Meet time: Monday, Wednesday, Friday 9:45am-10:50pm, Room 302, Russ Center
Professor: Dr. Xinhui Zhang
Email: xinhui.zhang@wright.edu
Office: 234 Russ Engineering Center
Office Hour: Monday, Wednesday, Friday 11:00 a.m. – 12:00 p.m.
Website: http://www.wright.edu/~xinhui.zhang/
Course Overview: This is an introductory course on Operations Research/Management Science/System Engineering. This course focuses on the deterministic models, especially linear, integer and network flow models as well as the solution techniques such as simplex method and branch and bound. Example problems will be drawn from real world applications in diverse fields such as manufacturing, transportation, and logistics, to name a few. Students are expected to demonstrate their ability to identify applications especially in their field of study, formulate approximate models, obtain and interpret results using standard yet state-of-art mathematical programming packages.
Textbooks: P.A. Jensen and J.F. Bard, Operations Research Models and Methods, John Wiley & Sons, 2003. ISBN: 0-471-38004-0
Reference: D. Bertsimas and J.N. Tsitsiklis, Introduction to Linear Optimization, Athena Scientific, Belmont, 1997. ISBN: 1-886529-19-1
L.A. Wolsey, Integer Programming, John Wiley and Sons, 1998. ISBN: 0-471283-66-5
Software: A state-of-art mathematical programming package Xpress-MP, will be used to solve most of the real world application problems. Please go to Dash Optimization’s web site, www.dashoptimizaiton.com to download a free student version and refer to their sample or menu for details.
Commercial version of this software is kept at the instructor’s lab and will be available for term projects usage upon request.
Grading Policy:
Homework/Quizzes – 10%
Term Project – 25%
Midterm
– 25%
Final Exam – 40%
|
Class |
Topic |
Homework |
|
1. |
Introduction, what is OR, Success stories, a facility location example |
|
|
2. |
Introduction to Math Programming & The use of XPress for the Facility Location & LQ problem |
HW1 |
|
3. |
Introduction to Mathematic modeling (I) |
|
|
4. |
Introduction to Model modeling (II), Formulation rules |
Hw2 |
|
5. |
Introduction to Model modeling (II), What is linear Programming, graphical and tableau techniques |
|
|
6. |
Simplex Algorithm: Tableau solution technique |
Hw3 |
|
7. |
Simplex Algorithm: Two-phase simplex method |
|
|
8. |
Sensitivity analysis, duality |
|
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9. |
Sensitivity analysis |
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10. |
Goal programming formulations |
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11. |
Introduction to integer programming (I) |
|
|
12. |
Integer programming models (II) |
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13. |
Mid term exam |
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14. |
LP, IP and Branch and Bound Algorithm |
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15. |
Introduction to Network models (I) |
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16. |
Network models (II) |
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17. |
Network Flow Methods |
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18. |
Solve Large IP using Commercial Solver -- Xpress |
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19. |
From Theory to Practice |
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20. |
Project Presentation |
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|
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TERM PROJECT DUE |
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Final |
In the week of Nov 14th to Nov 18th |
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Homework:
HW1: Solve the Two Examples using Xpress. Examine the solutions obtained.
HW2: Solve the Workforce Scheduling Problem with consecutive days off and any two days off. Answer the following question: Suppose that employees currently have two consecutive days off. Is it worthwhile to negotiate with say the union to provide a 5% increase of their salary, but give them any two days off?
HW3: LP Models: Chapter 2: problems 14,15.
HW4: Simple Algorithm 1: Chapter 3: problems 1, 5,10,19
Hw5: Integer Program: Chapter 7: Problems 2, 4a, 5
Hw6: Network Flow: Chapter 6: problems 9, 11, 18,
Hw7: Branch and Bound: Chapter 8: problems 1, 2, 3.
LP Model Sets: Blending problem, workforce scheduling, aggregate planning, power distribution, Power Distribution.... ….
LP Method Sets: Simplex Algorithm: Chapter 3: Problems 4, 5, 6, 8, 9, 10
Optimality, Infeasibility and Unbounded: Chapter 3: Problems 12, 13
Two Phase Simplex: Chapter 3: Problems 18 and 19
Understanding Simplex: Problem 20, 21
IP Problems Sets: Fixed Charge Model, Capacitated/uncapacitated Facility Location, Traveling Salesman Problem, Directed Minimal Spanning Tree Problem, Cutting Stock, Assembly Line Balancing, Manufacturing with nonlinear objective.
Chapter 7: Problems 2, 4,5,7,11,13,15,17,23
Chapter 8: Problems 1, 2 , 3, 10
Network Flow Sets: Assignment
Problem, Transportation Problem, Maximal Flow, Shortest Path and their LP/IP
models
Class Policies
1. I expect to see you in class and be active in class. If you are going to miss class, drop me an email and please spend time to make up material missed.
2. If you miss an exam without prior coordination with your instructor, you will receive a zero.
3. Quizzes will be given periodically throughout the quarter (4-5), with make-ups.
4. You are encouraged to solve the problems in the exercise especially if you want to get an A in the class. It is inadequate to rely solely on homework.
Term Project / Literature
Contribution:
Term Project for In-Class Students
In class students will be asked to work in a 2-3 person group to implement an optimization project of your own interests. You will be asked to identify a problem, build the mathematical model, code it in Xpress, interpret the result, implement it if possible and finally give a 15 minute presentation in class.
Literature Contribution for Distance Learning Students
Instead of term project, your can select to the literature contribution option. You are to select papers from journals such as Interfaces or papers related to Edelman competition. The paper should an application based paper but should have enough content on models. A paper can be used by only one student. Please give the title and source of your paper to me no later than the third week of the class so the paper will be reserved. For each paper present a typed abstract prepared with Microsoft Word. The abstract should be no more that four pages long and include: a formal reference for the article, a description of the content. The abstracts are due at the same due date of the term project.
Besides, you will also need to prepare for a 15 minute presentation slides. In case you can not present it or record it, email it to me and I will call you and the presentation will take place at one of the times that fits your schedule. Use a presentation program such as Power Point for slide preparation.
Honesty & Integrity:
Students are expected be aware of and to adhere to the university standards of academic honesty. Violations include, but are not limited to, submitting work which is not your own for credit. Students may discuss homework assignments with others but, with the exception of explicit group assignments, are expected to complete and turn in their own work. Copying or sharing of work (including computer files) is prohibited, except as explicitly authorized by the instructors.