 1,053,876,582 21,215 2.14 7.32 1.74

46 386,652 378,846 2,222 378,767 -7,885 7,885 1,032,317,785 20,925 2.04 7.20 1.39

47 394,721 381,205 2,224 381,068 -13,653 13,653 1,014,319,391 20,771 3.46 7.12 0.74

48 399,275 383,587 2,225 383,429 -15,846 15,846 998,419,045 20,668 3.97 7.06 -0.02

4.7 Trend-and Seasonality-Corrected Exponential Smoothing (Winter’s Model) First step: Level, Trend, and Seasonal factor estimation As the same procedure in static model, we already got the initial of level, trend, and seasonal factor value.

• For estimate initial Level and Trend By applying linear regression with de-seasonalized demand in static method, so we get L0 = 282360 and T0 = 1914.

• For estimate initial seasonal factors Seasonal factors for first 4 quarters are obtained as in the static forecasting case: SQ1 = 0.927 SQ2 = 1.018 SQ3 = 1.026 SQ4 = 1.051 Seasonal index of 12 periods from t = 1 to 12 is as below: S1 = S2 = S3 = SQ1 = 0.927 S4 = S5 = S6 = SQ2 = 1.018 S7 = S8 = S9 = SQ3 = 1.026 S10 = S11 = S12 = SQ4 = 1.051

44

• Trend and seasonality corrected In this model we consider α = 0.05, β = 0.01 and γ = 0.05 Level and trend corrected by using equations (2.13) and (2.14): L1 = α (D1 / S1) + (1-α) (L0 + T0) = 0.05*(293384/0.927) +(1-0.05)(282360+1914) =285894 T1 = β(L1 – L0) + (1-β)T0 = 0.01*(285894-282360) + (1-0.01)*1914 = 1931 Level and trend of period form t = 1 to 12 are estimated in the same method In this model we get p = 12, because trend of demand repeats after every 4 quarters (12 periods). Following the equation [2.15], we have seasonality corrected as below: S13 = γ (D1 / L1) + (1-γ) S1 = 0.05*(293384 / 285894) + (1-0.05) *0.927 = 0.932 S14 = γ (D2 / L2) + (1-γ) S2 = 0.05*(198795 / 284161) + (1-0.05) *0.927 = 0.915 For other Seasonal index of each periods is estimated by doing the same way. Second step: Estimate forecast value Base on the equation [2.12], we get: F1 = (L0 + T0) *SQ1 = (282360 + 1914) *0.927 = 263521 F2 = (L0 + T0) *SQ1 = 266667 F4 = (L0 + T0) *SQ2 = 295537 F7 = (L0 + T0) *SQ3 = 304356 F10 = (L0 + T0) *SQ4 = 318548 The forecasts for period 10 to 36 are calculated in the same way as above Next, we can estimate L48 = 375447 and L48 will be used to calculate forecast from period t = 49 to 60, because the Level and Trend are no more able to be estimated due to there is no actual demand during these periods. Apply equation (2.12): Ft+l = (Lt + lTt) *St+l F49 = (L48 + 1*T48) *S49 = (375447 + 1*1929) *0.945 = 356620 F50 = (L48 + 2*T48) *S50 = 337706 Forecasts for periods t = 49 to 60 are calculated in the same way.

Third step: α, β, γ selection and forecast error estimation Base on the equations form [2.17] to [2.24], forecast error is calculated

45

We need to determine α, β and γ value to get tracking signal value (TS) in rank of (±) 6 by changing α, β and γ value, where 0 < α, β, γ < 1. Forecasting result for periods from t = 49 to by finding out the suitable the value of α, β and γ. We should choose the appropriate values of α, β and γ by pair comparison forecast errors. Detail of forecast result and pair comparison of forecast error with various values of

andα β is showed in table blow (table 4.19)

