ECONOMIC LOT SCHEDULING PROBLEM IN IMPERFECT PRODUCTION SYSTEM WITH TWO KEY MODULES ECONOMIC LOT SCHEDULING PROBLEM IN IMPERFECT PRODUCTION SYSTEM WITH TWO KEY MODULES.
ECONOMIC LOT SCHEDULING PROBLEM
IN IMPERFECT PRODUCTION SYSTEM WITH TWO KEY MODULES
A THESIS
Submitted in Partial Fulfillment of the Requirement for the Bachelor Degree of
Engineering in Industrial Engineering
FILEMON YOGA ADHISATYA
10 14 06247
INTERNATIONAL INDUSTRIAL ENGINEERING PROGRAM
DEPARTMENT OF INDUSTRIAL ENGINEERING
FACULTY OF INDUSTRIAL TECHNOLOGY
UNIVERSITAS ATMA JAYA YOGYAKARTA
YOGYAKARTA
2015
2
3
ACKNOWLEDGEMENT
The author conducted the research on Economic Lot Scheduling Problem in
Imperfect Production System with Two Key Modules to fulfill partial requirement
to earn bachelor degree of Industrial Engineer of Universitas Atma Jaya
Yogyakarta.
The author would like to deliver highest appreciation to Mr. The Jin Ai, D.Eng.
and Mrs. Ririn Diar Astanti, D.Eng. as the faculty supervisor and co-supervisor for
the help to the author while conducting this research. Moreover, Mr. The Jin Ai,
D.Eng. and Mrs. Ririn Diar Astanti, D.Eng. have also been guiding and
encouraging the author to achieve highest achievements during his study in
Universitas Atma Jaya Yogyakarta.
The deepest appreciation for love and dedication goes to the author‟s parents,
Mr. Fidelis Priyo Djatmiko and Mrs. Zita Pancawesti. Their love and dedication for
the author have been the main power to start, conduct and finally finish this
research.
All other appreciation goes to author‟s family, relatives and friends in Himpunan
Mahasiswa Teknik Industri UAJY and Industrial Engineering batch 2010 for all
the supports given to the author to finish this thesis. Last but not least, author is
amicable for suggestions that boost the motivation for the next research.
4
TABLE OF CONTENT
CHAPTER
1
2.
TITLE
PAGE
Title Page
i
Identification Page
ii
Declaration of Originality
iii
Acknowledgement
iv
Table of Content
v
List of Table
viii
List of Figure
ix
Abstract
xi
Introduction
1
1.1. Background
1
1.2. Problem Formulation
2
1.3. Objectives
3
1.4. Scopes and Limitations
4
Literature Review and Theoretical Background
5
2.1. Economic Lot Scheduling Problem
5
2.2. Economic Production Quantity Model with Two Imperfect
Modules
8
2.3. ELSP Five Key Research Themes
3
9
2.4. Gap Analysis and Research Contributions
15
Research Methodology
17
3.1. Literature Review
17
3.2. Problem Identification
17
3.3. Problem Generation
18
3.4. Model Development
18
5
4
3.5. Result Analysis
19
3.6. Conclusion
20
Development of ELSP Model in Perfect Production System
22
4.1. Data and Problem Formulation
22
4.2. ELSP in Perfect Production System Using Independent
Solution Approach
24
4.3. ELSP in Perfect Production System Using Common Cycle
Approach
27
4.4. ELSP in Perfect Production System Using Basic Period
Approach
5
30
ELSP in Imperfect Production System with One Key Module
33
5.1. Data and Problem Formulation
33
5.2. ELSP in Imperfect Production System with One Key
Module
Using IS Approach
35
5.3. ELSP in Imperfect Production System with One Key
Module
Using CC Approach
6
39
Development of ELSP Model in Imperfect Production System
with Two Key Modules
42
6.1. Data and Problem Formulation
42
6.2. Economic Production Quantity Model in Imperfect
Production System with Two Key Modules
45
6.3. ELSP Model in Imperfect Production System with Two
Key
Modules
7
50
Result Analysis
60
6
7.1. Result Analysis on ELSP in Perfect Production System
60
7.2. Result Analysis on ELSP in Imperfect Production System
with One Key Module
61
7.3. Result Analysis on ELSP in Imperfect Production System
with Two Key Modules
62
7.4. Verification on ELSP Model in Imperfect Production
System
with Two Key Modules
8
63
Conclusion
68
Reference List
69
7
List of Table
Table 2.1.
