Operation and management

Ideally you should begin working on the exam immediately. It should be completed independently (in an ideal world) by each student. (Since no monitoring process can exist it will be OK for you to discuss the problems with other students in general terms. But it is better if you do the analysis by yourself and you must do your own computer work and written submissions.) If anyone submits a copy of an assignment or exam, everyone with that submission will get a zero on that assignment or exam. If you submit work done by someone else you will be in violation of the rules of academic integrity and reported to the Dean of Students Office. If something is unclear to you about the exam, ask me. Write your name on all pages you submit. Answers without written backup do not have any value; i.e. show your work. Either submit each problem on a separate page or make a summary sheet with your answers. INCLUDE this statement on your submission:

I, __________________, have not, and will not violate the rules of academic integrity (↑↑↑) on this exam.

(fill in name) Sign here if this statement is true. ________________________________

Question 9 and Question 10 are Extra Credit Questions

1. GCE is ready to award contracts for printing their annual report. For the past several years, the report has been printed by JP and LL. A new firm, BP, has inquired into the possibility of doing a portion of the printing. The quality and service level provided by LL has been extremely high; in fact, only 1% of their reports have had to be discarded because of quality problems. JP has also had a high quality level historically, producing an average of only 2% unacceptable reports. Since GCE has had no experience with BP, they have estimated their defective rate to be 10%. GC would like to determine how many reports should be printed by each firm to obtain 80,000 acceptable-quality reports. To ensure that BP will receive some of the contract, management has specified that the number of reports awarded to BP must be at least 15% of the volume given to JP. In addition, the total volume assigned to BP, JP, and LL should not exceed 25,000, 45,000, and 55,000 copies respectively. Because of the long-term relationship that has developed with LL, management has also specified that at least 25,000 reports should be awarded to LL. The cost per copy is $2.50 for BP, $2.60 for JP, and $2.80 for LL.

a. Formulate a linear program for determining how many copies should be assigned to each printing firm to minimize the total cost of obtaining 80,000 acceptable-quality reports.

b. Solve this problem using Excel.

c. Suppose that the quality level for BP is much better than estimated. How would this change your answer (in “b”).

d. Suppose that management is willing to reconsider the requirement that LL be awarded at least 30,000 reports? How would this change your answer (in “b”).

2. (WA) Bexter Labs produces three products: A, B, and C. Bexter can sell up to 30 units of product A, up to 20 units of product B, and up to 20 units of product C. Each unit of product C uses (up) 2 units of A and 3 units of B and incurs $5 in processing costs. Products A and B are produced from either raw material 1 or raw material 2. It costs $6 to purchase and process 1 unit of raw material 1. Each process unit of raw material 1 yields 2 units of A and 3 units of B. It costs $3 to purchase and process 1 unit of raw material 2. Each process unit of raw material 2 yields 1 unit of A and 2 units of B. The unit prices or the products are A,$5; B, $4; C,$25. The quality levels of each product are A,8; B, 7; C, 6. The average quality level of the units sold must be at least 7. Determine how to maximize Bexter’s profit.

3. GNO is a retail phone-catalog company that specializes in outdoor clothing and equipment. A phone station at the company will be staffed with either full-time operators of temporary operators eight hours per day. Full-time operators, because of their experience and training, process more orders and make fewer mistakes than temporary operators. However, temporary operators are cheaper because of a lower wage rate and they are not paid benefits. A full-time operator can process about 350 orders per week, whereas a temporary operator can process about 280 orders per week. A full-time operator will average 1 defective order per week and a part-time operator will incur about 3 defective orders per week. The company wants to limit defective orders to 175 per week. The cost of staffing a station with full-time operators is $700 per week and the cost of a station with part-time operators is $500 per week. Using historical data and forecasting techniques, the company has developed estimates of phone orders for an eight-week period as follows:

The company does not want to hire or dismiss full-time employees after the first week (i.e. the company wants a constant group of full-time operators over the eight-week period). The company wants to determine how many full-time operators it needs and how many temporary operators to hire each week to meet weekly demand while minimizing labor costs.

a. Formulate a linear programming problem for this problem.

b. Solve this problem using Excel.

GNO is going to alter its staffing policy. Instead of hiring a constant group of full-time operators for the entire eight-week planning, it has decided to hire and add full-time operators as the eight-week period progresses, although once it hires full-time operators it will not dismiss them.

c. Reformulate the linear programming to reflect this altered policy and solve to determine the cost savings (if any).

4. MW is a large discount store that operates seven days per week. The store needs the following number of full-time employees working each day of the week.

Each employee must work five consecutive days each week and then have two days off. For example, any employee who works Sunday through Thursday has Friday and Saturday off. The store currently has a total of 200 employees available to work. MW has developed the following set of prioritized goals for employee scheduling.

