Download May 20 , 2014

PRODUCTION ANALYSIS OF KENDANG JAIPONG AND KENDANG
PENCAK SILAT IN ONEJAVASENI SHOP USING INTEGER PROGRAMMING
AND SENSITIVITY ANALYSIS
Created by:
Michael Whizo Mayto (110212172)
Sakya Nabila Hapsari (1102121273)
Firda Ramadhena (1102121278)
TI-36-INT
Industrial Engineering Faculty
Telkom University
Bandung
2014
PREFACE
Assalamu’alaikum warahmatullahi wabarakatuh.
Praise be to God for the grace and His help that has given us ease to finish this report. May
prayers and peace always pour to our beloved king the Prophet Muhammad.
This report is structured to meet the final task in one of the courses, that is Operational
Research. The topic that we discuss in this report is a description of the case, mathematical
models, sensitivity analysis, and the solutions to maximize the profit from the art shop,
brand "one java art" in Bandung.
In compiling this report, we encountered a variety of obstacles. Be it from outside or from
the suthors themselves. But with great patience and especially the help of God finally this
report can be resolved. Authors also thanked to lecturer, Mrs. Amelia Kurniawati and her
assistant who have been guiding us in our understanding of Operational Research and this
final task.
Hopefully this report will give broader knowledge to readers. We realized that this report is
still far from perfect. Therefore, we need criticism and suggestions of readers that building.
Thank you.
May 20 , 2014
Authors
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CONTENT
PREFACE ..................................................................................................................................... i
CONTENT ................................................................................................................................... ii
CONTENT OF TABLE ................................................................................................................... i
CONTENT OF FIGURE ................................................................................................................. i
CHAPTER I INTRODUCTION ....................................................................................................... 1
1.1
Background ............................................................................................................... 1
1.2
Identification of Problem .......................................................................................... 1
1.3
Formula of Problem .................................................................................................. 1
1.4
Objective ................................................................................................................... 2
1.5
Limitation of Problem .............................................................................................. 2
1.6
Benefit ....................................................................................................................... 2
CHAPTER II BASIC THEORY ........................................................................................................ 3
2.1
Linear Programming.................................................................................................. 3
2.2
Integer Programming ................................................................................................ 4
CHAPTER III CASE STUDY AND ANALYSIS .................................................................................. 5
3.1
Case Study ................................................................................................................. 5
3.2
Analysis (Using Integer Programming) ...................................................................... 6
3.2.1
Mathematic model............................................................................................ 6
CHAPTER IV COVER ................................................................................................................. 17
4.1
Conclusion ............................................................................................................... 17
4.2
Suggestion ............................................................................................................... 17
APPENDIX ................................................................................................................................ 18
REFERENCE .............................................................................................................................. 20
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CONTENT OF TABLE
Table 1. Constraint of Kendang Jaipong and Kendang Pencak Silat ........................................ 5
Table 2. Constraint of Kendang Jaipong and Kendang Pencak Silat in Software QM ............... 7
Table 3. Table of Ranging both Kendang Jaipong and Kendang Pencak Silat ........................... 7
Table 4. Table of Iteration ......................................................................................................... 8
Table 5. Table of Solution......................................................................................................... 8
Table 6. Table of Solution List ................................................................................................... 9
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CONTENT OF FIGURE
Figure 1. Graph of Case Study ................................................................................................... 9
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CHAPTER I
INTRODUCTION
1.1
Background
There are so many companies in Bandung which grow very fast. All those companies
may have different sector, but the only reason why they establish the companies is
to gain revenue as much as possible. One of the sector that really promising to gain
high revenue in Bandung is creative sector.
OneJavaSeni is one of the company that moves in creative sector, particularly in
West Java traditional instrumental. They usually produce many products, such as
kendang, gamelan, angklung, suling, and many others. From those products,
kendang is the most preferable product that usually ordered by the customers,
especially Kendang Jaipong and Kendang Pencak Silat. Although they have accepted
many orders, sometimes they still have difficulty to find the best way to gain
maximum revenue. They need a better strategy in production line to keep getting
maximum revenue with available capacity of material.
1.2
Identification of Problem
Based on the background above, It can be identified issues related to linear
programming in our case study, which are: maximize revenue by utilizing existing
materials, sensitivity analysis, and graphic solutions.
1.3
Formula of Problem
1. What is material that used by OneJavaSeni shop to produce Kendang Jaipong
and Kendang Pencak Silat?
2. How to gained maximize revenue of OneJavaSeni shop?
3. How to analyze the sensivity of optimal value by changing the capacity of
buffalo skin?
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1.4
Objective
1. The reader will understand utilization of material is done by OneJavaSeni shop
to produce Kendang Jaipong and Kendang Pencak Silat.
1. The reader will know how to gained maximize revenue of OneJavaSeni shop.
2. The reader can understand how to analyze the sensivity by changing the
capacity of buffalo skin.
1.5
Limitation of Problem
We limit the constraints in order our observations are not distorted and overly
broad. Limitation constraint will facilitate us in getting the data and calculate. The
constraint that we take into account only the materials needed to manufacture the
Kendang. We do not take into account labor costs, capital employed, wood drying
time, etc.
1.6
Benefit
This research is expected to be useful:
1. Those students, to further improve the understanding of linear programming in
order to analyze the production process of a company.
2. For companies, can learn how to maximize revenue by leveraging existing
material.
3. For faculty, as research materials or data that have been done by the student.
4. For researchers, as an encouragement to further enhance the analytical skills so
as to improve the production system of a company.
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CHAPTER II
BASIC THEORY
2.1
Linear Programming
Linear programming (LP) involves minimizing or maximizing an objective function
subject to bounds, linear equality, and inequality constraints. Example problems
include design optimization in engineering, profit maximization in manufacturing,
portfolio optimization in finance, and scheduling in energy and transportation.
Linear programming is the mathematical problem of finding a vector x that
minimizes the function:
Subject to the linear constraints:
Ax ≤ b
Inequality constraint
Aeqx = beq
Equality constraint
Lb ≤ x ≤ ub
Bound constraint
The following algorithms are commonly used to solve linear programming problems:

Interior point: Uses a primal-dual predictor-corrector algorithm and is
especially useful for large-scale problems that have structure or can be
defined using sparse matrices.

Active-set: Minimizes the objective at each iteration over the active set (a
subset of the constraints that are locally active) until it reaches a solution.

Simplex: Uses a systematic procedure for generating and testing candidate
vertex solutions to a linear program. The simplex algorithm is the most
widely used algorithm for linear programming
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2.2
Integer Programming
An integer programming is a mathematical optimization or feasibility program in
which some or all of the variables are restricted to be integers. In many settings the
term refers to integer linear programming (ILP), in which the objective function and
the constraints (other than the integer constraints) are linear.
An integer linear program in canonical form is expressed as:
Maximize
cTx
Subject to
Ax ≤ b,
X ≥ 0,
And
xЄZ
and an ILP in standard form is expressed as
Maximize
cTx
Subject to
Ax = b,
X ≥ 0,
And
xЄZ
Where the entries of c,b are vectors and
is a matrix, having integer values. Note
that similar to linear programs, ILPs not in standard form can be converted to
standard form by eliminating inequalities by introducing slack variables and
replacing variables that are not sign-constrained with the difference of two signconstrained variable.
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CHAPTER III
CASE STUDY AND ANALYSIS
3.1
Case Study
OneJavaSeni is a shop which produces West Java traditional instrumental, located
on Jalan Soekarno Hatta, across Carrefour. The owner of this shop is Giri Hartono
and this shop has been established since four years ago. OneJavaSeni usually
produces two main products, which are Kendang Jaipong and Kendang Pencak Silat.
The price of Kendang Jaipong is Rp3.000.000,00, while the price of Kendang Pencak
Silat is Rp5.500.000,00. The main materials of those products are wood, bamboo,
and buffalo skin. The table below will show the amount of materials, work time, and
demand.
Table 1. Constraint of Kendang Jaipong and Kendang Pencak Silat
Kendang
Kendang
Jaipong
Pencak Silat
Wood
0.65
0.75
8
Bamboo (Wengku)
0.17
0.19
3
Buffalo Skin
1
2
4
Work Time
2
2
12
Demand of Kendang Jaipong
1
0
5
0
1
2
Demand of Kendang Pencak
Silat
Capacity
From the table above, we need to find the maximum revenue that can be gained by
OneJavaSeni. How much revenue that can be gained?
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3.2
Analysis (Using Integer Programming)
3.2.1
Mathematic model

