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AGGREGATE PRODUCTION PLANNING OF
VINILEX PAINT 25 KG PILE FOR RAMADHAN
SEASON 2018
By
Samuel Then
ID No. 004201400064
A Thesis presented to the Faculty of Engineering President
University in partial fulfillment of the requirements of Bachelor
Degree in Engineering Major in Industrial Engineering
2018
THESIS ADVISOR
RECOMMENDATION LETTER
This thesis entitled “Aggregate Production Planning of Vinilex
Paint 25 kg Pile for Ramadhan Season 2018” prepared and
submitted by Samuel Then in partial fulfillment of the requirements
for the degree of Bachelor Degree in the Faculty of Engineering has
been reviewed and found to have satisfied the requirements for a
thesis fit to be examined. I therefore recommend this thesis for Oral
Defense.
Cikarang, Indonesia, May 17th
, 2018
Prof. Dr. Ir. H.M. Yani Syafe’i, MT.
DECLARATION OF ORIGINALITY
I declare that this thesis, entitled “Aggregate Production Planning of
Vinilex Paint 25 kg Pile for Ramadhan Season 2018” is, to the best
of my knowledge and belief, an original piece of work that has not
been submitted, either in whole or in part, to another university to
obtain a degree.
Cikarang, Indonesia, May 17th
, 2018
Samuel Then
AGGREGATE PRODUCTION PLANNING OF
VINILEX PAINT 25 KG PILE FOR RAMADHAN
SEASON 2018
By
Samuel Then
ID No. 004201400064
Approved by
Prof. Dr. Ir. H.M. Yani Syafe’i, MT.
Thesis Advisor
Ir. Andira Taslim, M.T.
Program Head of Industrial Engineering
ACKNOWLEDGEMENT
Praise to Almighty God I can finish this Thesis Report. There are plenty of
valuable lessons and feedbacks I have obtained on the way of preparation of this
Thesis Report. I am truly grateful for the help, motivation, patience and support
from various parties this Thesis report can be finished successfully. Author’s
gratitude to:
1. Prof. Dr. Ir. H.M. Yani Syafe’i, MT. as my Thesis Advisor. Prof Yani has
always been knowledgeable, helpful and supportive in my progress of
writing this thesis. Other than that, he is an interesting and amusing man
who I enjoy talk to, because any topic is really connective for him. Last
but not least, I also apologise to have ever disappointed him by not coming
often for his counsel.
2. Ir. Andira Taslim, M.T as the Program Head of Industrial Engineering,
also my Academic Advisor who has reassured and motivated me to finish
Thesis report;
3. Mdm. Anastasia Lidya Maukar and Mr. Johan Krisnanto Runtuk, who
have also been encouraging and caring with my progress and pleasure to
talk with them;
4. Mr. Chan Fook Seng as onsite supervisor during my internship at PT
Nipsea Paint and Chemicals Indonesia, Operational Excellence division
who is generous manager to let me use the company data;
5. Mr. Afri Fauzi, former Human Resources Manager at PT Nipsea Paint
and Chemicals who was pleasurable man to let me get the data from
company;
6. Both of my parents who has never quit to support morally and materially;
7. Former work colleagues, and senior employees that were very supportive
during my internship and also helpful in data collection;
8. My friends at President University, especially Paramitha Santia P, Andreas
Gunawan, Lusyana Prastyaningrum, Digo Rizal Pratama, Widyan Farisy,
Dikri Husaeni, Jovian Agathon, Aberson Natanael Simarmata, Wu Fan,
Arie Purnomo Adjie, Rizky Rakhmadhani, Nico Chandra, Julius Kevin,
Michael Triatmojo and Rafif Fauzi as Industrial Engineering peers. And
also my friends from Mechanical Engineering: Ivan Junixsen, Muh. Wika
Gema and Yaummil Chairil. They are my unforgettable friends in my
campus life.
The author admits that his report is far to be perfect, therefore author expects
suggestions, comments, and advices, to improve this thesis report. Hopefully this
report can bring benefits to those who read, as well as the author himself in
purpose of knowledge, engineering and science development. Thank you.
LIST OF TERMINOLOGIES
Aggregate plan : process of developing, analyzing and maintaining a
preliminary, approximate schedule of overall operations.
Cycle time : the period required to complete one cycle of an operation
Emulsion paint : Water-based paint in which the paint material is dispersed in a
liquid that consists mainly of water
Enamel paint : A paint made of an opaque or semi transparent glassy
substance applied to metallic or other hard surfaces for
ornament or as a protective coating
Forecasting : The utilisation of historic data to determine the direction of
future trends
Lot sizing : a technique that is used to determine the quantity of order
MRP : Material Requirement Planning, a production planning,
scheduling and inventory control system to manage
manufacturing process
ABSTRACT
PT Nipsea Paint and Chemicals Indonesia or well known as Nippon Paint is a big
manufacturing company that works in paint and coating industry. The entire activities at PT
Nipsea Paint and Chemicals Indonesia matter as this company is well known as a company
with high standard of safety, particularly those involving in the core activity of production
planning. The most concern of company is coping with demand during incoming Ramadhan.
Even though there is an existing forecasting technique utilised by the MRP department of
company, it had experienced loss of sales during last year’s Ramadhan. At the production
site, the number of workers were not enough to produce enough, even with daily overtime,
hence underproduction. This research is conducted to analyze the forecasting technique used
to correspond with the demand trend which is categorised into time-series forecast at PT
Nipsea Paint and Chemicals, aggregate planning method to deal with labour cost and
inventory, and finally lot sizing matter for saving up cost.
Keywords: Paint, Production Planning, Sales Demand, Forecasting, Seasonal Forecasting,
Aggregate Planning, Lot Sizing.
CHAPTER I
INTRODUCTION
1.1. Problem Background
High demand brings a positive impact for other business fields related to the field of
construction. One of them is the producers and companies in the field of paint. This is
because every home needs paint to coat the wall / wall to give the impression clean
and improve its visual appearance or the need for malls and offices to repaint or
repaint the building makes paint demand soaring.
Lack of product can occur when the market demand is greater or equal to the
production planning done on a company. If the company continues to fail to meet
customer demand or market demand, it can lead to the loss of a company's fixed
customers so that if it continues then a company may incur losses and even
bankruptcy. It is therefore necessary that the finished product inventory be used as a
reserve in the event of a spike in market demand. However, the supply of products
used as reserves can cause the buildup of products in warehouses and may cause
swelling of capital costs and product inventory costs. Therefore, good production
planning is required to meet dynamic market needs (Herjanto, 2008).
The control of product inventory is a very important internal process for the
company's operational activities, especially in the paint industry because of the many
types, colours and size of the company's urgent packaging to stockpile and may still
fail to meet customer demand due to depletion of inventory, delivery delay and others
(Graystone, 1997).
Nipsea Paint and Chemicals Co Ltd or well known as Nippon Paint was established in
1881,that made Nippon Paint as the first Japanese paint manufacturing company.
Today, Nippon Paint is the number 1 brand of paint in Asia Pacific that spread over
18 countries. In Indonesia, Nippon Paint is the largest paint manufacturer that
dominates the main segments: decorative paints such as Vinilex.
Ramadhan, the ninth month of Islamic Calendar (Hijri Calendar) is the fasting month
and also of great importance in Indonesia, which is a predominantly Muslim country.
Approaching Ramadhan, the demand of any goods including decorative paints has
been very high. Many Muslim families purchase paints to furbish up their houses.
Therefore, the demand of Vinilex paints is incredibly high that even Nippon Paint
Indonesia in this last Ramadhan this year could not cope with the demand. The
forecasted demand for last year Ramadhan season missed by at least 20% margin.
Hence, Nippon Paint suffered underproduction and it is imperative to find out a way
not to lose sales anymore for adapting with the future Ramadhan next year.
Based on the explanation above, I, as the researcher, am interested to do a research
study regarding to the analysis of past demands, aggregate production planning and
lastly inventory management of lot sizing for the Vinilex paint sales in Jakarta facing
Ramadhan season in 2018.
1.2. Problem Statement
The background of the problem leads into statement below:
What is the least costly aggregate production planning method with minimum
error to improve the sales performance?
What is the most effective inventory control strategy to be implemented?
1.3. Research Objectives
The purposes of this research are:
To decide which aggregate planning method is the most effective to deal with
approaching next year’s Ramadhan
To be a reference for development for the intenvory control strategyl at Nippon
Paint Indonesia facing up Ramadhan 2018
1.4. Research Scope
Due to limited time and resources in doing this research, therefore we applied scope
such as:
The observation was conducted from May 2017 to October 2017
Vinilex, interior paint as particular paint product
Because there are multiple colours, the specific colour is white
The production plant in Purwakarta where Vinilex paints are mainly produced to
be distributed all over Jakarta
Make-to-stock product
1.5. Assumptions
Some assumptions ought to be made in order to analyse properly:
As it is about forecasting, the safety stock or inventory matters are not included in
this research
The product life cycle can last longer than one year and so on
The ingredients for making the paint liquid are similar with each other
The density of paint is constant
The Vinilex pile limits to 25 kg
There is no random error component in calculation
1.6. Research Outline
Chapter I : Introduction
This chapter comprises of the background of the problem occurred, problem
statements, research objectives, scope, assumptions and the description of research
outline.
Chapter II: Literature Study
This chapter incorporates the foundamentals of knowledge about production planning,
particularly on time-series forecast, the explanation of forecasting error, validation,
verificaton technique, aggregate planning and lot sizing as these literatures are used to
support the analysis of the research.
Chapter III: Research Methodology
This chapter involves systematicly calculated and well-structured steps that conducted
during the research. The steps are presented in the form of a flow chart completed
with a brief description.
Chapter IV: Data Collection & Analysis
This chapter includes the data or information necessary to analyze the existing
problems as well as data processing based on the forecasting method that has been
determined by comparing Before – After forecasting method.
Chapter V: Conclusion & Recommendation
This chapter provides conclusion of research’s entire analysis and the improvement
results, moreover gives the recommendation for the future research that will deal with
similar field of research
CHAPTER II
LITERATURE STUDY
2.1. Paint
Paints are dyes (in the form of liquids, thick liquids or flours) made from pigments and
binders to dye a wood surface, metal that serves as a protective or decorative layer
(Ministry of National Education, 2014). Cambridge Dictionaries Online (2015) says the
paint is a colored liquid applied to the walls to adorn the walls. According to the Oxford
Dictionaries (2015), paints are colored substances that are propagated or applied on a
surface that after drying will form a thin layer of decorative or protective.
Satisfying an aesthetic need is a human instinct and there is much evidence indicating
the use of some paints and coatings during the prehistoric era. In present times, many
products must have aesthetic appeal for their acceptance and sale. Therefore, decorative
value is one of the primary requirements of many paints and coatings. Since
industrialization, we have been using a large quantity of metals and alloys, besides
materials such as wood and masonry.