1. The store would like to avoid hiring any additional employees.

2. The most important day for the store to be fully staffed is Saturday, followed by Sunday, followed by Friday.

3. The store would like to fully staff the remaining four days of the week.

a. Use preemptive goal programming to determine MW employee scheduling for the week.

b. If each employee costs $800, each missing employee on Saturday costs $600, on Sunday $400, on Friday $300, and on Monday through Thursday $200 determine the new schedule which minimizes these costs (assuming there are no other priorities among the goals).

5. You are in charge of loading cargo ships for ICC at a major east coast port. You have been asked to prepare a loading plan for an ICC freighter bound for Africa. An agricultural commodities dealer would like to transport the following products aboard this ship:

You can elect to load any or all of the available commodities. However, the ship has three cargo holds with the following capacity restrictions:

More than one type of commodity can be placed in the same cargo hold. However, because of balance considerations, the weight in the forward cargo hold must be within 10% of the weight in the rear cargo hold, and the weight in the center cargo hold must be between 40% and 60% of the total weight on board.

a. Determine a profit-maximizing loading plan for the commodities. What is the maximum profit and the loading plan that achieves it.

b. Suppose each one of the cargo holds could be expanded. Which holds and which forms of expansion (weight or volume) would allow ICC to increase its profits on this trip, and what is the marginal value of each form of expansion?

6. State University must purchase 1100 computers from three vendors. Vendor 1 charges $500 per computer plus a total delivery charge of $5,000. Vendor 2 charges $350 per computer plus a total delivery charge of $4,000. Vendor 3 charges $250 per computer plus a total delivery charge of $6,000. Vendor 1 will sell the university at most 500 computers, vendor 2, at most 900, and vendor 3, at most 400. The minimum order from a vendor is 200 computers. Determine how to minimize the cost of purchasing the needed computers.

a. Interpretation “a” - Each vendor must supply at least the minimum. Hence all vendors are used and all delivery charges are incurred.

b. Interpretation “b” - Each vendor must supply at least the minimum only if that vendor is used. Hence delivery charges are incurred only for those vendors used. Hint - A fixed cost can be modeled by using a binary integer variable (to be discussed in class).

7. Hint - There may be multiple leases that are used.

Length of Lease Cost per Month ($)

1 4000

2 3700

3 3225

4 3040

The Managerial Report should be at most one page (plus back-up material) and include:

a. Answers to questions 1, 2, and 3 (see Managerial Report above).

b. A statement of any assumptions that you made (and why if appropriate).

c. Your relevant Excel output.

8. IF YOU DO EXTRA CREDIT QUESTION 9 YOU DO NOT HAVE TO DO QUESTION 8

Hint - This problem is best solved using binary integer variables.

To graduate from Southeastern University with a major in operations research (OR), a student must complete at least two math courses, at least two OR courses, and at least two computer courses. Some courses can be used to fulfill more than one requirement. Calculus can fulfill the math requirement; Operations Research can fulfill the math and OR requirements; Data Structures can fulfill the computer and math requirements; Business Statistics can fulfill the math and OR requirements; Computer Simulation can fulfill the OR and computer requirements; Introduction to Computer Programming can fulfill the computer requirement; and Forecasting can fulfill the OR and math requirements. Some courses are prerequisites for others: Calculus is a prerequisite for Business Statistics; Introduction to Computer Programming is a prerequisite for Computer Simulation and for Data Structures; and Business statistics is a prerequisite for Forecasting. Determine how to minimize the number of courses needed to satisfy the major requirements. (Hint: Because Calculus is a prerequisite for Business Statistics, for example, you will need a constraint that ensures that the changing cell for Calculus is greater than or equal to the changing cell for Business Statistics.)

OPR 3450 - Fall 2019 Exam 1 – due dates to be determined page 4 of 6

a. Formulate this problem as a binary integer programming model.

b. Solve this problem in Excel. What is her schedule? What is her GPA and her hours worked?

9. Assigning Art Case from textbook part a only (part b & c are optional)

(There is a helper Excel file which will save you some typing)

(SKIP TO THE NEXT PAGE and THEN RETURN TO THIS SPOT)

10. EXTRA CREDIT from textbook Do Cases 6-4 AND 7-3 below

SundayMondayTuesdayWednesdayThursdayFridaySaturday

Number of Employees19090110140135170215

Commodity1234

Tons Available4,0003,0002,0001,000

Volume per Ton (cu. Ft.)40256050

Profit per Ton ($)70506080

Cargo HoldForwardCenterRear

Weight Capacity (tons)3,0005,0002,000

Volume Capacity (cu ft)100,000150,000120,000

ProductSales LimitQualitySelling PriceCategoryCostsProducesNeeds

A308$5Raw Material 1$62A & 3B

B207$4Raw Material 2$31A & 2B

C206$25Product C$52A & 3B

Average Needed7

Week12345678

Orders20,00021,00026,00027,00033,00030,00027,00031,000