I N D U S T R I A L E N G I N E E R I N G P R O G R A M COURSE TITLE: OPERATIONS RESEARCH 1 (OPERES1)
1st Semester, Curriculum Year 2018-2019
Holy Angel University VMs
Vision: To become a role-model catalyst for countryside development and one of the most influential, best-managed Catholic universities in the Asia-Pacific region.
Mission: To offer accessible quality education that transforms students into persons of conscience, competence, and compassion.
School of Engineering and Architecture VMs Vision
A center of excellence in engineering and architecture education imbued with Catholic mission and identity serving as a role-model catalyst for countryside development
Mission
The School shall provide accessible quality engineering and architecture education leading to highly competent professional; continually contribute to the advancement of knowledge and technology through research activities; and support countryside development through environmental preservation and community involvement.
Institutional Student Learning Outcomes (ISLOs) 1. Show effective communication
2. Demonstrate appropriate value and sound ethical reasoning
4. Utilize civic and global learning
5. Use applied and collaborative learning 6. Employ aesthetic engagement
7. Show Information and Communication Technology (ICT) Literacy Program Educational Objectives (PEOs)
Within a few years after graduation, graduates of our BS Industrial Engineering programs are expected to have:
1. Demonstrated technical competence, including design and problem-solving skills, as evidenced by:
the sound technical designs and systems that conform with existing laws and ethical standards they produced
the recognition and certification they received for exemplary achievement 2. Shown a commitment to life-long learning as evidenced by:
the graduate degrees or further studies they pursue
the professional certifications which are locally and internationally recognized they possess
the knowledge and skills on recent technological advances in the field they continuously acquire 3. Exhibited success in their chosen profession evidenced by:
the key level positions they hold or promotions they get in their workplace
the good track record they possess
the professional visibility (e.g., publications, presentations, patents, inventions, awards, etc.) they are involved with
the international activities (e.g., participation in international conferences, collaborative research, employment abroad, etc.) they are engaged with
the entrepreneurial activities they undertake 4. Manifested faithful stewardship as evidenced by:
their participation in University-based community extension initiatives as alumni
their contribution to innovations/ inventions for environmental promotion and preservation, and cultural integration
their engagement in advocacies and volunteer works for the upliftment of the quality of life and human dignity especially the marginalized
Relationship of the Program Educational Objectives to the Mission of the School of Engineering & Architecture:
Industrial Engineering Program Educational Objectives (PEOs):
Within a few years after graduation, the graduates of the BS Industrial Engineering program should have:
Mission The School shall provide
accessible quality
engineering and architecture education leading to high professional competence.
The School shall continually contribute to the
advancement of knowledge and technology through research activities.
The School shall support countryside development through environmental preservation and community involvement.
1. Demonstrated professional competence, including design and problem solving skills as evidenced by:
the sound technical designs and systems that conform with existing laws and ethical standards they produced
the recognition and certification they received for exemplary achievement
2. Shown a commitment to life-long learning evidenced by:
the graduate degrees or further studies they pursue
the professional certifications which are locally and internationally recognized they possess
the knowledge and skills on recent technological advances in the field they continuously acquire
3. Exhibited success in their chosen profession evidenced by:
the key level positions they hold or promotions they get in their workplace
the good track record they possess
the professional visibility (e.g., publications, presentations, patents, inventions, awards, etc.)
they are involved with international activities (e.g., participation in international conferences, collaborative research, employment abroad, etc.)
they are engaged with the entrepreneurial activities they undertake
4. Manifested faithful stewardship evidenced by:
their participation in University-based community extension initiatives as alumni
their contribution to innovations/ inventions for environmental promotion and preservation, and cultural integration
their engagement in advocacies and volunteer works for the upliftment of the quality of life and human dignity especially the marginalized
Relationship of the Institutional Student Learning Outcomes to the Program Educational Objectives:
PEO 1 PEO 2 PEO 3 PEO 4
ISLO1: Show effective communication
ISLO2: Demonstrate appropriate value and sound ethical reasoning
ISLO3: Apply critical and creative thinking
ISLO4: Utilize civic and global learning
ISLO5: Use applied and collaborative learning
ISLO6: Employ aesthetic engagement
ISLO7: Show Information and Communication Technology (ICT) Literacy
BS Industrial Engineering Program Outcomes (POs) After finishing the program students will be able to:
a. Apply knowledge of mathematics, physical sciences, and engineering sciences to the practice of Industrial Engineering.