Table 4.19 Forecast Error with Various Values of α, β and γ

α β γ TS Rank

MAD MAPE %Error σ Forecast

Min Max 0.01 0.01 0.01 -4.47 6.43 20,102 6.68 1.33 25,127.81 393,960 0.05 0.01 0.05 -4.00 5.89 19,378 6.44 0.15 24222.71 398,674 0.1 0.1 0.05 -4.53 4.83 20,251 6.68 1.34 25,313.50 404,642 0.2 0.2 0.2 -4.21 2.91 19,091 6.26 6.77 23,863.89 426,308 0.1 0.2 0.3 -7.15 5.00 17,807 5.75 8.79 22,258.80 434,363 0.1 0.5 0.8 -4.11 4.04 18,639 5.85 14.13 23,298.63 455,682 0.5 0.3 0.1 -2.32 1.85 23,195 7.77 0.21 28,993.69 400,115 0.5 0.1 0.3 -2.98 1.96 19,949 6.61 4.00 24,936.22 415,231 0.1 0.5 0.8 -4.11 4.04 18,639 5.85 14.13 23,298.63 455,682 0.2 0.1 0.1 -3.84 3.70 19,974 6.60 3.71 24,967.87 414,094 0.3 0.2 0.2 -3.30 2.05 19,518 6.44 5.31 24,397.92 420,482 0.4 0.3 0.2 -2.61 1.46 20,538 6.82 3.34 25,672.88 412,597 0.5 0.3 0.4 -2.75 1.00 20,354 6.69 4.64 25,442.21 417,792

Among observed values sets above, value α = 0.05, β = 0.01 and γ = 0.05 gives a fairly well forecast error. Therefore, we can select α = 0.05, β = 0.01 and γ = 0.05 Forecasts from period t = 49 to 60 with α = 0.05, β = 0.01 and γ = 0.05 are presented in table 4.20

Table 4.20 Forecast of Winter’s Model

Year Period Month Forecast

2018

49 Jan 356,620 50 Feb 337,706 51 Mar 360,433 52 Apr 389,190 53 May 392,199 54 Jun 394,824 55 Jul 401,662 56 Aug 401,686 57 Sep 400,424 58 Oct 411,458

46

59 Nov 416,034 60 Dec 423,321

Forecast error of Winter’s model with α = 0.05, β = 0.01 and γ = 0.05 are presented in table 4.21