We now know the primary functions of paints and coatings and their importance in
enhancing and protecting many industrial and consumer products. In general, paints and
coatings are liquid mixtures that are applied onto the surfaces of products using a brush,
roller or spray. These mixtures are supplied in a variety of forms, such as waterborne or
solventborne, low viscosity or paste-like consistency, sprayable or brushable, to meet the
end use application requirements. Simply put, coatings are liquid mixtures that are
spread onto a surface as a thin uniform wet layer that dries to a hard and adherent film.
After application, the wet liquid film is then converted to a dry and adherent coating
through a physical drying or chemical curing process. The nature of the films formed
depends upon the composition of the paint, and varies, for example from transparent to
opaque, glossy to matte, and hard to soft. Looking at the diversity of coating types, it is
not surprising that different types of coatings would have different constituents. As one
would expect, all coatings must have an ingredient that forms a film. These film forming
ingredients, which are essentially polymeric materials, are called resins or binders.
Resins and binders have the capability of forming transparent and adherent films, but
they cannot hide or destroy the surface on which they are applied. Pigments, which are
finely divided insoluble particles, coloured or white, have the capability of provided
colour and opacity when dispersed into a medium.
2.2. Forecasting Demand
The starting point for virtually all planning systems is the actual or expected customer
demand. In most cases, however, the time it takes to produce and deliver the product or
service will exceed the customer expectation of delivery time. When that occurs, as is
usually the case, then production will have to begin before the actual demand from the
customer is known. That production will have to start from expected demand, which is
generally a forecast of the demand.
There are several types of forecasts, used for different purposes and systems. Some are
long-range, aggregated models used for long-range planning such as overall capacity
needs, developing strategic plans, and making long-term strategic purchasing decisions.
Others are short-range forecasts for particular product demand, used for scheduling and
launching production prior to actual customer order recognition. Regardless of the
purpose or system for which the forecast will be used, there are some fundamental
characteristics that are very important to understand:
Forecasts are almost always wrong.
The issue is almost never about whether a forecast is correct or not, but instead
the focus should be on "how wrong do we expect it to be" and on the issue of
"how do we plan to accommodate the potential error in the forecast." Much of
the discussion of buffer capacity and/or buffer stock the firm may use is
directly related to the size of the forecast error.
Forecasts are more accurate for shorter time periods.
In general, there are fewer potential disruptions in the near future to impact
product demand. Demand for extended time periods far into the future are
generally less reliable.
Every forecast should include an estimate of error.
The first principle indicated the importance to answer the question, "How
wrong is the forecast?" Therefore, an important number that should
accompany the forecast is an estimate of the forecast error. To be complete, a
good forecast has both the forecast estimate and the estimate of the error.
Forecasts are no substitute for calculated demand.
If you have actual demand data for a given time period, you should never
make calculations based on the forecast for that same time period. Always use
the real data, when available.
2.2.1. The Forecasting Categories
The forecasting tools and methods can be split into four general categories
(Georgoff, 1986):
Judgement Methods
Involving collection of expert opinions.
Market Research Methods
Involving Qualitative studies of consumer behaviour.
Time-series Methods
Mathematical methods in which future performance is extrapolated from
past performance.
Causal Methods
Mathematical methods in which forecasts are generated based on variety of
system variables.
2.2.2. The Forecasting Step
1. Specifying the Objective
2. Determining the Time Perspective
3. Making a Choice of Method for Demand Forecasting
4. Collection of Data and Data Adjustment
5. Estimation and Interpretation of Results
2.2.3. Data Model
The Randomness Component
It happens when the demand is random or uncertain.
Figure 2. 1.The Example Data Model of Randomness Component
The Cycles Component
It usually happens when the data is affected by the long-term fluctuation.
Figure 2. 2.The Example Data Model of Cycles Component
The Curvilinear Trend Component
It happens when the demand is increasing but not the same amount in each
period.
Figure 2. 3.The Example Data Model of Trend Component
It happens when the data is affected by seasonal factor like holiday, vacation,
weather etc.
Figure 2. 4. The Example Data Model of Seasonality Component
2.2.3. Selecting Appropriate Forecasting Technique
There are three questions as considerations to choose appropriate forecasting
technique (Chambers, Mullick and Smith, 1971):
The purpose of forecast and how it is to be used.
The dynamics of system which forecast to be made.
The importance of the past in estimating the future.
2.3. Time Series Forecasting
Time-series forecasts are among the most commonly used for forecasting packages
linked to product demand forecasts. They all essentially have one common assumption.
That assumption is that past demand follows some pattern and that if that pattern can be
analysed it can be used to develop projections for future demand, assuming the pattern
continues in roughly the same manner. Ultimately that implies the assumption that the
only real independent variable in the time series forecast is time. Since they are based
on internal data (sales), they are sometimes called intrinsic forecasts.
Time series are also the most commonly used by operations managers when they find
they need to forecast in order to make reasonable production plans. Such knowledge is
seldom easily available for an operations manager, who typically spends most of his or
her attention focused internally. Previous demand is, however, often readily available
for the operations manager.
Most time series forecasting models attempt to mathematically capture the underlying
patterns of past demand. One is a random pattern - under the assumption that demand
always has a random element. This implies what most people inherently know: the
customers who demand goods and services from a company do not demand those goods
and services in a completely uniform and predictable manner.
The second pattern is a trend pattern. The trends can either be increasing or decreasing,
and they can be either linear or nonlinear in nature.
The third major pattern is a cyclical pattern, of which a special but very common case is
a seasonal pattern. Even though called seasonal (since for many companies the most
common pattern of this type follows the seasons of the year), these patterns are actually
cyclical patterns, which major may not be linked to the yearly seasons. Cyclical
patterns then are demand patterns that follow some cycle of rising and falling demand.
In the special case where the pattern follows the seasons of the year, the cyclical pattern
is usually called seasonal.
There are five patterns which are constant, trend, seasonal (cyclical), seasonal variation
and trend with seasonal.
Table 2. 1. Constant, Trend, Seasonal, Seasonal Variation, Trend + Seasonal Methods
Component/Process Methods Component/Process Methods
Constant
Last Period Demand
Arithmetic Average (Average Methods)
Single Moving Average (SMA)
Weighted Moving Average (WMA)
Single Exponential Smoothing (SME)
Regression Analysis (Constant)
Trend
Double Moving Average (DMA)
Double Exponential Smoothing – Brown
Double Exponential Smoothing – Holt
Exponential Smoothing Pegels
Regression Analysis (Linear)
Seasonal
Triple Exponential Smoothing (TES) – Winter
Exponential Smoothing Pegels
Regression Analysis (Cyclical)
Seasonal Variations Ratio to moving average method (Seasonal Index)
Trend + Seasonal
Exponential Smoothing Pegels
Regression Analysis (Linear and Cyclical)
There are two methods of time-series forecast to be used in this research, excluding
Regression:
a. Simple Moving Average
Simple Moving Average, or in other words, Single Moving Average is
mathematical average of the last several periods of actual demand. It takes the
basic formula of:
𝑺𝑴𝑨 = 𝒅𝒕′ =
𝒅𝒕−𝟏+𝒅𝒕−𝟐+𝒅𝒕−𝟑+⋯+𝒅𝒕−𝑵
𝑵=
∑ 𝒅𝒕−𝒊𝒏𝒊=𝟏
𝑵 (2-1)
Where:
dt’ = forecasted demand for period t
dt = actual demand in period t-i
N = number of time periods included in moving average
The concept is much easier to see with an example below. Suppose we are using a
three-period moving average. The forecast for any time period then becomes the
average of the actual demand for the three previous periods. The calculations for
the table are fairly easy. To get the forecast for period 4, take the actual demand
for the three previous periods (periods 1 through 3) and find the average:
(24+26+22)/3 = 24. The forecast for period 5 comes from the average of the
demand for periods 2 through 4: (26+22+25)/3 = 24.3.
Figure 2. 5. The Example of Simple Moving Average Forecast Method (1)
Figure 2. 6. Actual Demand vs Forecasted Demand of SMA (1)
There are two important points that need to be made concerning the graph and the
moving average method as well.
First, it is fairly obvious to see that the forecast line is smoother than the
demand line, showing the impact of taking an average. The more periods
used in computing the moving average, the smoother this effect will be.
The reason is that with more periods being used in the average, anyone of
the demand points will have less overall influence.
Second, the forecast will always lag behind any actual demand. That is
not so obvious in this graph, but suppose we use the same method to
graph a demand pattern with an upward trend, as in Figure 2.7.
Figure 2. 7. The Example of Simple Moving Average Forecast Method (2)
Figure 2. 8. Actual Demand vs Forecasted Demand of SMA (2)
The implication of this lagging effect is that models such as simple moving
averages should normally not be used to forecast demand when the data clearly
follows any type of trend or regular cyclical pattern. It is important to note that
forecasting methods should not be arbitrarily selected, but instead should be
selected and developed to fit the existing data as closely as possible.
b. Holt-Winters Method
This method is used when the data shows trend and seasonality. To handle
seasonality, we have to add a third parameter. We now introduce a third equation
to take care of seasonality. The resulting set of equations is called the ”Holt-
Winters” (HW) method after the names of the inventors.
In this model, we assume that the time series is represented by the model
𝑦𝑡 = (𝑏1 + 𝑏2𝑡)𝑆𝑡 +∈𝑡 (2-2)
Where:
b1 is the base signal also called the permanent component
b2 is a linear trend component
St is a multiplicative seasonal factor
∈𝑡 is the random error component
Let the length of the season be L periods.
This model is appropriate for a time series in which the amplitude of the seasonal
pattern is proportional to the average level of the series, i.e. a time series
displaying multiplicative seasonality.
Let the current deseasonalized level of the process at the end of period T be
denoted by RT . At the end of a time period t, let
�̅�𝑡 be the estimate of the deseasonalized level.
�̅�𝑡 be the estimate of the trend
𝑆�̅� be the estimate of seasonal component (seasonal index)
The overall smoothing formula is below:
�̅�𝑡 =∝𝑦𝑡
𝑆�̅�−𝐿 + (1−∝) ∗ (�̅�𝑡−1 + �̅�𝑡−1) (2 - 3)
Where 0 < α < 1 is a smoothing constant.
The smoothing of the trend factor formula is below:
�̅�𝑡 = 𝛽 ∗ (𝑆�̅� − 𝑆�̅�−1) + (1 − 𝛽) ∗ �̅�𝑡−1 (2 – 4)
Where 0 < β < 1 is a second smoothing constant. The estimate of the trend
component is simply the smoothed difference between two successive estimates
of the deseasonalized level.