b. Design and conduct experiments, as well as to analyze and interpret data.
c. Design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability, in accordance with standards.
d. Function on multidisciplinary teams.
e. Identify, formulate and solve engineering problems.
f. Have an understanding of professional and ethical responsibility.
g. Demonstrate and master the ability to listen, comprehend, speak, write and convey ideas clearly and effectively, in person and through electronic media to all audiences.
h. Have broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context.
i. Recognition of the need for, and an ability to engage in life-long learning and to keep current of the development in the field.
j. Have knowledge of contemporary issues.
k. Use the techniques, skills, and modern engineering tools necessary for engineering practice.
l. Have knowledge and understanding of engineering and management principles as a member and leader in a team, to manage projects and in multidisciplinary environments.
m. Engage in service-learning program for the promotion and preservation to local culture and tradition as well as to the community.
n. Design, develop, implement and improve integrated systems that include people, materials, information, equipment and energy.
Relationship of the Engineering Program Outcomes to the Program Educational Objectives:
Industrial Engineering Student Outcomes (SOs)
At the time of graduation, BS Industrial Engineering program graduates should be able to: PEO 1 PEO 2 PEO 3 PEO 4 a. Apply knowledge of mathematics, physical sciences, and engineering sciences to the practice of
Industrial Engineering.
b. Design and conduct experiments, as well as to analyze and interpret data.
c. Design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and
sustainability, in accordance with standards.
d. Function on multidisciplinary teams.
e. Identify, formulate and solve engineering problems.
f. Have an understanding of professional and ethical responsibility.
g. Demonstrate and master the ability to listen, comprehend, speak, write and convey ideas clearly
and effectively, in person and through electronic media to all audiences.
h. Have broad education necessary to understand the impact of engineering solutions in a global,
economic, environmental, and societal context.
i. Recognition of the need for, and an ability to engage in life-long learning and to keep current of the
development in the field.
j. Have knowledge of contemporary issues.
k. Use the techniques, skills, and modern engineering tools necessary for engineering practice.
l. Have knowledge and understanding of engineering and management principles as a member and
leader in a team, to manage projects and in multidisciplinary environments.
m. Ability to design, develop, implement and improve integrated systems that include people,
materials, information, equipment and energy.
n. Engage in service-learning program for the promotion and preservation to local culture and tradition
as well as to the community.
Code Descriptor Description
I Introductory Course An introductory course to an outcome
E Enabling Course A course that strengthens the outcome
D Demonstrative Course A course demonstrating an outcome Course Outcomes (COs)
1. Discuss the Operations Research (OR) approach, its basic concepts, techniques and application areas.
2. Develop mathematical optimization models
3. Solve optimization models using the appropriate OR tools/techniques.
4. Interpret the results of computation as basis for recommending the best decision for a problem scenario.
a b c d e f g h i J k l m n
CO1.Discuss the Operations Research (OR) approach, its basic
concepts, techniques and application areas; I
CO2.Develop mathematical optimization models; E
CO3.Solve optimization models using the appropriate OR
tools/techniques. E
CO4.Interpret the results of computation as basis for recommending the
best decision for a problem scenario. D
I. Course Description : The subject deals with the development and application of fundamental deterministic optimization models and various solution methods. It includes quantitative modeling, formulation, analysis and interpretation of linear integer and non-integer models and network flow problems.
II. Course Credit : 3 Units
III. Prerequisite : ADVMATH-IE
IV. Textbook : Anderson, D. R. (2019).An introduction to management science: Quantitative approaches to decision making. (14thEd.).
Australia: Cengage Learning.