ELSP Papers Classified by Chan‟s Key Themes and ELSP Basic
Assumptions
16
Table 4.1.
Data of Bomberger‟s Stamping Problem
22
Table 5.1.
Modified Bomberger Stamping Problem for Imperfect Production
System with One Key Module
Table 6.1.
34
Modified Bomberger Stamping Problem for Imperfect Production
System with Two Key Modules
44
Table 7.1.
Result Comparison on ELSP in Perfect Production System
60
Table 7.2.
Result Comparison on ELSP in Imperfect Production System with
One Key Module
Table 7.3.
62
Result Comparison on ELSP in Imperfect Production System with
Two Key Modules
63
Table 7.4.
Total Costs of ELSP Cases
64
Table 7.5.
Total Cost Incurred when Applying Cycle Times of ELSP with
Perfect Production System to ELSP with Two Imperfect
Key Modules
67
8
List of Figure
Figure 3.1.
Research Methodology
20
Figure 4.1.
Solver for Independent Solution Perfect ELSP Model
24
®
Figure 4.2.
Microsoft Excel Spreadsheet of ELSP Model under IS
Approach
25
Figure 4.3.
Solver for Common Cycle Perfect ELSP Model
Figure 4.4.
Figure 4.5.
Figure 4.6.
Microsoft Excel Spreadsheet of ELSP Model under CC
Approach
28
Solver for Basic Period Perfect ELSP Model
30
®
Microsoft Excel Spreadsheet of ELSP Model under BP
Approach
Figure 5.1.
31
Solver for Independent Solution Imperfect ELSP Model with
One Key Module
Figure 5.2.
36
®
Microsoft Excel Spreadsheet of ELSP Model for Imperfect
Production System with One Key Module under IS Approach
Figure 5.3.
37
Solver for Common Cycle Imperfect ELSP Model with
One Key Module
Figure 5.4.
27
®
39
®
Microsoft Excel Spreadsheet of ELSP Model for Imperfect
Production System with One Key Module under CC Approach
40
Figure 6.1.
Production Uptime Segmentation
45
Figure 6.2.
Solver for Independent Solution Imperfect ELSP Model with Two
Key Modules
Figure 6.3.
53
®
Microsoft Excel Spreadsheet of ELSP Model for Imperfect
Production System with Two Key Modules under IS Approach
Figure 6.4.
Solver of Common Cycle Approach for Imperfect ELSP Model
with Two Key Modules
Figure 6.5.
54
57
®
Microsoft Excel Spreadsheet of ELSP Model for Imperfect
Production System with Two Key Modules under CC Approach
9
58
ABSTRACT
The thesis entitled “Economic Lot Scheduling Problem in Imperfect Production
System with Two Key Modules” began with the problem identification based on
literature review under the theme Economic Lot Scheduling Problem (ELSP). It
was revealed that no paper had been discussing about ELSP in imperfect
production system with two key modules. Discussion of ELSP in imperfect
production context had only been written under one key module problem. Based
on this literature review, the problem in this research was defined as finding the
cycle times for ten items of modified Bomberger (1966) stamping problem under
ELSP in imperfect production system with two key modules context in order to
minimize the total cost covering holding cost, setup cost and quality-related cost
of producing non-conforming items.
In pursue of these optimum cycle times, the algorithm of finding the cycle times
was developed through a series of modeling from ELSP in perfect production
system, ELSP in imperfect production system with one key module and finally the
ELSP in imperfect production system with two key modules. Solver function in
Microsoft® Excel 2010 was used to obtain the optimum cycle times under
Independent Solution (IS) and Common Cycle (CC) approaches. Before applying
this model to ELSP in imperfect production system with two key modules, an
Economic Production Quantity (EPQ) model with two imperfect modules
proposed by Gong et al. (2012) must be proved. Only if the formula of expected
number of non-conforming items in the EPQ can be proved, this formula can be
used in ELSP context with adjustments.
Since the formula to calculate the expected number of non-conforming items
could be proven, the model and algorithm development of ELSP in imperfect
production system with two key modules could be done. Under the IS approach,
the cycle times for modified Bomberger (1966) stamping problem was calculated
as T={33.2, 23.6, 22.6, 11.2, 52.5, 85.9, 160, 20.7, 18.6, 38.6} for item 1, β, …,
10, respectively with total cost in one year of $101,307.9. Under the CC
approach, the cycle time for modified Bomberger (1966) stamping problem was
calculated as T=31.892 with total cost in one year of $247,592.43. These two
costs were higher than those of perfect production system problem since there
was involvement of imperfect production system parameters α, , μ, γ and u.