The smoothing of the seasonal index formula is below:
𝑆�̅� = 𝛾 ∗ (𝑦𝑡/�̅�𝑡) + (1 − 𝛾) ∗ 𝑆�̅�−𝐿 (2 – 5)
where 0 < γ < 1 is the third smoothing constant. The estimate of the seasonal
component is a combination of the most recently observed seasonal factor given by the
demand yt divided by the deseasonalized series level estimate Rt and the previous best
seasonal factor estimate for this time period.
c. Seasonal Index Method
Many sales, production, and other series fluctuate with the seasons. The unit of
time reported is either quarterly or monthly. Seasonal variation is another of the
components of a time series. In the area of production, one of the reasons for
analysing seasonal fluctuations is to have a sufficient supply of raw materials on
hand to meet the varying seasonal demand. The typical sales are expressed as
indexes. Each index represents the average sales for a period of several years.
Determining a Seasonal Index
A typical set of monthly indexes consists of 12 indexes that are representative
of the data for a 12-month period. Several methods have been developed to
measure the typical seasonal fluctuation in a time series. The method most
commonly used to compute the typical seasonal pattern is called the ratio-to-
moving-average method. It eliminates the trend, cyclical, and irregular
components from the original data (Y). In the following discussion, T refers to
trend, C to cyclical, S to seasonal, and I to irregular variation. The numbers
that results are called the typical seasonal index.
Six Steps to determine the quarterly seasonal index
Step 1: Determine the four quarters moving total each year. This procedure is
continued for the quarterly sales for each of the six years. Check the total
frequently to avoid arithmetic errors.
Step 2: Each quarterly moving total is divided by 4 to give the four-quarter
moving average. All the moving averages are still positioned between quarters.
Step 3: The moving averages are then centred. It is calculated from the average
of two moving average. Centred moving average is positioned on a particular
quarter.
Figure 2. 6. Example of Seasonal Index Method
Step 4: The specific seasonal for each quarter is then computed by dividing the
demand by centred moving average. The specific seasonal reports the ratio of
the original time series value to the moving average.
Figure 2. 7. Example of Seasonal Index Method up to Seasonal Multipliers
Step 5: The specific seasonal should be organized in other table. This table
will help us locate the specific seasonal for the corresponding quarters. A
reasonable method to find a typical seasonal index is to average the specific
seasonal values.
Figure 2. 8. Example of Seasonal Index Method up to Seasonal Adjusted Forecast
Step 6: Calculate the correction factor and determine the seasonal index.
Figure 2. 9. Actual Demand vs Forecasted Demand of Seasonal Index Method
Figure 2. 10. Finding Error on Seasonal IndexMethod
Now if we look at the graphical comparison between the actual demand and the
seasonally adjusted regression forecast in Figure 2.12, it can easily be seen how
closely they compare. In addition, the forecast for period 9 will give us a fair
confidence, given how closely other quarters track (in fact, on this graph it is very
difficult to distinguish that there are in fact two separate lines). To show how closely
they track, Table 2.12 shows the percentage error between the seasonal forecast and
the actual demand.
It also should be noted that even though the discussion of seasonal indexes was
presented in the context of time series regression, the concept of developing and
applying seasonal indexes can be used for virtually any of the time series models.
2.4. Forecasting Fitting Error
Fitting error is the difference between the actual demand and the forecast value. Since
the fitting error is derived from the same scale, the comparison of the fitting error can
only be made on the same scale.
Mean Square Error
Mean Squared Error (MSE) is a method to evaluate forecasting methods. Each error
or residual squared, then totaled and added to the total number of observations. This
approach set the forecasting error is large because it is squared errors. The method
produces errors while the chances are better for small mistakes, but sometimes
makes a large difference.
Formula:
MSE = ∑ (𝑑𝑡−𝑑𝑡
′)21313
𝑡−1
n (2-6)
Where:
dt = actual demand at period t
dt’ = demand forecast at period t
n = number of period
Mean Absolute Deviation
Mean Absolute Deviation (MAD) is a method for evaluating a forecasting method
using the sum of absolute errors. MAD measure forecast accuracy by averaging the
alleged error (absolute value of each error). MAD useful when measuring forecast
error in the same units as the original series.
Formula:
MAE = ∑ |𝑑𝑡−𝑑𝑡′|𝑛
𝑡−12
𝑛 (2-7)
Mean Absolute Percentage Error
Mean Absolute Percentage Error (MAPE) is calculated using the absolute error in
each period divided by the actual observation for that period. Then, averaging the
absolute percentage error. This approach is useful when a large size or forecast
variables are important in evaluating the accuracy of the forecast. MAPE indicates
how big a mistake in divination than the real value.
Formula:
PE = the percentage of error
Pet = (𝒅𝒕−𝒅𝒕′
𝒅𝒕) (2-8)
MAPE = ∑ |𝑷𝑬𝒕|𝒏
𝒕−𝟏
𝒏 (2-9)
i. Verification Method
Verification method is verifying as well as determining the model of forecast.
Verification Test
Verification test is a test that aims to test the effectiveness of the methods used in
the forecasting process. In the verification tests there are some standards that are
used as constraints; the data below is an example of the limits used in forecasting.
Formula:
MR = ∑ |𝑀𝑅𝑡|𝑛
𝑡−2
𝑛−1 (2-10)
MRt = |(𝑑𝑡′ − 𝑑𝑡) − (𝑑𝑡−1
′ − 𝑑𝑡)| (2-11)
UCL = + 2,66 MR
LCL = - 2,66 MR
Figure 2. 11. Range of UCL and LCL
Product is out of control if:
1. There is a point outside the UCL or LCL
2. 3 consecutive point from 2 point or more located at A
3. 5 consecutive point from 3 point or more located at B
4. 3 consecutive point from 2 point or more located at A
5. 8 consecutive point located at one side
ii. Tracking Signal Test
Tracking Signal is a measure of how well a forecast estimates the actual values.
Signal tracking value can be calculated using those following formulas:
Formula:
Tracking signal – trigg = ±1
MAD = MAE = ∑ |𝑑𝑡−𝑑𝑡′|𝑛
𝑡−12
𝑛 (2-12)
Tracking signal = 𝑑𝑡−𝑑𝑡′
𝑀𝐴𝐷 (2-13)
Tracking positive signal indicates that the actual value is greater demand than forecast,
whereas a negative signal tracking means that the actual value is smaller than the demand
forecast. Tracking signal is called good if it has a low RSFE (dt-dt’), and has a lot of
positive same error or balanced by a negative error, so the centre of the tracking signal is
close to zero. Tracking the signal that has been calculated can be made map controls to
look at the feasibility of data in the upper control limit and lower control limits.
The tracking signal emphasizes an important trade-off: it would be time consuming and
possibly costly to evaluate and modify the forecasting method too frequently, but how
often is too frequently? By the same token, to allow the method to proceed too long
without evaluation could produce serious deterioration of the forecasts. The tracking
signal, therefore, allows a systematic method to determine when the forecasting method
should be evaluated or not.
2.5. Aggregate Planning
Basically aggregate planning is composed of design a preferred output over an
intermediate span from three months to a year. It needs logical, common unit of
measuring output such as gallons or tonnes of paint in paint factory. As he forecast goes
further to the future, the accuracy of forecast will be less probable. During the short
range period, better forecasts turn to be available for individual products, disaggregation
and comprehensive scheduling become feasible.
Numerous aggregate planning strategies involve the inventory control, production rate,
labour needs, capacity and other manageable variables. There are two types of strategies:
pure and mixed strategies. The pure strategies are Chase strategy (workers) and Level
strategy (inventory), excluding Subcontracting strategy for this thesis. The mixed
strategy or oftenly called hybrid strategy is the combination of pure strategies such as
managing numbers of workers and inventory.
There are several costs related to aggregate planning:
Regular Labour Wage and Overtime Cost
A significant part of regular time production cost is used up as full-time
workforce wages. The overtime cost is the cost that can be increased when the
production is undergone below the desired capacity.
Changing Production Rate Cost
Changing production rate cost is attributed mainly to changes of workforce size.
Inventory, Backorder and Shortage Cost
All costs are associated with inventory. The cost of carrying inventory typically
hovers around 5% to 50% of the value of items stored.
CHAPTER III
RESEARCH METHODOLOGY
In this chapter, the course of the entire research process is explained. The stages were
arranged before the research is done, hence they ought to become guidance for the
researcher to commence and conduct the research effectively until the research
objectives are achieved. The flowchart and the research methodology descriptions made
by researcher are shown below.
3.1 Initial Observation
In this section, the identified problem is analysis of the actual demand for the last
Ramadhan which was over the forecasted demand used with Simple Moving Average
Method, therefore losing sales. Also, the condition inside the production plant where the
number of workers might be not enough, less production lines, so it led to
underproduction.
3.2 Problem Identification
Based on the initial observation, it is identified that current forecasting method and
aggregate planning might lead to underproduction coping to Ramadan. Therefore, to
mitigate this, the researcher needs to pinpoint what kind of PPIC method does bring the
significant effect on their sales performance for upcoming Ramadhan.
3.3 Literature Study
In this step of research methodology, the researcher seeks for the literature references
coming from journals and books that can be used as supporting theories for this research.
The theories are used to guide the researcher to find the main goal of the research which
is to find the best way to improve the forecasted demands of Vinilex paints. Then the
result will be assessed using the hypothesis stated in the research.
3.4 Data Collection & Analysis
3.4.1. Data Collection Method
In the step of data collection, the researcher gathers all the primary data related to the
demand and forecasted demand on the site. The observation of gathering data was
done directly at Nippon Paint Indonesia. The data taken in the production was in the
form of quantitative data represented by graph as well.
3.4.2. Data Analysis Method
The next step taken after all data needed for research had been gathered was the
analysis of all that information. With the current condition of the data and the method,
the researcher analysed how each forecasting method have their own unique selling
points can affect the performance of the Vinilex sales. As the data graph pattern of
demands resembles more likely to be constant seasonal where the peak is on certain
period with multiplications of fluctuations, either the constant or seasonal forecasting
type is chosen. Then the after stage analysis would be continued with the aggregate
planning to choose which method is cost-effective After that, the analysis continues to
lot sizing to choose which method does serve the most efficient to keep inventory. At
last the analysis was also done to observe the improvement of whole production
planning and inventory control that had been made by assuming the result of its
performance.
To validate the statistical data by using assumption statistical testing, there are three
tests to be implemented:
a. Normality Test
According to Imam Ghozali (2011: 160-165), the normality test aims to determine
whether the residuals of the analyzed data are normally distributed, near normal, or
not. A good gradient model should be normally distributed or near normal. One of the
ways in this test is done by Kolmogorov-Smirrnov Test. The results of this test can be
seen in the SPSS output on the Kolmogorov-Smirnov One-Sample Test table. The
value of Asymptote. Sig. (2-tailed) must be greater than the specified alpha value. In
this study the alpha value used is 5%.
