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KAAU
College of Engineering

Industrial Engineering Department
P.O. Box 80204
Jeddah, Saudi Arabia 21589

IE511 Assignment #1

(LP & ILP)

Advanced Optimization Techniques
 

Assignment 1 has three (3) problems.  This assignment can be completed by teams of 6 or 7.  If you work with a partner, only submit one assignment.  Use any optimization software available to  complete the assignment.  Handwritten assignments will not be accepted!  A well-done assignment includes the problem definition, the problem formulation, the solution procedure, and a brief explanation of the results.  Due on the date discussed in class.

 

 
Number  1
 

       Expedition Outfitters manufactures a variety of specially clothing for hiking, skiing, and mountain climbing.  They have decided to begin production on two new parkas designed for use in extremely cold weather; the names selected for the two models are the Mount Everest Parka and the Rocky Mountain Parka.  Their manufacturing plant has 120 hours of cutting time and 120 hours of sewing time available for producing these two parkas.  Each Mount Everest Parka requires 30 minutes of cutting time and 45 minutes of sewing time, and each Rocky Mountain Parka requires 20 minutes of cutting time and 15 minutes of sewing time.  The labor and material cost is $150 for each of Mount Everest Parka and $50 for each Rocky Mountain Parka, and the retail prices through the firm’s mail order catalog are $250 for the Mount Everest Parka and $200 for the Rocky Mountain Parka.  Because management believes that the Mountain Everest Parka is unique coat that will enhance the image of the firm, they have specified that at least 20% of the total production must consist of this model.  Assuming that Expedition Outfitters can sell as many coats of each type as they can produce, how many units of each model should they manufacture to maximize the total profit contribution?

 
 
Number 2
 

      The program manager for Channel 10 would like to determine the best way to allocate the time for the 11:00—11:30 evening news broadcast. Specifically, he would like to determine the number of minutes of broadcast time to devote to local news, national news, weather, and sports. Over the 30-minute broadcast, 10 minutes are set aside for advertising. The station's broadcast policy states that at least 15% of the time available should be devoted to local news coverage; the time devoted to local news or national news must be at least 50% of the total broadcast time; the time devoted to the weather segment must be less than or equal to the time devoted to the sports segment; the time devoted to the sports segment should be no longer than the total time spent on the local and national news; and at least 20% of the time should be devoted to the weather segment. The production costs per minute are $300 for local news, $200 for national news, $100 for weather, and $100 for sports.

       Formulate and solve the above problem using a mathematical programming technique to determine how the 20 available should be used

 
 
Number 3
 

       The Clark County Sheriff’s Department schedules police officers for 8-hour shifts.  The beginning times for the shifts are 8:00 A.M., noon, 4:00 P.M., 8:00 A.M.  An officer beginning a shift at one of these times works for the next 8 hours.  During normal weekday operations, the number of officers needed varies depending on the time of day.  The department staffing guidelines require the following minimum number of officers on duty:   

Time of Day

Minimum Officers on Duty

8:00 A.M. – noon

5

Noon – 4:00 P.M.

6

4:00 P.M. – 8:00 P.M.

10

8:00 P.M. – midnight

7

Midnight – 4:00 A.M.

4

4:00 A.M. – 8:00 A.M.

6

          Determine the number of police officers that should be scheduled to begin the 8-hour shifts at each of the six times (8:00 A.M., noon, 4:00 P.M., 8:00 P.M., midnight, and 4:00 A.M.) to minimize the total number of officers required.

 
 

 

Prof. Dr. Reda.M.S. Abd El-Aal

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