Principles of Operation Research
MSCI 603 (Online) Fall 2013
Take Home Midterm Exam (Due date: November 3, 2013)
The midterm exam is divided into two sections: Theoretical section and Programming Section. The
first section worth 110 Points distributed over 5 questions. The programming section consists of
two parts, reading part and implementation part and it worth 40 points. Scan your solution and
submit a studentID.zip fie (that contains .pdf for your midterm solution and .xls f or your excel
solver programming part) into the Midterm Drop box on LEARN.
Section I: Theory of Linear Programming [ 110 Points]
Problem 1. [20 Points] Comfortable Hands is a company which features a product line of winter
gloves for the entire family Ã¢â‚¬â€ men, women, and children. They are trying to decide what mix of
these three types of gloves to produce. Comfortable HandsÃ¢â‚¬â„¢ manufacturing labor force is
unionized. Each full-time employee works a 40-hour week. In addition, by union contract, the
number of full-time employees can never drop below 20. Nonunion, part -time workers can also be
hired with the following union-imposed restrictions: (1) each part -time worker works 20 hours per
week, and (2) there must be at least 2 full-time employees for each part -time employee. All three
types of gloves are made out of the same 100% genuine cowhide leather. Comfortable Hands has
a long term contract with a supplier of the leather, and receives a 5,000 square feet shipment of the
material each week. The material requirements and labor requirements, along with the gross profit
per glove sold (not considering labor costs) is given in the following table.
Each full-time employee earns $13 per hour, while each part -time employee earns $10 per hour.
Management wishes to know what mix of each of the three types of gloves to produce per week,
as well as how many full-time and how many part -time workers to emplo y. They would like to
maximize their net profit Ã¢â‚¬â€ their gross profit from sales minus their labor costs. Formulate a linear
programming model for this problem.
Problem 4. [20 Points] Consider the following linear Program, find the optimal solution (if exists)
using the big M Method
Problem 5. [20 Points] Consider the following LP problem of a company that prepares an
advertisement plan. In this problem, x1 represents the number of advertisements placed on radio
and x2 represents the number of advertisements placed on TV.
The feasible region and optimality function (the isoprofit line called F) is shown in the following
figure. The optimal solution is on point C, which lies on the intersection of the lines representing
constraints 1 and 2 (?1 and ?2).
1. Find the shadow price for constraint 2 and interpret it?
2. Suppose that the coefficient of x1 in the objective function is not estimated correctly. It
should be 9,000 instead of 10,000. In that case, is point C still optimal?
3. Suppose that the budget is increased to 66,000 from 44,000. Is the constraints 1 and 2 are
still binding? That is, does the optimal solution still lies on the intersection of ?1 and ?2?
Section II: Practice of Linear Programming [40 Points]
You can see below a list of articles that based on real-life problems, modeled and solved using
O.R. techniques. You can select any paper from the below list:
Part 1 [20 points]: once you select your paper, read it carefully and summarize it, and write a 4
pages report that
1. Describe the problem in terms of general context and framework.
2. Discuss the mathematical model.
3. Discuss the strengths and limitations of the model.
4. Discuss the approach adopted to solve the model.
5. Discuss the implementation of the solution, its managerial implications and savings.
Part 2 [20 points]: Mini-Case Implementation
1. Write a mini-case (half a page) as a replica of the problem discussed in the paper.
2. Choose an example and generate hypothetical data for it
3. Write the mathematical model and solve it using your favourite software
The mini-case/ example should be small, preferably a particular case of the problem discussed in
the article. It should not be oversimplified nor complicated. Use your judgment to come -up with a
mini case that is representative enough of the article or parts of it and that is easy to understand.
List of articles
1. Bixby, Ann, Brian Downs, and Mike Self. -A scheduling and capable -to-promise
application for Swift & Company.- Interfaces 36.1 (2006): 69-86.
2. Tyagi, Rajesh, et al. -GE plastics optimizes the two-echelon global fulfillment
network at its high performance polymers division.- Interfaces 34.5 (2004): 359-366.
3. Ahire, Sanjay L., et al. -Operations research helps reshape operations strategy at
Standard Register Company.- Interfaces 37.6 (2007): 553-565.
4. Fleischmann, Bernhard, Sonja Ferber, and Peter Henrich. -Strategic planning of
BMWÃ¢â‚¬â„¢s global production network.- Interfaces 36.3 (2006): 194-208
5. Chung, Casey, et al. -A Short-Range Scheduling Model for Blockbuster's OrderProcessing Operation.- Interfaces 41.5 (2011): 466-484.
6. Gordon, Lynn, and Erhan Erkut. -Improving volunteer scheduling for the Edmonton
Folk Festival.- Interfaces 34.5 (2004): 367-376
7. Pajunas, Anthony, et al. -Optimizing Highway Transportation at the United States
Postal Service.- Interfaces 37.6 (2007): 515-525.
8. Yang, De-Li, and Weiqin Mou. -An integrated decision support system in a Chinese
chemical plant.- Interfaces 23.6 (1993): 93-100.
9. Muñoz, David Fernando, et al. -Indeval develops a new operating and settlement
system using operations research.- Interfaces 41.1 (2011): 8-17.
10. LeBlanc, Larry J., et al. -Nu-koteÃ¢â‚¬â„¢s Spreadsheet Linear-Programming Models for
Optimizing Transportation.- Interfaces 34.2 (2004): 139-146.