Here are the decision-making criteria:
1. If Asymp Sig < α (0,05), means data is not distributed normally
2. If Asymp Sig ≥ α (0,05), means data is distributed normally
b. T-Test
This is the statistical test to test whether an independent variable individually affects
the dependent variable. The steps that can be done in hypothesis testing of regression
coefficients are as follows:
Hypothesis used in this research are:
a. Determining the hypothesis
H0: βi = 0
Ha: βi> 0
b. Determine the error rate (α) = 0.05
c. Basic decision-making can be seen in the table Coefficient, namely:
1) Reject H0 when P-value (sig-t) <α (0.05). This means that the regression
coefficient is significant (the independent variable is a significant explanation of the
dependent variable).
2) Do not reject H0 when P-value (sig-t) ≥ α (0,05). This means the regression
coefficient is not significant (independent variable is not a significant explanation of
the dependent variable).
c. Autocorrelation Test
According to Imam Ghozali (2011: 110-138), the autocorrelation test aims to test
whether in the linear regression model there is a correlation between the confounding
error in period t with the intruder error in period t-1 (previous). If there is a correlation,
then there is called an autocorrelation problem. A good regression model is a model
independent of autocorrelation. To detect the presence or absence of autocorrelation,
Breusch-Godfrey test is used. The research will be said to be autocorrelated if the
value of significance on the RES_2 variable is above 0.05.
3.5 Conclusion & Recommendation
The final step of the research is to give conclusion and recommendation. The conclusion
contains the summary of the whole process of research until the researcher accomplished
the research objectives. In conclusion the problems stated would be answered with the
come up of the proposed forecasting technique with its own advantages. When the
Initial Observation
Problem
Identification
Literature Study
Data Collection &
Analysis
Conclusion &
Recommendation
researcher arrived to the conclusion part, it means that the research objectives had been
achieved.
The conclusion part also must be followed by the recommendation given by the
researcher. The recommendation is the part where the suggestion
and advice given for the readers or those who would like to do some
kind of research with a similar topic with this research. This is
purposed to the betterment of research in the future.
Initial Observation:
1. Loss of sales in last Ramadhan
2. The production planning were not up to the challenge yet
Problem Identification:
1. What is the least costly aggregate production planning method
with minimum error to improve the sales performance?
2. What is the most effective lot sizing method to improve the
inventory control system?
Literature Study:
1. Definition of Paint 4. Lot Sizing
2. Forecasting
3. Aggregate Planning
Data Collection:
1. Data of Vinilex sales (demand and forecasted demand) within last
25 months
2. Data of daily salary, overtime wage and number of labours
Data Analysis:
1. Analysis of production planning by aggregate planning and lastly
lot sizing statistically
2. Find out the most effective and least costly method from each of
them and utilise them concurrently
Conclusion:
1. Conclusion of calculation and analysis
2. Recommendation of PPIC method
CHAPTER IV
DATA COLLECTION AND ANALYSIS
4.1. Data Collection
There are several data collected for this research topic: Sales Demand,
Aggregate Planning and Inventory lots
4.1.1. Sales Demand
The first data collection consists of last 25 months demand of Vinilex
paint restricted to white colour and Jakarta. This data is primary, directly
from the company. The demand is not in terms of units but volume in
tonnes.
Table 4. 1. Last 25 Months Demand
Period Demand (in tonnes) Period Demand (in tonnes)
Feb-16 471 Mar-17 654
Mar-16 568 Apr-17 679
Apr-16 612 May-17 753
May-16 698 Jun-17 729
Jun-16 672 Jul-17 643
Jul-16 567 Aug-17 543
Aug-16 456 Sept-17 431
Sept-16 324 Oct-17 456
Oct-16 365 Nov-17 378
Nov-16 298 Dec-17 467
Dec-16 412 Jan-18 453
Jan-17 478 Feb-18 589
Feb-17 564
The diagram of demand over period is shown below to explain the demand
pattern from the table above:
Figure 4. 1. Vinilex White Demand Chart
The graph shows that the demand of the Vinilex white paint in Jakarta area
both are constant and seasonal. During April-July 2016, the demand of paint
was at the peak, particularly in May-June 2016 because of Ramadan month
in June 2016. The Ramadan in 2017 was in June as well so it was peaking
higher than the previous year.
4.1.2. Aggregate Production Planning Data
The second data collection consists of those needed for aggregate planning
of Vinilex paint such as daily wage, number of labour, number of shift and
working hours, production cycle, unit production per one worker. There is
no hiring cost and layoff cost as the worker is bonded by contract. Also,
there is no inventory cost because the company does have own warehouse
to store its inventory. Furthermore, there is no backorder because the
finished products are sent to Jakarta local warehouses and retail shops.
Table 4. 2 .Information of Wage and Number of Labour
Shifts per day 1
Working hours/shift 8
Cycle time for 1 batch (6 tonnes) /
hour 2
Unit production per one batch 4
Worker Salary/month Rp 3,445,617
Maximum Overtime hour/day 3
0
200
400
600
800
Demand (in tonnes)
Overtime Wage of 1 hour Rp 50,000
Overtime Wage of 2 hours Rp 110,000
Overtime Wage of 3 hours Rp 180,000
Workers available pre-March 2018 10
Vinilex 25 kg Market Price Rp 450,000
The Worker Salary amount is according to UMK (Upah Minimum
Kota/Kabupaten or Region Minimum Wage) of Purwakarta which is
actually Rp 3,445,616.90 per month. There is no more than one shift per
day. The working hours per day is from 8:00 until 12:00 WIB then
continue after 1 hour lunch break from 13:00 until 17:00 WIB. The
production lead time from premixing process to packaging takes 2 hours.
The daily production of Vinilex white for Jakarta is accounted for 24
tonnes, among 200-250 tonnes daily produced for all Emulsion paint
products.
4.1.3. Lot Sizing Data
The third data collection consists of lot sizing plan of Vinilex paint such as
order cost per week and holding cost of 1 ton for inventory at warehouse.
Table 4. 3. Information of Lot Sizing Cost
Order Cost/week Rp 1,250,000
Holding Cost/1 ton Rp 11,000
4.2. Data Analysis
4.2.1. Forecasting
1. Forecasting Method Choices
There are several forecasting techniques listed on the table below. to find
the very best method, I tried those two methods which is constant method
and seasonal method. The company should calculate the MSE, MAD,
and MAPE to compare which methods is the best one and do the tracking
signal and verification to validation the method. The table below will
show the summary of the calculation of each method.
Table 4. 4. Summary of Vinilex Forecasting
Method
Vinilex
MAE MSE MAPE Tracking Signal Verification
LPD 76.17 7047.67 15.59% Valid Valid
AM 120.90 19068.20 25.42% X X
SMA’ 90.96 10355.77 18.39% Valid X
WMA 81.96 9102.97 16.66% X Valid
SES 0.9 99.03 20745.77 19.55% X Valid
Linear Regression 108.57 15985.69 22.44% X X
Deseasonal (MA 3) 653.06 538865.7 10.26% X X
Holt-Winters 91.65 3246.62 17.39% Valid Valid
Cyclic Regression” 50.23 3866.18 10.23% X X
Seasonal Index 125.36 78353.11 24.98% X X
‘= the company uses Simple Moving Average of 2 months as their
forecasting method. See Appendix I part 2 for results
“= cyclical regression with period of 11 months cycle. See Appendix I
part 7 for results
The table above shows the result of the forecast calculation of constant
and seasonal methods. After doing the validation of each method, it is
found that there are two options of forecasting techniques having passed
both validation test and verification test. The first is LPD (Last Period
Demand) method having MAE, MSE and MAPE values of 76.17,
7047.67 and 15.59% respectively. The other one is Holt-Winters (Triple
Exponential Smoothing) technique having MAE, MSE and MAPE values
of 91.65, 3246.62 and 17.39% respectively.
From the table above, LPD has less MAE and MAPE results while Holt-
Winters has less MSE than LPD.
These two methods are to be elaborated below by using tables and
graphs, then the comparison between them are to be explained later on.
Table 4. 5. Forecasting Vinilex Using LPD Method
Month Demand Forecast Error
Abs
error Square Error
Error
Proportion
Absolute Error
Proportion
Feb-16 471
Mar-16 568 471 97 97 9409 0.17 0.17
Apr-16 612 568 44 44 1936 0.07 0.07
May-16 698 612 86 86 7396 0.12 0.12
Jun-16 672 698 -26 26 676 -0.04 0.04
Jul-16 567 672 -105 105 11025 -0.19 0.19
Aug-16 456 567 -111 111 12321 -0.24 0.24
Sept-16 324 456 -132 132 17424 -0.41 0.41
Oct-16 365 324 41 41 1681 0.11 0.11
Nov-16 298 365 -67 67 4489 -0.22 0.22
Dec-16 412 298 114 114 12996 0.28 0.28
Jan-17 478 412 66 66 4356 0.14 0.14
Feb-17 564 478 86 86 7396 0.15 0.15
Mar-17 654 564 90 90 8100 0.14 0.14
Apr-17 679 654 25 25 625 0.04 0.04
May-17 753 679 74 74 5476 0.10 0.10
Jun-17 729 753 -24 24 576 -0.03 0.03
Jul-17 643 729 -86 86 7396 -0.13 0.13
Aug-17 543 643 -100 100 10000 -0.18 0.18
Sept-17 431 543 -112 112 12544 -0.26 0.26
Oct-17 456 431 25 25 625 0.05 0.05
Nov-17 378 456 -78 78 6084 -0.21 0.21
Dec-17 467 378 89 89 7921 0.19 0.19
Jan-18 453 467 -14 14 196 -0.03 0.03
Feb-18 589 453 136 136 18496 0.23 0.23
Mar-18 589 Total 1828 169144 Total 3.74
Apr-18 589
May-18 589 n MAD MSE
MAPE
24 76.16667 7047.666667 15.59149005
Table 4. 6. Forecasting Vinilex Using LPD Method (Continued)
Month Demand
RSFE
Cumulative
Absolute RSFE
Cumulative
Period
Code MAD
Tracking
Signal MRt
Feb-16 471
Mar-16 568 97 97 1 97 1
Apr-16 612 141 141 2 70.5 2.00 53
May-16 698 227 227 3 75.66667 3.00 42
Jun-16 672 201 253 4 63.25 3.18 112
Jul-16 567 96 358 5 71.6 1.34 79
Aug-16 456 -15 469 6 78.16667 -0.19 6
Sept-16 324 -147 601 7 85.85714 -1.71 21
Oct-16 365 -106 642 8 80.25 -1.32 173
Nov-16 298 -173 709 9 78.77778 -2.20 108
Dec-16 412 -59 823 10 82.3 -0.72 181
Jan-17 478 7 889 11 80.81818 0.09 48
Feb-17 564 93 975 12 81.25 1.14 20
Mar-17 654 183 1065 13 81.92308 2.23 4
Apr-17 679 208 1090 14 77.85714 2.67 65
May-17 753 282 1164 15 77.6 3.63 49
Jun-17 729 258 1188 16 74.25 3.47 98
Jul-17 643 172 1274 17 74.94118 2.30 62
Aug-17 543 72 1374 18 76.33333 0.94 14
Sept-17 431 -40 1486 19 78.21053 -0.51 12
Oct-17 456 -15 1511 20 75.55 -0.20 137
Nov-17 378 -93 1589 21 75.66667 -1.23 103
Dec-17 467 -4 1678 22 76.27273 -0.05 167
Jan-18 453 -18 1692 23 73.56522 -0.24 103
Feb-18 589 118 1828 23 79.47826 1.48 150
Total 1807
MR 78.56522
LCL 208.9835
UCL -208.983
The table above shows the result of the LPD calculation, below is the
explanation of the calculation:
LPD Forecasting (dt’) = 𝒅𝒕−𝟏
Example: Forecasting of Sep 2017 = demand of Aug 2017 = 543 tonnes
Error = (dt– dt’)
Example : Error of Mar 2016 = ( d2 – d2’ ) = 568 – 471 = 97
Absolute Error = absolute (dt– dt’)
Example: Absolute error of Mar 2016 = absolute(d2 – d2’)
= absolute (568 – 471) = 97
Square error = (dt– dt’)2
Example : Square error of Mar 2016 = (568 – 471)2 = (97)
2 = 9409
Error Proportion = ((dt– dt’)/dt)*100%
Example: Error Proportion of Mar 2016 = ((568 – 471)/ 568)*100%
= 0.17* 100% = 17%
MRt = |((dt’ – dt) – (dt-1’ – dt-1))|
Example: MR4 = |(612 – 568) – (568 – 471)| = | 44 – 97 | = 53
RSFE Cummulative = (dt– dt’) +(dt-1 – dt-1’)
Example: RSFE Cum Apr 2016 = (612 – 568) + (568 – 471) = 44 + 97 =
141
MAD = absolute (RSFE Cummulative) / n
Example : MAD of Apr 2016 = 141/2 = 70.5
Tracking Signal = RSFE Cumulative / MAD
Example: Tracking Signal of Apr 2016 = 141/70.5 = 2.0
After Calculating all this on that table, the company measure the error of
forecasting with MAE, MSE and MAPE of Single Exponential
Smoothing.