10
IN IMPERFECT PRODUCTION SYSTEM WITH TWO KEY MODULES
A THESIS
Submitted in Partial Fulfillment of the Requirement for the Bachelor Degree of
Engineering in Industrial Engineering
FILEMON YOGA ADHISATYA
10 14 06247
INTERNATIONAL INDUSTRIAL ENGINEERING PROGRAM
DEPARTMENT OF INDUSTRIAL ENGINEERING
FACULTY OF INDUSTRIAL TECHNOLOGY
UNIVERSITAS ATMA JAYA YOGYAKARTA
YOGYAKARTA
2015
2
3
ACKNOWLEDGEMENT
The author conducted the research on Economic Lot Scheduling Problem in
Imperfect Production System with Two Key Modules to fulfill partial requirement
to earn bachelor degree of Industrial Engineer of Universitas Atma Jaya
Yogyakarta.
The author would like to deliver highest appreciation to Mr. The Jin Ai, D.Eng.
and Mrs. Ririn Diar Astanti, D.Eng. as the faculty supervisor and co-supervisor for
the help to the author while conducting this research. Moreover, Mr. The Jin Ai,
D.Eng. and Mrs. Ririn Diar Astanti, D.Eng. have also been guiding and
encouraging the author to achieve highest achievements during his study in
Universitas Atma Jaya Yogyakarta.
The deepest appreciation for love and dedication goes to the author‟s parents,
Mr. Fidelis Priyo Djatmiko and Mrs. Zita Pancawesti. Their love and dedication for
the author have been the main power to start, conduct and finally finish this
research.
All other appreciation goes to author‟s family, relatives and friends in Himpunan
Mahasiswa Teknik Industri UAJY and Industrial Engineering batch 2010 for all
the supports given to the author to finish this thesis. Last but not least, author is
amicable for suggestions that boost the motivation for the next research.
4
TABLE OF CONTENT
CHAPTER
1
2.
TITLE
PAGE
Title Page
i
Identification Page
ii
Declaration of Originality
iii
Acknowledgement
iv
Table of Content
v
List of Table
viii
List of Figure
ix
Abstract
xi
Introduction
1
1.1. Background
1
1.2. Problem Formulation
2
1.3. Objectives
3
1.4. Scopes and Limitations
4
Literature Review and Theoretical Background
5
2.1. Economic Lot Scheduling Problem
5
2.2. Economic Production Quantity Model with Two Imperfect
Modules
8
2.3. ELSP Five Key Research Themes
3
9
2.4. Gap Analysis and Research Contributions
15
Research Methodology
17
3.1. Literature Review
17
3.2. Problem Identification
17
3.3. Problem Generation
18
3.4. Model Development
18
5
4
3.5. Result Analysis
19
3.6. Conclusion
20
Development of ELSP Model in Perfect Production System
22
4.1. Data and Problem Formulation
22
4.2. ELSP in Perfect Production System Using Independent
Solution Approach
24
4.3. ELSP in Perfect Production System Using Common Cycle
Approach
27
4.4. ELSP in Perfect Production System Using Basic Period
Approach
5
30
ELSP in Imperfect Production System with One Key Module
33
5.1. Data and Problem Formulation
33
5.2. ELSP in Imperfect Production System with One Key
Module
Using IS Approach
35
5.3. ELSP in Imperfect Production System with One Key
Module
Using CC Approach
6
39
Development of ELSP Model in Imperfect Production System
with Two Key Modules
42
6.1. Data and Problem Formulation
42
6.2. Economic Production Quantity Model in Imperfect
Production System with Two Key Modules
45
6.3. ELSP Model in Imperfect Production System with Two
Key
Modules
7
50
Result Analysis
60
6
7.1. Result Analysis on ELSP in Perfect Production System
60
7.2. Result Analysis on ELSP in Imperfect Production System
with One Key Module
61
7.3. Result Analysis on ELSP in Imperfect Production System
with Two Key Modules
62
7.4. Verification on ELSP Model in Imperfect Production
System
with Two Key Modules
8
63
Conclusion
68
Reference List
69
7
List of Table
Table 2.1.
ELSP Papers Classified by Chan‟s Key Themes and ELSP Basic
Assumptions
16
Table 4.1.
Data of Bomberger‟s Stamping Problem
22
Table 5.1.
