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

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

CONTENT OF TABLE

Table 1. Constraint of Kendang Jaipong and Kendang Pencak Silat........................................5Table 2. Constraint of Kendang Jaipong and Kendang Pencak Silat in Software QM...............7Table 3. Table of Ranging both Kendang Jaipong and Kendang Pencak Silat...........................7Table 4. Table of Iteration........................................................................................................8Table 5. Table of Solution........................................................................................................8Table 6. Table of Solution List..................................................................................................9

CONTENT OF FIGURE

Figure 1. Graph of Case Study..................................................................................................9

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.

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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

2.2 Integer ProgrammingAn 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 x Є Z

and an ILP in standard form is expressed as

Maximize cTx

Subject to Ax = b,

X ≥ 0,

And x Є Z

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 sign-

constrained 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

Jaipong

Kendang

Pencak SilatCapacity

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

Demand of Kendang Pencak

Silat0 1 2

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 : X1 + 2 X2 + 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

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Solution List

Table 6. Table of Solution List

Graph

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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

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

11

X1 + 2X2 <= 4

12

X1 + 2X2 <= 5

X1 + 2X2 <= 6

13

X1 + 2X2 <= 7

14

X1 + 2X2 <= 8

15

X1 + 2X2 <= 9

X1 + 2X2 <= 10

16

X1 + 2X2 <= 11

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Sensitivity Table of Buffalo Skin

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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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

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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