Table 4.21 Forecast Error of Winter’s Model

Periods Demand Forecast Error AE MSE MAD %Error MAPE TS

1 293,384 263,522 -29,862 29,862 891,739,163 29,862 10.18 10.18 -1.00

2 198,795 266,667 67,872 67,872 2,749,179,686 48,867 34.14 22.16 0.78

3 310,517 265,028 -45,489 45,489 2,522,541,153 47,741 14.65 19.66 -0.16

4 301,455 295,537 -5,918 5,918 1,900,660,651 37,285 1.96 15.23 -0.36

5 287,826 297,788 9,962 9,962 1,540,376,734 31,821 3.46 12.88 -0.11

6 310,172 299,240 -10,932 10,932 1,303,566,495 28,339 3.52 11.32 -0.51

7 319,709 304,356 -15,353 15,353 1,151,015,342 26,484 4.80 10.39 -1.12

8 316,187 307,104 -9,083 9,083 1,017,451,627 24,309 2.87 9.45 -1.60

9 304,058 309,542 5,484 5,484 907,743,447 22,217 1.80 8.60 -1.50

10 305,951 318,548 12,597 12,597 832,837,646 21,255 4.12 8.15 -0.97

11 313,642 319,940 6,298 6,298 760,731,086 19,896 2.01 7.59 -0.72

12 352,906 321,644 -31,262 31,262 778,780,233 20,843 8.86 7.70 -2.19

13 333,847 288,538 -45,309 45,309 876,791,126 22,725 13.57 8.15 -4.00

14 241,575 287,361 45,786 45,786 963,900,289 24,372 18.95 8.92 -1.85

15 300,323 292,746 -7,577 7,577 903,467,208 23,252 2.52 8.50 -2.27

16 309,610 321,645 12,035 12,035 856,053,642 22,551 3.89 8.21 -1.81

17 312,565 322,193 9,628 9,628 811,150,683 21,791 3.08 7.91 -1.43

18 328,146 324,750 -3,396 3,396 766,727,650 20,769 1.04 7.52 -1.66

19 321,889 329,937 8,048 8,048 729,782,288 20,100 2.50 7.26 -1.32

20 313,357 331,191 17,834 17,834 709,194,883 19,986 5.69 7.18 -0.43

21 312,578 331,526 18,948 18,948 692,519,633 19,937 6.06 7.13 0.52

22 322,813 339,979 17,166 17,166 674,436,218 19,811 5.32 7.05 1.39

23 334,208 341,438 7,230 7,230 647,385,365 19,264 2.16 6.83 1.80

24 344,719 344,967 248 248 620,413,529 18,472 0.07 6.55 1.89

25 335,026 308,662 -26,364 26,364 623,398,709 18,787 7.87 6.60 0.46

26 224,198 301,592 77,394 77,394 829,802,230 21,041 34.52 7.68 4.09

27 328,695 308,310 -20,385 20,385 814,460,218 21,017 6.20 7.62 3.12

28 331,842 338,238 6,396 6,396 786,833,303 20,495 1.93 7.42 3.51

29 338,423 339,085 662 662 759,716,232 19,811 0.20 7.17 3.67

30 329,712 342,748 13,036 13,036 740,056,604 19,585 3.95 7.06 4.38

31 373,571 346,637 -26,934 26,934 739,585,759 19,822 7.21 7.07 2.96

32 352,868 349,082 -3,786 3,786 716,921,584 19,321 1.07 6.88 2.85

33 317,679 350,361 32,682 32,682 727,563,647 19,726 10.29 6.98 4.44

34 332,744 358,601 25,857 25,857 725,828,805 19,906 7.77 7.01 5.70

35 359,524 360,094 570 570 705,100,129 19,354 0.16 6.81 5.89

36 412,975 364,370 -48,605 48,605 751,136,960 20,166 11.77 6.95 3.25

47

37 345,599 329,417 -16,182 16,182 737,913,288 20,059 4.68 6.89 2.46

38 266,963 315,920 48,957 48,957 781,568,337 20,819 18.34 7.19 4.72

39 384,390 329,583 -54,807 54,807 838,548,925 21,691 14.26 7.37 2.00

40 360,766 361,796 1,030 1,030 817,611,743 21,174 0.29 7.19 2.10

41 393,300 363,164 -30,136 30,136 819,820,981 21,393 7.66 7.20 0.67

42 383,967 367,896 -16,071 16,071 806,450,674 21,266 4.19 7.13 -0.08

43 384,713 375,537 -9,176 9,176 789,654,177 20,985 2.39 7.02 -0.52

44 390,308 375,881 -14,427 14,427 776,437,699 20,836 3.70 6.95 -1.22

45 384,713 375,792 -8,921 8,921 760,951,932 20,571 2.32 6.84 -1.67

46 386,652 387,184 532 532 744,415,651 20,135 0.14 6.70 -1.67

47 394,721 391,397 -3,324 3,324 728,812,058 19,778 0.84 6.57 -1.87

48 399,275 398,674 -601 601 713,636,010 19,378 0.15 6.44 -1.94

4.8 Auto Regressive Integrated Moving Average (ARIMA) Model First step: Estimate and Verify the Model The ARIMA model, as mentioned, can be described by the following equation ϕ∗(L)yt=ϕ(L)(1−L)Dyt =c + θ(L)εt Where: L is the lag operator Liyt=yt−I ϕ∗(L) is the AR operator θ(L) is the MA operator. In order to determine the model, let’s first look as the data

Figure 4.2 Data Estimate and Verify the ARIMA Model

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As we can see, the data shows un-stationary and seasonal attributes. We need then to compute the difference to get the stationary model for the forecasting data. We split the 48-data to two groups: the first 36 is used to find the model, the next 12 to verify. As we observe the data, there is a seasonal affect with the 12-lags. The difference is computed as below

Figure 4.3 Difference at 12-lags

For this set of data, the multiplicative seasonal model was proposed by Box, Jenkins, and Reinsel