V. Requirements : Seatworks
Assignments Boardwork Case Studies Written Exam VI. Learning Outline
Week/
Hours
CodeCO
Link Learning Output Student
Output Topics / Course Content Core values
Sub valuesand Methodology Evaluation/
Learning Assessment 3 hourWk 1 At the end of course
or topic the student will be able to:
Learn the importance of subject through the course outcomes
Recognize the different classroom policies
Get familiarized with and use the online learning platforms to
OSPRES1 Subject Orientation
Course outcomes Classroom policies
Attendance
Assignments
Quizzes and major examinations
Case studies
Critique
Subject final output requirement
Christ-
centeredness Indicators:
Obedience and prayerfulness Excellence Indicators:
Competence, expertise, analytical, and logical
Subject orientation conducted by teacher.
be used in class Grading System
Academic Dishonesty Online Learning Platform
Canvas LMS
Zoom Cloud Meetings
Societal responsibility Indicators:
Commitment andInvolvement
3 hoursWk 2 CO1 At the end of course or topic the student will be able to:
Define operations research, its origin and development
Describe the OR approach and methodology
Understand the OR application areas and give real-life examples
Recitation Introduction
Origin and Development of Operations Research
OR approach and methodology
OR Application Areas
Christ-
centeredness Indicators:
Obedience and prayerfulness Excellence Indicators:
Competence, expertise, analytical, and logical
Community Indicators:
Solidarity and Respect for others Integrity Indicators:
Accountability,
Transparency and Honesty Societal responsibility Indicators:
Media-supported lecture/ PowerPoint presentation
Class discussions by teachers and
students (face-to- face/online)
Interactive student- centered activities like Think-Pair-Share, Brainstorming, Buzz Session etc.
Hands-on
demonstrations and exercises/ problem
setsCoaching (special assistance provided for students learning difficulty in the course)
Recitation
Written examinations
Alternative summative assessments (reflection papers/
critical analysis)
Answer Key
Assessment Rubric is to be used for theevaluation of theclassroom activities
Commitment andInvolvement
Asynchronous
teaching and learning using Canvas LMS Platform in providing offline content
resources (readings, lecture notes,
recorded lectures, detailed guides, etc., in print or digital format) and other activities.
Synchronous
teaching and learning through webinars, live broadcasts, chats and teleconferences for real-time teacher- student engagement.
3 hoursWk 3 CO1 CO2CO3 CO4
At the end of course or topic the student will be able to:
Define the concepts of linear
programming
Outline the steps in the formulation of linear programming problems.
Solve and formulate linear programming problems
Seatwork
Assignment
Written exam
Board Work
Problem Set
Linear Programming (LP)
Definition and
Characteristics of the LP Problem
Mathematical
modeling/Formulation of the LP Problem
Christ-
centeredness Indicators:
Obedience and prayerfulness Excellence Indicators:
Competence, expertise, analytical, and logical
Community Indicators:
Media-supported lecture/ PowerPoint presentation
Class discussions by teachers and
students (face-to- face/online)
Interactive student- centered activities like Think-Pair-Share, Brainstorming, Buzz Session etc.
Hands-on
demonstrations and exercises/ problem
Answer Key
Assessment Rubric is to be used for theevaluation of theclassroom activities
Solidarity and Respect for others Integrity Indicators:
Accountability,
Transparency and Honesty Societal responsibility Indicators:
Commitment andInvolvement
setsCoaching (special assistance provided for students learning difficulty in the course)
Recitation
Written examinations
Alternative summative assessments (reflection papers/
critical analysis)
Asynchronous
teaching and learning using Canvas LMS Platform in providing offline content
resources (readings, lecture notes,
recorded lectures, detailed guides, etc., in print or digital format) and other activities.
Synchronous
teaching and learning through webinars, live broadcasts, chats and teleconferences for real-time teacher- student engagement.
Wk 4-5
6 hours CO1 CO2CO3 CO4
At the end of course or topic the student will be able to:
Solve LP problems using the different methods –
graphical, simplex and matrix
approach.
Understand special cases in linear programming such as degeneracy, infeasibility, alternative optima and unbounded solution
Seatwork
Assignment
Written exam
Board Work
Problem Set
Solution Approaches to LP Problems
Graphical Method
Simplex Method: Big-M Technique, Two-Phase Method
Matrix Approach to LP
Special Cases -
Degeneracy, Infeasibility, Alternative Optima, Unbounded Solution
Christ-
centeredness Indicators:
Obedience and prayerfulness Excellence Indicators:
Competence, expertise, analytical, and logical
Community Indicators:
Solidarity and Respect for others Integrity Indicators:
Accountability,
Transparency and Honesty Societal responsibility Indicators:
Commitment andInvolvement
Media-supported lecture/ PowerPoint presentation
Class discussions by teachers and
students (face-to- face/online)
Interactive student- centered activities like Think-Pair-Share, Brainstorming, Buzz Session etc.