MAE = ∑ |𝑑𝑡−𝑑𝑡′|𝑛
𝑡=1
𝑛
MAE = 1828
34 = 76.17
MSE = ∑ (𝑑𝑡−𝑑𝑡′)
2𝑛𝑡=1
𝑛
MSE = 169144
24 = 7,047.67
MAPE = ∑ |𝑃𝐸𝑡|𝑛
𝑡=1
𝑛 with PEt as Absolute error proportion, the result in
percentage
MAPE = 3740%
24 = 15.59%
After the forecast error is found, it is necessary to check whether the
method is valid or invalid by using the verification method and tracking
signal method. For trying the tracking signal and verification method, I
should find the Upper Control Limit and the lower control limit. For the
tracking signal, it is decided to be 4 for the UCL and -4 for the LCL, and
for the verification method, it is found that the limit is like on the table
below:
Table 4. 7. Control Limit For Verification of LPD Method
UCL LCL
1 208.98 -208.98
2/3 139.32 -139.32
1/3 69.66 -69.66
To verify that the method is valid, a graph is made to show whether the
limit is still in control or out of control, the graph is shown below:
Figure 4. 2. Actual Demand vs Forecast Demand of LPD
Figure 4. 3. Tracking Signal Test of LPD Method
Figure 4. 4. Verification Test of LPD Method
0
200
400
600
800
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Actual Demand vs Forecasting Vinilex (LPD)
Actual Demand Forecast Demand
-6
-4
-2
0
2
4
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Tracking Signal Test Vinilex (LPD)
LPD
UCL
LCL
-300
-200
-100
0
100
200
300
Period
Verification Test Vinilex (LPD)
Series1
UCL
Series3
Series4
1/3 LCL
Series6
Series7
The graphics above, both in the tracking signal and verification prove that
the result is still in control. The forecast result of the next three months is:
Table 4. 8. Forecast Demand of LPD
Month Forecast Demand (Tonnes)
March 589
April 589
May 589
The next one to be explained is Holt-Winters Method below.
Table 4. 9. Forecast Result by Holt-Winters Method
Month Demand Level Trend Seasonal Forecast Error
Abs
error
Square
Error
Feb-16 471 0.86
Mar-16 568 1.03
Apr-16 612 550.33333 1 1.11
May-16 698 789.14 119.91 1.09 471.8558 226.14 226.14 51141.18
Jun-16 672 676.89 3.83 1.08 938.2326 -266.23 266.23 70879.82
Jul-16 567 526.95 -73.06 1.08 756.9982 -190.00 190.00 36099.31
Aug-16 456 422.15 -88.93 1.08 494.4284 -38.43 38.43 1476.74
Sept-16 324 303.41
-
103.83 1.08
359.7531 -35.75 35.75 1278.28
Oct-16 365 324.33 -41.46 1.08 215.3987 149.60 149.60 22380.54
Nov-16 298 276.76 -44.51 1.08 305.3204 -7.32 7.32 53.59
Dec-16 412 367.13 22.93 1.09 250.4214 161.58 161.58 26107.64
Jan-17 478 436.26 46.03 1.09 422.4009 55.60 55.60 3091.26
Feb-17 564 517.22 63.50 1.09 521.9865 42.01 42.01 1765.13
Mar-17 654 599.91 73.09 1.09 630.8401 23.16 23.16 536.38
Apr-17 679 629.36 51.27 1.09 731.7138 -52.71 52.71 2778.75
May-17 753 691.20 56.55 1.09 740.235 12.76 12.76 162.95
Jun-17 729 677.90 21.63 1.09 813.425 -84.43 84.43 7127.59
Jul-17 643 602.37 -26.95 1.08 760.3463 -117.35 117.35 13770.16
Aug-17 543 507.05 -61.13 1.08 625.5825 -82.58 82.58 6819.87
Sept-17 431 401.77 -83.21 1.08 484.268 -53.27 53.27 2837.48
Oct-17 456 410.40 -37.29 1.08 345.3737 110.63 110.63 12238.17
Nov-17 378 351.49 -48.10 1.08 404.0169 -26.02 26.02 676.88
Dec-17 467 418.85 9.63 1.09 328.2117 138.79 138.79 19262.19
Jan-18 453 418.70 4.74 1.09 464.7951 -11.80 11.80 139.12
Feb-18 589 531.45 58.75 1.09 458.9241 130.08 130.08 16919.73
Mar-18
641.5 Total 2016.23 297542.78
Apr-18
705.03 n MAD MSE
May-18
770.40 22 91.65 3246.62
Table 4. 10. Forecast Result by Holt-Winters Method (Continued)
Month
Error
Proportion
Absolute Error
Proportion
RSFE
Cumulative
Absolute RSFE
Cumulative MAD Tracking Signal MRt
Feb-16
Mar-16
Apr-16
May-16 0.32 0.32 226.14 226.14 226.1442 1
Jun-16 -0.40 0.40 -40.09 492.38 246.1884 -0.16 492.3768
Jul-16 -0.34 0.34 -230.09 682.38 227.4583 -1.01 76.23445
Aug-16 -0.08 0.08 -268.52 720.80 180.2008 -1.49 151.5698
Sept-16 -0.11 0.11 -304.27 756.56 151.3113 -2.01 2.675306
Oct-16 0.41 0.41 -154.67 906.16 151.0263 -1.02 185.3543
Nov-16 -0.02 0.02 -161.99 913.48 130.4969 -1.24 156.9217
Dec-16 0.39 0.39 -0.41 1075.06 134.3821 0.00 168.899
Jan-17 0.12 0.12 55.19 1130.66 125.6284 0.44 105.9795
Feb-17 0.07 0.07 97.20 1172.67 117.2669 0.83 13.58558
Mar-17 0.04 0.04 120.36 1195.83 108.7117 1.11 18.85356
Apr-17 -0.08 0.08 67.65 1248.54 104.0453 0.65 75.87375
May-17 0.02 0.02 80.41 1261.31 105.109 0.77 65.47883
Jun-17 -0.12 0.12 -4.01 1345.73 112.1444 -0.04 97.19004
Jul-17 -0.18 0.18 -121.36 1463.08 121.9233 -1.00 32.92129
Aug-17 -0.15 0.15 -203.94 1545.66 128.8052 -1.58 34.76381
Sept-17 -0.12 0.12 -257.21 1598.93 133.2442 -1.93 29.3145
Oct-17 0.24 0.24 -146.58 1709.56 142.463 -1.03 163.8943
Nov-17 -0.07 0.07 -172.60 1735.57 144.6311 -1.19 136.6432
Dec-17 0.30 0.30 -33.81 1874.36 156.1968 -0.22 164.8052
Jan-18 -0.03 0.03 -45.60 1886.16 157.1797 -0.29 150.5834
Feb-18 0.22 0.22 84.47 2016.23 168.0194 0.50 141.871
Total 3.83
Total 2465.789
MAPE
MR 117.4185
17.39
UCL 312.3333
LCL -312.333
The table above shows the result of Holt-Winters calculation, below is the
explanation of the calculation:
Holt-Winters Forecast = 𝑦𝑡 = (𝑏1 + 𝑏2𝑡)𝑆𝑡
Example: Forecasting of January 2017 = {367.13+(22.93)} 1.08 = 422.4
tonnes
Error = (dt– dt’)
Example : Error of January 2017 = 478 – 422.4 = 55.6
Absolute Error = absolute (dt– dt’)
Example: Absolute error of January 2017 = absolute(478 – 422.4) = 55.6
Square error = (dt– dt’)2
Example : Square error of January 2017 = (55.6)2 = 3,091.26
Abs Error Proportion = |((dt– dt’)/dt)*100% |
Example: Error Proportion of January 2017 = |((478 – 422.4)/478)*100% |
= | 0.12* 100%} = 12%
MAE = ∑ |𝑑𝑡−𝑑𝑡′|𝑛
𝑡=1
𝑛
MAE = 944.58
22 = 78.72
MSE = ∑ (𝑑𝑡−𝑑𝑡′)
2𝑛𝑡=1
𝑛
MSE = 297542.78
22 = 3,246.62
MAPE = ∑ |𝑃𝐸𝑡|𝑛
𝑡=1
𝑛 with PEt as Absolute error proportion, the result in
percentage
MAPE = 383%
22 = 17.39%
MRt = |((dt’ – dt) – (dt-1’ – dt-1))|
Example: MR12 = |55.6– 161.58|| = 105.98
RSFE Cummulative = (dt– dt’) +(dt-1 – dt-1’)
Example: RSFE Cum January 2017 = 55.6 + 161.58 = 217.18
MAD = absolute (RSFE Cummulative) / n
Example : MAD of January 2017 = 1130.66/9= 125.63
Tracking Signal = RSFE Cumulative / MAD
Example: Tracking Signal of January 2017 = 55.19/125.63 = 0.44
After the forecast error is found, it is necessary to check whether the
method is valid or invalid by using the verification method and tracking
signal method For trying the tracking signal and verification method, I
should find the Upper Control Limit and the lower control limit. For the
tracking signal, it is decided to be 4 for the UCL and -4 for the LCL, and
for the verification method, it is found that the limit is like on the table
below:
Table 4. 11. Control Limit Results of Holt-Winters Method
UCL LCL
1 312.33 -312.33
2/3 208.22 -208.22
1/3 104.11 -104.11
Figure 4. 5. Actual Demand vs Forecast Demand of Holt-Winters Method
0
500
1000
Feb
-16
Mar
-16
Ap
r-16
Mei
-16
Jun
-16
Jul-
16
Agu
st-…
Sep
-16
Okt
-16
No
p-1
6
Des
-16
Jan
-17
Feb
-17
Mar
-17
Ap
r-17
Mei
-17
Jun
-17
Jul-
17
Agu
st-…
Sep
-17
Okt
-17
No
p-1
7
Des
-17
Jan
-18
Feb
-18
Actual vs Forecast Demand Vinilex (HW)
Series1 Series2
Figure 4. 6. Tracking Signal Test of Holt-Winters Method
Figure 4. 7. Verification Test of Holt-Winters Method
The graphics above, both in the tracking signal and verification prove that
the result is still in control. The forecast result of the next three months is:
Table 4. 12. Forecast Demand of Holt-Winters Method
Month Forecast Demand
(Tonnes)
March 641.50
April 705.03
May 770.40
-6
-4
-2
0
2
4
6
Tracking Signal Test Vinilex (HW)
Series1
Series2
Series3
-400.00
-300.00
-200.00
-100.00
0.00
100.00
200.00
300.00
400.00
Jun
-16
Jul-
16
Agu
st-1
6
Sep
-16
Okt
-16
No
p-1
6
Des
-16
Jan
-17
Feb
-17
Mar
-17
Ap
r-17
Me
i-1
7
Jun
-17
Jul-
17
M
R
t
Month
Verification Test Vinilex (HW)
HW
UCL
2/3 UCL
1/3 UCL
1/3 LCL
2/3 LCL
LCL
The comparison between Actual Demand vs Forecast Demand referring to
Figure 4.2 (LPD) and Figure 4.5 (Holt-Winters) is obvious. On Figure 4.2,
LPD method of determining forecast demand using previous month tends
to lagging behind the actual demand. On the other hand, the forecasted
demand by Holt-Winters method on some months, i.e. June 2016 and June
2017 which are the peaks, displayed the forecasted demands were more
than actual demand to follow up seasonal pattern.
