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.

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