AMS 341 Fall 2018

AMS 341, Operations Research I: Deterministic Models Fall 2018

Class Time and Place: TTh 11:30 -12:50 pm, Harriman 137

Instructor: Prof. Alan Tucker

Office: Eng 127 (back right corner room);

Office Hours:TuTh 1:00-2:20, Wed 11am - 1pm, Fri 10am - noon, and by appointment.

How to Reach Prof. Tucker: telephone: 2-9941; e-mail:

Course Assistants-- all office hours in Harriman 132:
Course Text: Operations Research , by Wayne L. Winston, 4th edition.

Tests: one mid-term and a (non-cumulative) final. The final is Friday, Dec. 19th, 11:15am-1:45pm in regular classroom. Tests will be closed book but a one-page sheet of notes will be permitted for the final. The mid-term counts 35% of the grade and the final 50% of the grade.

Homework: There will be 9 homework assignments, due approximately weekly. They will count about 15% of the grade. Homework will be submitted through Blackboard and graded with scores oF 5,4,3,2,1,0.

Software: LP's can be solved by many software programs. The textbook uses Lindo and you can download 'classic' Lindo free at
Americans with Disabilities Act: If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC(Educational Communications Center) Building, Room 128, (631)632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.
Academic Integrity: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website at
Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.
COURSE OUTLINE: The following topics will be covered: (Background recommended reading Chapters 1-2), LP formulations (Chapter 3), The Simplex method (Chapter 4), Sensitivity analysis (Chapter 5 Sections 1-3) Duality, (Chapter 6, Sections 4-8), Transportation and Assignment problems (Chapter 7 Sections 1-3, 5), Integer programming (Chapter 9 Sections 1-4, 8) and Dynamic Programming (Chapter 13, Sections 1-2, 4-5).
Learning outcomes:

1.Become familiar with the many optimization problems arising in diverse settings that can modeled as linear programs, and
  gain experience in constructing mathematical models for an array of such optimization problems.
 * Maximizing income subject to supply constraints;
 * Minimizing costs subject to minimum requirements;
 * Scheduling problems;
 * short-term and long-term financial planning problems;
 * blending problems;
 * multi-period planning problems.

2.Learn to solve linear programs geometrically and with the simplex algorithm.
 * putting linear programs in standard form with slack and excess variables;
 * finding an initial basic feasible solution (using big M or two-phase simplex for min problems);
 * choosing which variable enters and which variable leaves the basis;
 * handling unbounded and infeasible problems.

3.Understand sensitivity analysis and its connection with the theory of dual linear programs.
 * shadow prices and reduced costs;
 * range for objective function coefficients and right-hand sides;
 * connections to the dual linear programs and complementary slackness.

4.Learn specialized algorithms for solving network problems, such as transportation problems  and critical path problems.
 * traansportation problem;
 * assignment problems;
 * critical path problem.

5.Model discrete optimization problems with integer programs and solve using a branch-and-bound strategy.
 * model various discrete optimization problems as integer programs;
 * solve integer problems using a branch-and-bound strategy.

6.Solve simple dynamic programming problems.
 * model a class of discrete optimization problems as dynamic programs;
 * solve simple dynamic programs using a squential solution technique

WEEK-BY-WEEK SYLLABUS and HOMEWORK Week 1-- Aug28-30: Formulations, Read Chap. 3,Sect. 1-5. Homework 1 due on Tues. Sept 4: p.63 #6, p.68 #2,3,7,8, p. 71 #4, p.76 #6 Week 2&3-- Sept 4 - 6 and Sept 11 : More Formulation, Read Chap. 3, Sect. 8-12. Homework 2 due on Thurs. Sept 13: p. 92-3 #2,9, p.98: #2, p. 104 #4, p. 109 #8. Week 4--Sept 13 and 18-20: Simplex Method, Read Chap. 4, Sect. 1-6. Homework 3 due on Tues. Sep 25: p. 139 #3, p.149 #3,#5. Week 5&6--Sept 25-27, Oct 2; More Simplex, Read Chap.4, Sect. 7-13. Homework 4 due on Thurs. Oct 4: p. 154 #5, p. 158 #3, p. 178 #1,#4, then resolve #1,#4 using 2-phase method. Week 7-- Oct 4, 11-16: Sensitivity and Duality, Read Ch. 5, Sec. 1-3, Ch. 6, Sec. 5,6. Tucker tableau Homework 5 due on Thurs. Oct. 18: p. 256 #5abc, p 301 #4, 346-7 #4abcd, solve Giapetto problem by Tucker tableau and give statement and solution of dual problem. Check your answers usingLindo, Excel, etc. Make sure you show your calculations, not just answers. Week 8-- Oct 18-23: Review and Mid-Term Test (Tues. Oct 23). Practice MidTerm Midterm Solutions Solutions to HWs 1-5 Week 9&10-- Oct 25-30 & Nov 1-6: Transportation Problem, Read Chap. 7, Sec.1-3. Better transportation problem presentation Homework 6 due Thurs. Nov 8: p.371-2 #1, 3, 6, for each, FORMULATE as a tableau(like p.364) and find an initial basic feasible solution for using the northwest corner rule. SOLVE problems #1 and #6, once starting with a) northwest corner rule, AND once starting with b) min-cost method (in total,four solutions). Week 11-- Nov 8-13: Assignment and Network Problems, Read Ch. 7, Sec. 5,6; Ch. 8 Sec. 2,4. Homework 7 due on Thurs Nov 15: p. 398-9 #1,2, p. 403 #2, p.418 #3,4, p. 447 #5,6,7. Week 12&13--Nov15-20, 21: Integer Programming, Read Chap 9, Sec. 1-3. Homework 8 due on Thurs. Nov 26: p. 503 #1,2,4,14, p. 522 #1 (show branch-bound tree). Week 13&14-- Nov 27-29, Dec 4-6: Dynamic Programming and Review, Read Ch. 18, Sec. 2,4. Homework 9 due on Thurs. Dec 6: p. 985 #1,2 (solve #2 both ways). Solutions to Homeworks#6-8 Spring 2012 final Solutions to Spring 2012 Final

Final Exam: Wed. Dec 19th,11:15 to 1:45; regular classroom. You may bring one page (possibly two-sided) with general solution procedures. NO NUMERICAL EXAMPLES ALLOWED. If there are numbers on your page, it will be removed.