Hands-on
demonstrations and exercises/ problem
setsCoaching (special assistance provided for students learning difficulty in the course)
Recitation
Written examinations
Alternative summative assessments (reflection papers/
critical analysis)
Asynchronous
teaching and learning using Canvas LMS Platform in providing offline content
resources (readings, lecture notes,
Answer Key
Assessment Rubric is to be used for theevaluation of theclassroom activities
recorded lectures, detailed guides, etc., in print or digital format) and other activities.
Synchronous
teaching and learning through webinars, live broadcasts, chats and teleconferences for real-time teacher- student engagement.
6 P R E L I M E X A M I N A T I O N
Wk 7-9
8 hours CO1 CO2CO3 CO4
At the end of course or topic the student will be able to:
Discuss the basic concept of primal- dual relationship
Outline the steps in the formulation and interpretation of dual problems.
Solve problems using dual simplex method
Understand the role of sensitivity
analysis
Seatwork
Assignment
Written exam
Board Work
Problem Set
Duality and Sensitivity Analysis
Primal-Dual Relationship
Formulation and
Interpretation of the Dual Problem
Dual Simplex Method
Sensitivity analysis
Christ-
centeredness Indicators:
Obedience and prayerfulness Excellence Indicators:
Competence, expertise, analytical, and logical
Community Indicators:
Solidarity and Respect for others Integrity Indicators:
Media-supported lecture/ PowerPoint presentation
Class discussions by teachers and
students (face-to- face/online)
Interactive student- centered activities like Think-Pair-Share, Brainstorming, Buzz Session etc.
Hands-on
demonstrations and exercises/ problem
setsCoaching (special assistance provided for students learning difficulty in the course)
Answer Key
Assessment Rubric is to be used for theevaluation of theclassroom activities
Accountability,
Transparency and Honesty Societal responsibility Indicators:
Commitment andInvolvement
Recitation
Written examinations
Alternative summative assessments (reflection papers/
critical analysis)
Asynchronous
teaching and learning using Canvas LMS Platform in providing offline content
resources (readings, lecture notes,
recorded lectures, detailed guides, etc., in print or digital format) and other activities.
Synchronous
teaching and learning through webinars, live broadcasts, chats and teleconferences for real-time teacher- student engagement.
Wk 9-11
7 hours CO1 CO2CO3 CO4
At the end of course or topic the student will be able to:
Define the basic concepts integer linear programming
Outline the steps in formulating Integer
Seatwork
Assignment
Written exam
Board Work
Problem Set
Integer Linear Programming (ILP)
Concepts and Formulation of ILP Problems
Solution Approaches - Graphical, Implicit
Enumeration, Branch and Bound Algorithm, Gomory's
Christ-
centeredness Indicators:
Obedience and prayerfulness Excellence Indicators:
Media-supported lecture/ PowerPoint presentation
Class discussions by teachers and
students (face-to- face/online)
Interactive student-
Answer Key
Assessment Rubric is to be used for theevaluation of the
linear programming problems
Solve problems using different approaches like Graphical, Implicit Enumeration, Brand and Bound
algorithm, and Gomory’s Cutting Plane algorithm
Cutting Plane Algorithm Competence, expertise, analytical, and logical
Community Indicators:
Solidarity and Respect for others Integrity Indicators:
Accountability,
Transparency and Honesty Societal responsibility Indicators:
Commitment andInvolvement
centered activities like Think-Pair-Share, Brainstorming, Buzz Session etc.
Hands-on
demonstrations and exercises/ problem
setsCoaching (special assistance provided for students learning difficulty in the course)
Recitation
Written examinations
Alternative summative assessments (reflection papers/
critical analysis)
Asynchronous
teaching and learning using Canvas LMS Platform in providing offline content
resources (readings, lecture notes,
recorded lectures, detailed guides, etc., in print or digital format) and other activities.
Synchronous
teaching and learning through webinars, live broadcasts, chats
classroom activities
and teleconferences for real-time teacher- student engagement.