Modified Bomberger Stamping Problem for Imperfect Production
System with One Key Module
Table 6.1.
34
Modified Bomberger Stamping Problem for Imperfect Production
System with Two Key Modules
44
Table 7.1.
Result Comparison on ELSP in Perfect Production System
60
Table 7.2.
Result Comparison on ELSP in Imperfect Production System with
One Key Module
Table 7.3.
62
Result Comparison on ELSP in Imperfect Production System with
Two Key Modules
63
Table 7.4.
Total Costs of ELSP Cases
64
Table 7.5.
Total Cost Incurred when Applying Cycle Times of ELSP with
Perfect Production System to ELSP with Two Imperfect
Key Modules
67
8
List of Figure
Figure 3.1.
Research Methodology
20
Figure 4.1.
Solver for Independent Solution Perfect ELSP Model
24
®
Figure 4.2.
Microsoft Excel Spreadsheet of ELSP Model under IS
Approach
25
Figure 4.3.
Solver for Common Cycle Perfect ELSP Model
Figure 4.4.
Figure 4.5.
Figure 4.6.
Microsoft Excel Spreadsheet of ELSP Model under CC
Approach
28
Solver for Basic Period Perfect ELSP Model
30
®
Microsoft Excel Spreadsheet of ELSP Model under BP
Approach
Figure 5.1.
31
Solver for Independent Solution Imperfect ELSP Model with
One Key Module
Figure 5.2.
36
®
Microsoft Excel Spreadsheet of ELSP Model for Imperfect
Production System with One Key Module under IS Approach
Figure 5.3.
37
Solver for Common Cycle Imperfect ELSP Model with
One Key Module
Figure 5.4.
27
®
39
®
Microsoft Excel Spreadsheet of ELSP Model for Imperfect
Production System with One Key Module under CC Approach
40
Figure 6.1.
Production Uptime Segmentation
45
Figure 6.2.
Solver for Independent Solution Imperfect ELSP Model with Two
Key Modules
Figure 6.3.
53
®
Microsoft Excel Spreadsheet of ELSP Model for Imperfect
Production System with Two Key Modules under IS Approach
Figure 6.4.
Solver of Common Cycle Approach for Imperfect ELSP Model
with Two Key Modules
Figure 6.5.
54
57
®
Microsoft Excel Spreadsheet of ELSP Model for Imperfect
Production System with Two Key Modules under CC Approach
9
58
ABSTRACT
The thesis entitled “Economic Lot Scheduling Problem in Imperfect Production
System with Two Key Modules” began with the problem identification based on
literature review under the theme Economic Lot Scheduling Problem (ELSP). It
was revealed that no paper had been discussing about ELSP in imperfect
production system with two key modules. Discussion of ELSP in imperfect
production context had only been written under one key module problem. Based
on this literature review, the problem in this research was defined as finding the
cycle times for ten items of modified Bomberger (1966) stamping problem under
ELSP in imperfect production system with two key modules context in order to
minimize the total cost covering holding cost, setup cost and quality-related cost
of producing non-conforming items.
In pursue of these optimum cycle times, the algorithm of finding the cycle times
was developed through a series of modeling from ELSP in perfect production
system, ELSP in imperfect production system with one key module and finally the
ELSP in imperfect production system with two key modules. Solver function in
Microsoft® Excel 2010 was used to obtain the optimum cycle times under
Independent Solution (IS) and Common Cycle (CC) approaches. Before applying
this model to ELSP in imperfect production system with two key modules, an
Economic Production Quantity (EPQ) model with two imperfect modules
proposed by Gong et al. (2012) must be proved. Only if the formula of expected
number of non-conforming items in the EPQ can be proved, this formula can be
used in ELSP context with adjustments.
Since the formula to calculate the expected number of non-conforming items
could be proven, the model and algorithm development of ELSP in imperfect
production system with two key modules could be done. Under the IS approach,
the cycle times for modified Bomberger (1966) stamping problem was calculated
as T={33.2, 23.6, 22.6, 11.2, 52.5, 85.9, 160, 20.7, 18.6, 38.6} for item 1, β, …,
10, respectively with total cost in one year of $101,307.9. Under the CC
approach, the cycle time for modified Bomberger (1966) stamping problem was
calculated as T=31.892 with total cost in one year of $247,592.43. These two
costs were higher than those of perfect production system problem since there
was involvement of imperfect production system parameters α, , μ, γ and u.
10