Using MATLAB, we find the fitting model %declaring model Mdl = arima('Constant',0,'D',1,'Seasonality',12,'MALags',1,'SMALags',12); %fit the model Estmdl = estimate (Mdl, data(1:36)) The result of the fit model is: ARIMA (0,1,1) Model Seasonally Integrated with Seasonal MA(12): --------------------------------------------------------------- Distribution: Name = 'Gaussian' P: 13 D: 1 Q: 13 Constant: 0 AR: {}

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SAR: {} MA: {-0.608957} at Lags [1] SMA: {-0.925316} at Lags [12] Seasonality: 12 The result of ARIMA equation is

∆∆𝟏𝟏𝟏𝟏𝒚𝒚𝒕𝒕 = (𝟏𝟏 − 𝟎𝟎.𝟔𝟔𝟏𝟏)(𝟏𝟏 − 𝟎𝟎.𝟗𝟗𝟗𝟗𝑳𝑳𝟏𝟏𝟏𝟏)𝜺𝜺𝒕𝒕

The following set of data is obtained by apply the model for 12-next period, in order to verify the model Second step: Forecasting using ARIMA (0,1,1) with calculated coefficients

Table 4.22 Forecast of ARIMA

Year Period Month Forecast

2018

49 Jan 320958 50 Feb 303935 51 Mar 324390 52 Apr 350271 53 May 352979 54 Jun 355342 55 Jul 361496 56 Aug 361517 57 Sep 360382 58 Oct 370312 59 Nov 374431 60 Dec 380989

Third step: Forecast error estimation Base on the equations form [2.17] to [2.24], forecast error is calculated and showed in table below (table 4.23)

Table 4.23 Forecast Error of Winter’s Model

Periods (Pi)

Demand (Di) Forecast Error AE MSE MAD %Error MAPE TS

1 293,384

2 198,795

3 310,517 4 301,455 5 287,826 6 310,172 7 319,709 8 316,187

50

9 304,058 10 305,951 11 313,642 12 352,906 13 333,847 14 241,575 15 300,323 16 309,610 17 312,565 18 328,146 19 321,889 20 313,357 21 312,578 22 322,813 23 334,208 24 344,719 25 335,026 26 224,198 27 328,695 28 331,842 29 338,423 30 329,712 31 373,571 32 352,868 33 317,679 34 332,744 35 359,524

36 412,975

37 345,599 377,585 31,986 31,986 27,652,314 864 9.26 9.26 37.00

38 266,963 272,778 5,815 5,815 27,814,504 995 2.18 5.72 38.00

39 384,390 370,213 -14,177 14,177 32,254,602 1,333 3.69 5.04 17.73

40 360,766 362,894 2,128 2,128 31,561,454 1,353 0.59 3.93 19.04

41 393,300 355,942 -37,358 37,358 64,830,721 2,231 9.50 5.04 -5.20

42 383,967 371,603 -12,364 12,364 66,926,637 2,472 3.22 4.74 -9.70

43 384,713 380,822 -3,891 3,891 65,722,383 2,505 1.01 4.21 -11.12

44 390,308 376,908 -13,400 13,400 68,309,845 2,753 3.43 4.11 -14.99

45 384,713 365,650 -19,063 19,063 74,867,652 3,115 4.96 4.20 -19.36

46 386,652 368,656 -17,996 17,996 80,280,616 3,439 4.65 4.25 -22.78

47 394,721 377,004 -17,717 17,717 85,251,443 3,742 4.49 4.27 -25.66

48 399,275 409,236 9,961 9,961 85,542,347 3,872 2.49 4.12 -22.23

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CHAPTER 5 CONCLUSION AND RECOMMENDATION

5.1 Selection In order to select the most appropriate forecast model, we need to consider forecast error first and we get the final forecast result. In conclusion, the table below (table 5.1) is showed the details of forecast error of all models. Base on the constraints and conditions, the model will be chosen with tracking signal value (TS) in rank of (±) 6.