12 M I D T E R M E X A M I N A T I O N
Wk 13-15
9 hours CO1 CO2CO3 CO4
At the end of course or topic the student will be able to:
Define the concepts of the special types of LP models like Transportation model,
transshipment model and
assignment model
Outline the steps in solving
transportation, transshipment, and assignment
problems
Solve problems involving transportation, transshipment, and assignment models
Seatwork
Assignment
Written exam
Board Work
Problem Set
Special Types of LP Models:
Modeling and Solution Algorithms
Transportation Model
Transshipment Model
Assignment Model
Christ-
centeredness Indicators:
Obedience and prayerfulness Excellence Indicators:
Competence, expertise, analytical, and logical
Community Indicators:
Solidarity and Respect for others Integrity Indicators:
Accountability,
Transparency and Honesty Societal responsibility Indicators:
Commitment and
Media-supported lecture/ PowerPoint presentation
Class discussions by teachers and
students (face-to- face/online)
Interactive student- centered activities like Think-Pair-Share, Brainstorming, Buzz Session etc.
Hands-on
demonstrations and exercises/ problem
setsCoaching (special assistance provided for students learning difficulty in the course)
Recitation
Written examinations
Alternative summative assessments (reflection papers/
critical analysis)
Asynchronous
teaching and learning
Answer Key
Assessment Rubric is to be used for theevaluation of theclassroom activities
Involvement using Canvas LMS Platform in providing offline content
resources (readings, lecture notes,
recorded lectures, detailed guides, etc., in print or digital format) and other activities.
Synchronous
teaching and learning through webinars, live broadcasts, chats and teleconferences for real-time teacher- student engagement.
16-17
6 hours CO1 CO2CO3 CO4
At the end of course or topic the student will be able to:
Define the concepts of networks and networking techniques
Define the concepts of shortest route, minimal spanning tree, and maximal flow algorithms
Outline the steps in solving shortest route, minimal spanning tree, and maximal flow
Seatwork
Assignment
Written exam
Board Work
Problem Set
Network Models
Definition
Shortest Route Algorithms
Minimal Spanning Tree Algorithm
Maximal Flow Algorithm
Project Management: PERT and CPM
Christ-
centeredness Indicators:
Obedience and prayerfulness Excellence Indicators:
Competence, expertise, analytical, and logical
Community Indicators:
Solidarity and Respect for
Media-supported lecture/ PowerPoint presentation
Class discussions by teachers and
students (face-to- face/online)
Interactive student- centered activities like Think-Pair-Share, Brainstorming, Buzz Session etc.
Hands-on
demonstrations and exercises/ problem
setsCoaching (special
Answer Key
Assessment Rubric is to be used for theevaluation of theclassroom activities
problems
Solve problems involving shortest route, minimal spanning tree, and maximal flow algorithms
Identify the concepts and use of PERT to plan and control projects
Outline the steps in constructing a PERT network.
Define the concepts of critical path method
Show the use of CPM in the planning and control of projects
Outline the steps in determining the critical path
Solve problems involving PERT and CPM
others Integrity Indicators:
Accountability,
Transparency and Honesty Societal responsibility Indicators:
Commitment andInvolvement
assistance provided for students learning difficulty in the course)
Recitation
Written examinations
Alternative summative assessments (reflection papers/
critical analysis)
Asynchronous
teaching and learning using Canvas LMS Platform in providing offline content
resources (readings, lecture notes,
recorded lectures, detailed guides, etc., in print or digital format) and other activities.
Synchronous
teaching and learning through webinars, live broadcasts, chats and teleconferences for real-time teacher- student engagement.
18 F I N A L E X A M I N A T I O N
References:
Anderson, D. R. (2019).An introduction to management science: Quantitative approaches to decision making. (14thEd.).
Australia: Cengage Learning.
Cobb & Douglas (2018).Operations research.Forest Hills, NY: Willford Press.
Hillier, F. (2015).Introduction to operations research(10thed.). New York: McGraw-Hill Education.
Render, B., Stair, T. et.al. (2015).Quantitative analysis for management(12thed.). Boston: Pearson Education Inc.
San Cristobal Mateo, J. R. (2015).Management science, operations research and project management: modelling, evaluation, scheduling, monitoring. England: Gower.
Rardin, R. (2017).Optimization in operations research 2nd ed.Boston: Pearson.
San Pedro, L. S.L. (2017).Operations research for business management. Manila: Unlimited Books Library Services & Publishing Sirug, W. (2015).Basic quantitative methods for business: an introduction to operations research/management science(revised).
Intramuros: Mindshapers Co.