For the comparison between Forecasted Demand based on Table 4.8
(LPD) and Table 4.10 (Holt-Winters), LPD method results of the
upcoming 3 months are the same using the previous month demand which
is February 2018 demand. The upcoming 3 months demands are constant
because in April and May 2018, the demand of March and April 2018
(previous months respectively) is unknown. Meanwhile, Holt-Winters
method can forecast demand ahead by using Seasonal Index since this
method is seasonal instead of constant method like LPD.
Even though these descriptions of Forecasted Demand vs Actual Demand
and Forecasted Demand results of 3 months ahead show some different
points, it is necessary to undergo 3 type of sample testings to choose the
final method. These 3 testings are Normality test, T-test and
Autocorrelation test.
2. Normality Test
This test is to determine whether the data of absolute error residues are
normally distributed or not. For this research, I am going to use
Kolmogorov-Smirnov Test. The LPD method result is first then followed
by HW method.
Table 4. 13. Normality Test Table for LPD Method
Month
Abs
error Proportion of (Absolute) Error Cumulative Error Z-score F(x) Difference
Feb-16
Mar-16 97 0.05 0.05 0.5777 0.7183 0.6652
Apr-16 44 0.02 0.08 -0.8920 0.1862 0.1621
May-16 86 0.05 0.12 0.2727 0.6074 0.5604
Jun-16 26 0.01 0.14 -1.3911 0.0821 0.0679
Jul-16 105 0.06 0.20 0.7995 0.7880 0.7306
Aug-16 111 0.06 0.26 0.9659 0.8330 0.7722
Sept-16 132 0.07 0.33 1.5482 0.9392 0.8670
Oct-16 41 0.02 0.35 -0.9752 0.1647 0.1423
Nov-16 67 0.04 0.39 -0.2542 0.3997 0.3630
Dec-16 114 0.06 0.45 1.0491 0.8529 0.7906
Jan-17 66 0.04 0.49 -0.2819 0.3890 0.3529
Feb-17 86 0.05 0.53 0.2727 0.6074 0.5604
Mar-17 90 0.05 0.58 0.3836 0.6494 0.6001
Apr-17 25 0.01 0.60 -1.4188 0.0780 0.0643
May-17 74 0.04 0.64 -0.0601 0.4760 0.4356
Jun-17 24 0.01 0.65 -1.4466 0.0740 0.0609
Jul-17 86 0.05 0.70 0.2727 0.6074 0.5604
Aug-17 100 0.05 0.75 0.6609 0.7457 0.6910
Sept-17 112 0.06 0.81 0.9936 0.8398 0.7785
Oct-17 25 0.01 0.83 -1.4188 0.0780 0.0643
Nov-17 78 0.04 0.87 0.0508 0.5203 0.4776
Dec-17 89 0.05 0.92 0.3559 0.6390 0.5903
Jan-18 14 0.01 0.93 -1.7239 0.0424 0.0347
Feb-18 136 0.07 1 1.6592 0.9515 0.8771
Total 1828 1
Table 4. 14. Normality Test Result of LPD Method
Mean 76.17
Mean-sq 5801.36
sq-sum/n 7047.67
VarP 1246.31
Var 1300.49
Standard Deviation 36.06
Standard Error 7.36
Dn=max 0.88
Dn,alpha 0.28
Fit for Normal
Distribution? No
The table above shows the result of normality test of LPD, below is the
explanation of the calculation:
Proportion of Absolute Error = Absolute Error of dt / Total of
Absolute Error
Example: Proportion of Absolute Error on Mar 2016 = 97 / 1828 = 0.05
Cumulative Error = Sum of Proportion of Absolute Error until dt
Example : Cumulative Error of Apr 2016 = 0.053 + 0.024 = 0.077
Mean = MAE/MAD
Mean = MAE of LPD method = 76.17
Mean-sq = Mean2
Mean-sq of LPD = 76.172 = 5801.36
VarP = (error sq-sum/n} – Mean-sq
VarP of LPD = (169,144 / 24) – 5801.36 = 1,246.31
Var = VarP*n/(n – 1)
Var of LPD = 1,246.31*24 / (24 – 1) = 1,300.49
Standard Deviation = √𝑉𝑎𝑟
Standard Deviation of LPD = √1300.49 = 36.06
Standard Error = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 √𝑛⁄
Standard Error of LPD = 36.06 √24⁄ = 7.36
Z-score of dt = STANDARDIZE(absolute error of dt; mean; standard
deviation)
Using Excel formula
Example: Z-score of Mar 2016 = STANDARDIZE(97; 76.17; 36.06) =
0.5777
F(x) of dt = using Excel formula =NORMSDIST(Z-score of dt)
Example: F(x) of Mar 2016 = NORMSDIST(0,5777) = 0.7183
Difference of dt = F(x) of dt – Proportion of Absolute Error of dt
Example: Difference of Mar 2016 = 0.7183 – 0.053 = 0.6652
Dn=max = Max of Difference value
Dn=max of LPD = 0.8771 -> 0.88
Dn,alpha = 1.36 √𝑛⁄
Dn,alpha of LPD = 1.36 √24⁄ = 0.28
If Dn=max < Dn;alpha, then the data is normally distributed. However, as
Dn,alpha > Dn=max, the data is not normally distributed.
Then, the Holt-Winters is going to be tested.
Table 4. 15. Normality Test Table for Holt-Winters Method
Month Abs error
Proportion
of
(Absolute)
Error
Cumulative
Error Z-score F(x) Difference
Feb-16
Mar-16
Apr-16
May-16 226.14 0.11 0.11 1.83545188 0.96678062 0.85
Jun-16 266.23 0.13 0.24 2.3825301 0.99140294 0.859358315
Jul-16 190.00 0.09 0.34 1.34217652 0.91023062 0.815996344
Aug-16 38.43 0.02 0.36 -0.7262609 0.23383941 0.214779908
Sept-16 35.75 0.02 0.38 -0.7627702 0.22280022 0.205067609
Oct-16 149.60 0.07 0.45 0.79088904 0.78549563 0.71129721
Nov-16 7.32 0.00 0.45 -1.1507838 0.12491059 0.121279842
Dec-16 161.58 0.08 0.53 0.95434084 0.83004443 0.749905561
Jan-17 55.60 0.03 0.56 -0.4919368 0.31138201 0.283806296
Feb-17 42.01 0.02 0.58 -0.677336 0.24909641 0.22825879
Mar-17 23.16 0.01 0.59 -0.934626 0.17499053 0.163503797
Apr-17 52.71 0.03 0.62 -0.5313108 0.2976017 0.271456983
May-17 12.76 0.01 0.63 -1.0764831 0.14085563 0.134524516
Jun-17 84.43 0.04 0.67 -0.0985553 0.46074566 0.418872988
Jul-17 117.35 0.06 0.73 0.35071375 0.63709845 0.578897648
Aug-17 82.58 0.04 0.77 -0.1236997 0.45077653 0.409817694
Sept-17 53.27 0.03 0.79 -0.5237477 0.300227 0.273807412
Oct-17 110.63 0.05 0.85 0.25900661 0.60218493 0.547317112
Nov-17 26.02 0.01 0.86 -0.8956372 0.18522327 0.172319539
Dec-17 138.79 0.07 0.93 0.64332718 0.73999409 0.671158622
Jan-18 11.80 0.01 0.94 -1.0897188 0.13791851 0.132068435
Feb-18 130.08 0.06 1 0.52443062 0.70001047 0.635496146
Total 2016.23 1
Table 4. 16. Normality Test Result of HW Method
Mean 91.65
Mean-sq 8399.16
sq-sum/n 13524.67
VarP 5125.51
Var 5369.58
Standard Deviation 73.28
Standard Error 15.62
Dn=max 0.86
Dn,alpha 0.29
Fit for Normal
Distribution? No
The table above shows the result of normality test of Holt-Winters, below
is the explanation of the calculation:
Proportion of Absolute Error = Absolute Error of dt / Total of
Absolute Error
Example: Proportion of Absolute Error on Mar 2016 = 226.14 / 2016.23 =
0.11
Cumulative Error = Sum of Proportion of Absolute Error until dt
Example : Cumulative Error of Apr 2016 = 0.13 + 0.11 = 0.24
Mean = MAE/MAD
Mean = MAE of LPD method = 91.65
Mean-sq = Mean2
Mean-sq of LPD = 91.652 = 8,399.16
VarP = (error sq-sum/n} – Mean-sq
VarP of LPD = (297,542.78 / 22) – 8,399.16 = 5,125.51
Var = VarP*n/(n – 1)
Var of LPD = 5,125.51*22 / (22 – 1) = 5,369.58
Standard Deviation = √𝑉𝑎𝑟
Standard Deviation of LPD = √5,369.58 = 73.28
Standard Error = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 √𝑛⁄
Standard Error of LPD = 73.28 √22⁄ = 15.62
Z-score of dt = STANDARDIZE(absolute error of dt; mean; standard
deviation)
Using Excel formula
Example: Z-score of Mar 2016 = STANDARDIZE(226.14; 91.65; 15.62)
= 1.835
F(x) of dt = using Excel formula =NORMSDIST(Z-score of dt)
Example: F(x) of Mar 2016 = NORMSDIST(1.835) = 0.967
Difference of dt = F(x) of dt – Proportion of Absolute Error of dt
Example: Difference of Mar 2016 = 0.967 – 0.11 = 0.855
Dn=max = Max of Difference value
Dn=max of LPD = 0.855 -> 0.86
Dn,alpha = 1.36 √𝑛⁄
Dn,alpha of LPD = 1.36 √22⁄ = 0.29
If Dn=max < Dn;alpha, then the data is normally distributed. However, as
Dn,alpha > Dn=max, the data is not normally distributed.