Table 5.1 Forecast Error of All Models

Method TS rank

AE % Error MAD MAPE

σ

Forecast %σ vs F min max

Simple Linear Regression -6.14 5.68 15669 3.92 20551 7.02 25688.8 383606 6.70

Time series Decomposition 0.01 21.30 44074 11.04 31930 10.09 39912.8 355201 11.2

Moving Average -23.69 5.54 25186 6.31 19864 8.12 24829.5 374089 6.64 Simple Exponential Smoothing -3.04 3.90 5792 1.45 27879 9.38 34848.7 393483 8.86

Static Method -4.60 6.31 6115 1.53 20198 6.72 25247.3 393160 6.42

Holt's Model -6.09 5.97 15846 3.97 20668 7.06 25834.9 383429 6.74

Winter's Model -4.01 5.89 601 0.15 19378 6.44 24238.1 398674 6.08 Time Series ARIMA -25.66 38 9961 2.49 3872 4.122 4840.03 409236 1.18

From table 5.1 above, it is observed that:

1. Simple linear regression model has TS = [-6.14 : 5.68], out of rank +/- 6; therefore, this method will be rejected.

2. Time series Decomposition model has TS = [0.01: 21.3], out of rank +/- 6; therefore, this method will be rejected.

3. Moving average model has TS = [-23.69 : 5.54], out of rank +/- 6; therefore, this method will be rejected.

4. Simple exponential smoothing gives forecast from period t = 49 to 60 = 393483. Therefore, it is rejected and not recommended to use to do forecast for long future.

5. Static model has TS = [-4.60 : 6.31], out of rank +/- 6; therefore, this method will be rejected.

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6. Holt’s model has TS = [-6.09 : 5.89], out of rank +/- 6; therefore, this method will be rejected.

7. Winter’s method gives a very close value of errors.

8. Time series ARIMA has TS = [-25.66: 38], out of rank +/- 6; therefore, this method will be rejected.

Figure 5.1 Line Chart of Winter’s Forecasts

5.2 Conclusion In this project, Winter’s Model is recommended to do forecasting the volume of containers for Cat Lai Terminal port in 2018. 5.3 Recommendation The objective of this research is to build alternative forecasting models to predict the volume of containers for 12 months in 2018 at Cat Lai terminal. Because of limited time, knowledge, this thesis just considered some simple forecasting techniques for short-term forecast where the main focus is on presenting and investigating all the necessary steps required in conducting an efficient forecast. The research has mainly been on quantitative forecasting methods and quantitative forecasting methods are appropriate for future predictions of container volumes in the port industry. This limitation will be addressed in the future expansion of the medium and long-term forecasts.

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REFERENCES

[1] Ali, Mohammad M., and John E. Boylan. “On the Effect of Non-Optimal Forecasting Methods on Supply Chain Downstream Demand.” (2012): 81–98. Web.

[2] Box, G E P, G M Jenkins, and G C Reinsel. Time Series Analysis: Forecasting & Control. N.p., 1994. Web.

[3] Chopra, Sunil, and Peter Mendl. Supply Chain Management. N.p., 2013. Print.

[4] Syntetos, Aris et al. “Supply Chain Forecasting: Theory, Practice, Their Gap and the Future.” European Journal of Operational Research (2015): n. pag. Web.

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APPENDIX MATLAB code function [mdl,std]=fitmdl(data,x,y,z) base=data(1:42); check=data(43:48); %check fit with base std=[] %start with arima(1,1,0) mdl=arima(1,1,0); estmdl=estimate(mdl,base); [yf,ymse]=forecast(estmdl,6); mse=0; for i=1:6 mse=mse+(yf(i)-data(i))*(yf(i)-data(i)); end sdv=sqrt(mse); std=[std sdv] for i=1:x for j=1:y for k=0:z mdl=arima(i,j,k); estmdl=estimate(mdl,base); [yf,ymse]=forecast(estmdl,6); mse=0 for l=1:6 mse=mse+(yf(l)-data(l))*(yf(l)-data(l)) end sdv=sqrt(mse) std=[std sdv] end end end end