Taha, H.A. (2017).Operations research: an introduction(10thed.) England: Pearson Education Limited Online References:
Books 24x7
AccessEngineering EBSCODantzig, E-book:
G.B. (2016).Linear programming and extensions.Retrieved from eBook Collection (EBSCOhost) database.
Truma, Y. (2014).Linear programming: Theory, algorithms and applications.Retrieved from eBook Collection (EBSCOhost) database.
Expectations from Students
Students are held responsible for meeting the standards of performance established for each course. Their performance and compliance with other course requirements are the bases for passing or failing in each course, subject to the rules of the University. The students are expected to take all examinations on the date scheduled, read the assigned topics prior to class, submit and comply with all the requirements of the subject as scheduled, attend each class on time and participate actively in the discussions.
Furthermore, assignments such as reports, reaction papers and the like shall be submitted on the set deadline as scheduled by the faculty. Extension of submission is approved for students with valid reasons like death in the family, hospitalization and other unforeseen events. Hence, certificates are needed for official documentation. Students assigned by the University in extracurricular activities (Choral, Dance Troupe and Athletes) are excused from attending the class, however, said students are not excused from classroom activities that coincide the said University activities. Special quiz is given to students with valid reasons like death in the family, hospitalization and other unforeseen events. Hence, certificates are needed for official documentation. Likewise, special major examination is given to students with the same reasons above. Attendance shall be checked every meeting. Students shall be expected to be punctual in their classes. And observance of classroom decorum is hereby required as prescribed by student’s handbook.
Academic Integrity
It is the mission of the University to train its students in the highest levels of professionalism and integrity. In support of this, academic integrity is highly valued and violations are considered serious offenses. Examples of violations of academic integrity include, but are not limited to, the following:
1.Plagiarism– using ideas, data or language of another without specific or proper acknowledgment. Example: Copying text from the Web site without quoting or properly citing the page URL, using crib sheet during examination. For a clear description of what constitutes plagiarism as well as strategies for avoiding it, students may refer to the HAU Student Handbook 2019-2020, Table of Offenses and Corresponding Sanctions B.7. For citation styles, students may refer to APA Style 6th Edition.
2.Cheating – using or attempting to use unauthorized assistance, materials, or study aids during examination or other academic work. Examples: using a cheat sheet in a quiz or exam, altering a grade exam and resubmitting it for a better grade. For the Policy in Cheating, students may refer to the HAU Student Handbook 2019-2020, Appendix I.
3.Fabrication– submitting contrived or improperly altered information in any academic requirements. Examples: making up data for a research project, changing data to bias its interpretation, citing nonexistent articles, contriving sources. Student may refer to HAU Student Handbook 2019-2020, Table of Offenses and Corresponding Sanctions B.7.
Policy on Absences
1. Students should not incur absences of more than 20% of the required total number of class and laboratory periods in a given semester.
a. The maximum absences allowed per semester are:
For subjects held 1x a week, a maximum of 3 absences;
For subjects held 2x a week, a maximum of 7 absences; and For subjects held 3x a week, a maximum of 10 absences.
2. A student who incurs more than the allowed number of absences in any subject shall be given a mark of “FA” as his final rating for the semester, regardless of his performance in the class.
3. Attendance is counted from the first official day of regular classes regardless of the date of enrolment.
Other Policies
Departmentalized when it comes to major exams such as Prelim, Midterms and Finals.
Minimum of two (2) quizzes for every one (1) unit course will be given per semester.
Drills, Exercises, Seat works, Projects, Recitation/Role playing will be given to the students and will be graded as part of class standing.
Homework Policy will be given at the discretion of the faculty and will be graded as part of class standing.
Grading System (Campus ++):
Class Standing: 60%
Seatworks
Assignments
Boardwork
Quizzes
Critiques
Case Studies
Final Output (Research) Major Exams: 40%
DatePrepared: Date
Effectivity: Prepared By: Reviewed By: Checked By: Certified By: Approved By:
May 2020 May 2020 Maria Elena Y.
Timbang, PIE Faculty
Engr. Ruselle Andrew P. Manalang
OBE Facilitator
Melani B. Cabrera, PIE Chairperson, Industrial
Engineering Program
Dr. Bonifacio V. Ramos Director,
University Library
Dr. Filipina I. De Guzman Dean, School of Engineering
and Architecture