To conclude, both LPD and Holt-Winters methods do not have normally
distributed absolute error data.
3. T- Test (Partial Test)
This test is to determine whether independent variable individually affects
the forecast. Let’s start with LPD then followed by Holt-Winters.
Table 4. 17. T-test Result of LPD Method
T-test
Hyp Mean 0
Alpha 0.05
Tails 1
df 23
t stat 10.3470513
p value 2.00025E-10
t critical 2.06865761
Significant? Yes
The table above shows the result of T-test of LPD, below is the
explanation of the calculation: (Note than Hyp Mean, Alpha and Tails are
given values)
Df: n – 1
Df = 22 – 1 = 21
T-stat value = (Mean or MAE – Hyp Mean) / Standard Error
T-stat value = (76.17 – 0)/7.36 = 10.347
P value = use Excel formula =TDIST(ABS(T-stat value);df;Tails)
P value = TDIST(10.347;21;1) = 2E - 10
T critical value = use Excel formula =TINV(alpha;df)
T critical value = TINV(0.05;21) = 2.06865
If p value < alpha, then the data is significant. As p value is lower than
alpha, then LPD is significant by T-test. Then, continuing to Holt-Winters
Method
Table 4. 18. T-test Result of Holt-Winters Method
T-test
Hyp Mean 0
Alpha 0.05
Tails 1
df 21
t stat 5.866227919
p value 4.00489E-06
t critical 2.079613845
Significant? Yes
The table above shows the result of T-test of Holt-Winters, below is the
explanation of the calculation: (Note than Hyp Mean, Alpha and Tails are
given values)
Df: n – 1
Df = 22 – 1 = 21
T-stat value = (Mean or MAE – Hyp Mean) / Standard Error
T-stat value = (91.65 – 0)/15.62 = 5.866
P value = use Excel formula =TDIST(ABS(T-stat value);df;Tails)
P value = TDIST(5.866;21;1) = 4.0049E - 06
T critical value = use Excel formula =TINV(alpha;df)
T critical value = TINV(0.05;21) = 2.0796
If p value < alpha, then the data is significant. As p value is lower than
alpha, then Holt-Winters is significant by T-test.
To conclude, both LPD and Holt-Winters methods have significant result
of T-test.
4. Autocorrelation Test
This test is to determine whether the absolute error in this forecasting
model has correlation between them. The d-lower and d-upper values are
known to be 1.045 and 1.35 respectively.
Table 4. 19. Autocorrelation Test Result of LPD Method
Autocorrelation
d 1.251590361
d-lower* 1.045
d-upper* 1.35
Significant? Unclear
d value = use Excel formula =SUMXMY2(Array of Error from
Mar2016 to Jan 2018;array of Error from Apr2016 to Feb
2018)/SUMSQ(array of Error whole)
d value of LPD = 1.2516
If d value < d-lower, then the data has significant autocorrelation. If d-
value > d-upper value, the data does not have significant autocorrelation.
Otherwise if d-value is between d-lower and d-upper value, the
significance of autocorrelation is unclear. As d value is above d-lower
and below d-upper, the LPD has unclear autocorrelation. Let’s continue
with Holt-Winters one.
Table 4. 20. Autocorrelation Test Result of Holt-Winters Method
Autocorrelation
d 0.54853199
d-lower* 1.045
d-upper* 1.35
Significant? Yes
d value = use Excel formula =SUMXMY2(Array of Error from
Mar2016 to Jan 2018;array of Error from Apr2016 to Feb
2018)/SUMSQ(array of Error whole)
d value of Holt-Winters = 0.5485
If d value < d-lower, then the data has significant autocorrelation. If d-
value > d-upper value, the data does not have significant autocorrelation.
Otherwise if d-value is between d-lower and d-upper value, the
significance of autocorrelation is unclear. As d value is below d-lower
value, the Holt-Winters has significant autocorrelation.
Therefore, the better choice of forecasting method is Holt-Winters.
4.2.2. Aggregate Planning
There are several conditions to find out which one has the least cost for
aggregate production planning: 10 workers only in March 2018, 10
workers in both March and April 2018, Chase strategy, Level strategy
and Hybrid strategy. The forecasted demands for this analysis are based
on the previous forecasted method analysis which passed the criteria,
none other than Holt-Winter method results. The table below is the
comparison between results of each condition:
Table 4. 21. Results of Each Aggregate Production Planning Method
Number of
Labour
(Mar/Apr/May)
10 Workers 10/10/11 10/11/11 10/11/12 10/12/12 10/12/13
Labour Cost Rp 103,368,510 Rp 106,814,127 Rp 110,259,744 Rp 113,705,361 Rp 117,150,978 Rp 120,596,595
Overtime Cost Rp 96,900,000 Rp 100,500,000 Rp 88,110,000 Rp 91,710,000 Rp 77,220,000 Rp 79,420,000
Total Cost Rp 200,268,510 Rp 207,314,127 Rp 198,369,744 Rp 205,415,361 Rp 194,370,978 Rp 200,016,595
Max Overtime
Hours in a
Month
3 (Both April and
May)
3 (Both April
and May) 3 (only May) 3 (only May)
2 (Both April and
May)
2 (Both April
and May)
Production Left
by End of May -24 tonnes 46 tonnes 4 tonnes 74 tonnes 17 tonnes 77 tonnes
Under
production /
Over
production
Under production Over production Over production Over production Over production Over production
Production
Target Not Achieved Not Achieved Achieved Not Achieved Achieved Not Achieved
The calculations of Labour Cost, Overtime Cost, Total Cost, Maximum Overtime, Production Left are explained later. The production
target is determined whether the ending inventory in May 2018 has some products left (positive) or underproduction (negative).
Table 4. 22. Results of Each Aggregate Production Planning Method (Continued)
Number of
Labour
(Mar/Apr/May)
10/12/14 10/13/13 10/13/14 10/14/14 10/13/15 10/14/15
Labour Cost Rp 124,042,212 Rp 124,042,212 Rp 127,487,829 Rp 130,933,446 Rp 130,933,446 Rp 134,379,063
Overtime Cost Rp 81,620,000 Rp 66,130,000 Rp 67,130,000 Rp 68,600,000 Rp 68,130,000 Rp 52,800,000
Total Cost Rp 205,662,212 Rp 190,172,212 Rp 194,617,829 Rp 199,533,446 Rp 199,063,446 Rp 187,179,063
Max Overtime
Hours in a
Month
2 (Both April and
May) 2 (only April) 2 (only April) 2 (only May) 2 (only April)
1 (Both April
and May)
Production Left
by End of May 137 tonnes 10 tonnes 60 tonnes 116 tonnes 110 tonnes 26 tonnes
Under
production /
Over production
Over production Over production Over production Over production Over production Over production
Production
Target Not Achieved Achieved Not Achieved Not Achieved Not Achieved Achieved
Table 4. 23. Results of Each Aggregate Production Planning Method (Continued)
Number of
Labour
(Mar/Apr/May)
10/15/17 10/17/17 10/17/19
(Chase)
Labour Cost Rp 144,715,914 Rp 151,607,148 Rp 158,498,382
Overtime Cost Rp 38,850,000 Rp 40,100,000 Rp 23,100,000
Total Cost Rp 183,565,914 Rp 191,707,148 Rp 181,598,382
Max Overtime
Hours in a
Month
1 (in April) 1 (in May) 0
Production Left
by End of May 8.5 tonnes 105 tonnes 15 tonnes
Under
production /
Over
production
Over production Over production Over production
Production
Target Achieved Not Achieved Achieved
From the results above, the Chase Strategy with number workers in March, April
and May period are 10, 17 and 19 workers respectively have the least costly among
all conditions. Another thing to consider is by using 10,17 and 18 workers (Hybrid)
in March, April and May respectively, the inventory left is the highest in amount
among all the scenarios, even though a bit more cost than the Chase strategy, hence
yielding the most possible net profit. Therefore, if the company opts to maximise net
profit, the Hybrid Strategy of 10/17/18 number of workers is chosen. The result table
is shown below:
Table 4. 24. Chase Strategy Workers Aggregate Planning
Month March 2018 April 2018 May 2018 Total
Period 1 2 3
Forecast 641.5 705.03 770.4
Forecast (Rounded) 642 706 771
Beginning Inventory 30 18 26
Ending Inventory 0 0 0
Forecast Needed 612 688 745 2045
Working Days 21 21 20 62
Working Shifts 21 21 20
Workers Needed 10 16.38 18.62
Workers Used 10 17 19
Change in Workforce 0 7 2
Workers' Wage Rp34,456,170 Rp58,575,489 Rp65,466,723 Rp158,498,382
Actual Production 420 714 760
Inventory Left Before Overtime -192 26 15
Amount Needed to be Produced Overtime 192 0 0
Overtime Days 4.8 0 0
Overtime hr/day 1.828571429 0 0
Overtime hr/day (Rounded) 2 0 1
Overtime Production 210 0 0
Overtime Salary Rp23,100,000 Rp0 Rp0 Rp23,100,000
Inventory Left After Overtime 18 26 15
Net Inventory 18 26 15
Inventory Holding Cost Rp0 Rp0 Rp0 Rp0
Total Cost Rp57,556,170 Rp58,575,489 Rp65,466,723 Rp181,598,382
Figure 4. 8. Workforce Change of Hybrid 10/17/18 Workers
0
2
4
6
8
March 2018 Apr-18 May 2018
Ch
ange
in
Wo
rkfo
ece
Period
Workforce Change over Period
Figure 4. 9. Net Inventory of Hybrid 10/17/18 Workers
The results of calculation from Hybrid 10/17/18 Workers are shown below:
Beginning Inventory = Inventory from previous month
Example: BI of April 2018 = Net Inventory of March 2018 = 18 tonnes
Forecast Needed = Forecast (Rounded) – Beginning Inventory
Example: FN of March 2018 = 642 – 30 = 612 tonnes
Working Days = Based on Indonesian National Calendar of Year 2018
Working Shifts = Working Days/Month * Number of Shifts/Day
Example: WS of March 2018 = 21 * 1 = 21 Shifts/Day
Workers’ Wage = Number of Workers * UMK (Monthly Salary)
Example: WW of March 2018 = 10 * Rp 3,445,617 = Rp 34,456,170
Actual Production = Number of Workers * Working Days * Unit
production/worker
Example: AP of April 2018 = 17 worker * 21 * 2 tonnes/worker = 714 tonnes
Inventory Left before Overtime = Actual Production – Forecast Needed
Example: ILBO of April 2018 = 714 – 688 = 26 tonnes
Amount Needed to be Produced Overtime = abs(ILBO) if ILBO is negative
Example: ANPO of May 2018 = abs(-25) = 25 tonnes, means need to produce 25
tonnes more if ILBO is negative
Overtime Days = ANPO / (Number of Workers * unit batch production)
Example: OD of March 2018 = 192 / (10*4) = 4.8 days
Overtime Hours/Day = Overtime Days * 8 / Working Days
0
10
20
30
March 2018 Apr-18 May 2018
U
n
i
t
s
Period
Net Inventory in relation to Production per day by each worker
Series2
Example: OH/D of March 2018 = 4.8 * 8 / 21 = 1.8 hours / day -> 2 hours/day
rounded
Overtime Production = OH/D (Rounded) / OH/D * ANPO
Example: OP of March 2018 = 2 / 1.8 * 192 = 210 tonnes
Overtime Salary = Working Days * Number of Workers * Overtime Salary
Example: OS of March 2018 = 21 * 10 * Rp 110,000 = Rp 23,100,000
Net Inventory = Inventory Left Before/After Overtime = AP + OP – FN
Example: NI of March 2018 = 420 + 210 – 612 = 18 tonnes
To describe Figure 4.8 and Figure 4.9 respectively, Figure 4.8 consists of the number
of workforce change per period while Figure 4.9 consists of net inventory over period.