Decision Variable
X1 = Amount of Kendang Jaipong
X2 = Amount of Kendang Pencak Silat

Objective Function
Max Z = 3000000 X1 + 5500000 X2

Constraints
Wood
: 0.65 X1 + 0.75X2 ≤ 8
Bamboo (Wengku) : 0.17 X1 + 0.19 X2 ≤ 3

Buffalo Skin
: X1 + 2 X2 ≤ 4
Work Time
: 2 X1 + 2 X2 ≤ 12
Demand X1
: X1 ≤ 5
Demand X2
: X2 ≤ 2
Non-negative
: X1, X2 ≥ 0
Standard form
Max Z = 3000000 X1 + 5500000 X2 + 0X3 + 0X4 + 0X5 + 0X6 + 0X7 + 0X8
Wood
: 0.65 X1 + 0.75X2 + X3 = 8
Bamboo (Wengku) : 0.17 X1 + 0.19 X2 + X4 = 3
Buffalo Skin
: X 1 + 2 X 2 + X5 = 4
Work Time
: 2 X1 + 2 X2 + X6 = 12
Demand X1
: X1 + X7 = 5
Demand X2
: X2 + X8 = 2
Non-negative
: X1, X2 ≥ 0
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
Table of Constraints
Table 2. Constraint of Kendang Jaipong and Kendang Pencak Silat in Software QM

Ranging
Table 3. Table of Ranging both Kendang Jaipong and Kendang Pencak Silat
7

Iteration
Table 4. Table of Iteration

Solution
Table 5. Table of Solution
8

Solution List
Table 6. Table of Solution List

Graph
Figure 1. Graph of Case Study
From the table above, we can conclude that OneJavaSeni will gain maximum
revenue if the amount Kendang Jaipong are four and the amount of Kendang
Pencak Silat is none. So, the maximum revenue is Rp 12.000.000,00 per month. But
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in reality they need to produce both of products. So, we need to do sensitivity
analysis by changing the capacity of buffalo skin as follows:

X1 + 2X2 <= 1

X1 + 2X2 <= 2
10

X1 + 2X2 <= 3

X1 + 2X2 <= 4
11

X1 + 2X2 <= 5

X1 + 2X2 <= 6
12

X1 + 2X2 <= 7

X1 + 2X2 <= 8
13

X1 + 2X2 <= 9

X1 + 2X2 <= 10
14

X1 + 2X2 <= 11
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
Sensitivity Table of Buffalo Skin
Constraint
X1
X2
Z
X1 + 2X2 ≤ 1
2
0
3000000
X1 + 2X2 ≤ 2
3
0
9000000
X1 + 2X2 ≤ 3
4
0
1200000
X1 + 2X2 ≤ 4
4
0
12000000
X1 + 2X2 ≤ 5
5
0
15000000
X1 + 2X2 ≤ 6
4
1
17500000
X1 + 2X2 ≤ 7
5
1
20500000
X1 + 2X2 ≤ 8
4
2
23000000
X1 + 2X2 ≤ 9
4
2
23000000
X1 + 2X2 ≤ 10
4
2
23000000
X1 + 2X2 ≤ 11
4
2
23000000
From the sensitivity table of buffalo skin, we can conclude that by changing capacity
of buffalo skin, we can find the maximum revenue with producing both of the
products. The maximum revenue is Rp23.000.000,00 if OneJavaSeni produces four
Kendang Jaipong dan two Kendang Pencak Silat.
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CHAPTER IV
COVER
4.1
Conclusion
By using integer programming, we can find out how much product that should be
produced in integer amount. Besides that, we can count the maximum revenue, so
the company can calculate and rearrange the better way in production system. But
to find out the limitation of production to get maximum revenue, we can also use
sensitivity analysis. It can be changing capacity or amount of materials.
4.2
Suggestion
The company should arrange the production system by using integer programming
and sensitivity analysis to maximize revenue by available capacity of materials, so
production system will be more efficient.
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APPENDIX
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REFERENCE
http://www.mathworks.com/discovery/linear-programming.html
http://www.wikipedia.org/integer-programming.html
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