The workforce change per period has been increasing by 7 workers in April then 2
additional workers in May, reinforcing Chase strategy. For the net inventory, there
were 18 tonnes of inventory left in March after overtime, while 26 tonnes and 15
tonnes in April and May respectively are caused by overproduction without overtime
by increasing number of labour.
4.2.3. Lot Sizing
After aggregate production planning analysis, the lot sizing is to be determined for
inventory management. The net requirement of weekly demand is based on the
previous result of aggregate production planning by using Chase strategy.
Table 4. 25. Net Requirement Over Weekly Period
Period Date Number of
Holiday
Number of
Working Days Net Requirement
1 1-2 March 0 2 57
2 5 – 9 March 0 5 146
3 12 – 16 March 0 5 146
4 19 – 23 March 0 5 146
5 26 – 30 March 1 4 117
6 2 – 6 April 0 5 164
7 9 – 13 April 0 5 164
8 16 – 20 April 0 5 164
9 23 – 27 April 0 5 164
10 30 April – 4 May 1 4 144
11 7 – 11 May 1 4 149
12 14 – 18 May 0 5 186
13 21 – 25 May 0 5 186
14 28 – 31 May 1 3 112
There are several methods for lot sizing: Lot for lot, EOQ (Economic Order Quantity),
Least Unit Cost, Least Total Cost, Silver Meal and Wagner Within. The summary of
results by each method is below:
Table 4. 26. Lot Sizing Method Choices
Method Cost
Lot for Lot Rp 16,250,000
Economic Order Quantity Rp 20,980,000
Least Unit Cost Rp 16,250,000
Least Total Cost Rp 16,232,000
Silver Meal Rp 16,232,000
Wagner Within Rp 16,232,000
From the list of methods above, 3 methods bear the least cost of lot sizing: Least
Total Cost, Silver Meal and Wagner Within with cost of Rp 16,232,000 for entire 3
months period. The researcher will choose Silver Meal method to solve the lot sizing
problem in Nippon Paint warehouse. The calculation is explained below with the
tables representing Silver Meal method:
Table 4. 27. Silver Meal Approach for Vinilex
Period Net
Requirement
Trial Period Trial Lot
Size
Cumulative
Cost
Cost Per Period
(CC/Num of
TPC)
(t) (Dt) Combined (Cum. Net) (IDR) (IDR)
1 146 1 146 1,250,000 1,250,000*
2 146 1,2 292 2,856,000’ 1,428,000”
Choose period 1 because cost per period minimum
2 146 2 146 1,250,000 1,250,000
3 146 2,3 292 2,856,000 1,428,000
Choose period 2 because cost per period minimum
3 146 3 146 1,250,000 1,250,000
4 117 3,4 263 2,537,000 1,268,500
Choose period 3 because cost per period minimum
4 117 4 117 1,250,000 1,250,000
5 164 4,5 281 3,054,000 1,527,000
Choose period 4 because cost per period minimum
5 164 5 164 1,250,000 1,250,000
6 164 5,6 328 3,054,000 1,527,000
Choose period 5 because cost per period minimum
6 164 6 164 1,250,000 1,250,000
7 164 6,7 328 3,054,000 1,527,000
Choose period 6 because cost per period minimum
7 164 7 164 1,250,000 1,250,000
8 164 7,8 328 3,054,000 1,527,000
Choose period 7 because cost per period minimum
8 164 8 164 1,250,000 1,250,000
9 144 8,9 308 2,834,000 1,417,000
Choose period 8 because cost per period minimum
9 144 9 144 1,250,000 1,250,000
10 149 9,10 293 2,889,000 1,444,500
Choose period 9 because cost per period minimum
10 149 10 149 1,250,000 1,250,000
11 186 10,11 335 3,296,000 1,648,000
Choose period 10 because cost per period minimum
11 186 11 186 1,250,000 1,250,000
12 186 11,12 372 3,296,000 1,648,000
Choose period 11 because cost per period minimum
12 186 12 186 1,250,000 1,250,000
13 112 12,13 298 2,482,000 1,241,000
Combine period 12 and 13 because cost per period minimum
Cost per Period = Cumulative Cost / Number of Periods Combined
Where:
* = Cumulative Cost / Number of Period = 1,250,000 / 1 = 1,250,000
“ = Cumulative Cost / Number of Period = 2,856,000 / 2 = 1,428,000
‘ = Cumulative Cost = Order Cost + Holding Cost of t+1
= 1,250,000 + 146*11,000 = 2,856,000
From the Table 4.28 above, it means that ordering is necessary in most of the
periods (12 weeks) then the inventory is 112 units
Table 4. 28. Silver Meal Approach Net Requirement
Week Net Requirement Lot Sizing Inventory
1 146 146 0
2 146 146 0
3 146 146 0
4 117 117 0
5 164 164 0
6 164 164 0
7 164 164 0
8 164 164 0
9 144 144 0
10 149 149 0
11 186 186 0
12 186 298 112
13 112 0 0
Ordering Cost: 12 order x IDR 1,250,000/ order = IDR 15,000,000
Holding Cost : 112 tons x IDR 11,000/ton = IDR 1,232,000
Total Cost = IDR 16,232,000
The result by using the Silver Meal method is the company should order 12 times
with the total order cost is Rp 15,000,000 and with additional of holding cost of 112
tons which leads to Rp 1,232,000, so the total cost is Rp 16,232,000.
CHAPTER V
CONCLUSION AND RECOMMENDATION
5.1. Conclusion
The forecast method, Simple Moving Average Method used by MRP department is
not effective and more likely to be erroneous and not accurate enough to represent
trend. The proposed improvement by using new forecast method, Holt-Winters is to
have a better glance on the trend of demand sales which resembles seasonal trend.
The proposed forecasting method is advisable to be implemented. Chase Strategy is
the most appropriate aggregate planning method in order to save the least inventory
and cost. Last but not least, for the lot sizing method, there are three methods possible
to be chosen, the author opts for Silver Meal as one of the methods to save the cost.
5.2. Recommendation
The recommendation for this matter is the MRP department of company for
Ramadhan this year should discard Simple Moving Average method for forecasting to
be replaced by Holt-Winters to be spared from possibility of losing sales. Losing sales
especially too late to fulfill the demand sales can be detrimental for company. Then,
applying Chase strategy is the most beneficial to save cost by assigning other workers
from different department or assignment who are idle which is preferable, or hiring
new labours. In order to saving holding cost and not stocking too many inventory, the
lot sizing method of Silver Meal shall be implemented.
REFERENCES
Chapman, Stephen N. (2006). “The Fundamentals of Production Planning and Control”. New
Jersey: Pearson Education, Inc.
Christopher, M. (2005). “Logistics and Supply Chain Management: Creating Value-adding
Networks”. Third Edition. London: Prentice Hall International
Graystone, J. Surface Coatings International, Part B: Coating Transactions. Chemistry and
Materials Science, Vol. 80, No. 11, 516-524, 1997.
Ghozali, Imam. (2011). Aplikasi Analisis Multivariate Dengan Program IBM. SPSS 19 (edisi
kelima.) Semarang: Universitas Diponegoro.
Herjanto, E. 2008. Manajemen Operasi. Edisi Ketiga. Jakarta : PT. Grasindo
Narasimhan, Seetharama L., McLeavey, Dennis W., and Billington, Peter J. (1995).
“Production Planning and Inventory Control”. 2nd Edition, Prentice Hall International
Editions, New Jersey.
Simchi-Levi, D., Kaminsky, P., and Simchi-Levi, E. (2008). “Designing and Managing the
Supply Chain: Concepts, Strategies and Case Studies”. 3rd Edition, McGraw-Hill Irwin,
Boston.
Sipper, Daniel and Robert L. Buffin. “Production Planning, Control, and Integration”. United
States of America: McGraw Hill Companies. Inc. 1997. Print
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