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Extra Credit Problem 5 Page 76 Gothams Finest

Extra Credit Problem 5 Page 76 Gothams Finest. Group 3 Saud Aldegaiter Daniel Bonneville Tamara Vail October 18, 2011 IE 416 Dr. Parisay. Outline. Problem Statement Summary of Problem Formulation of Problem WinQSB Inputs and Solution Solution Summary

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Extra Credit Problem 5 Page 76 Gothams Finest

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  1. Extra CreditProblem 5 Page 76Gothams Finest Group 3 Saud Aldegaiter Daniel Bonneville Tamara Vail October 18, 2011 IE 416 Dr. Parisay

  2. Outline • Problem Statement • Summary of Problem • Formulation of Problem • WinQSB Inputs and Solution • Solution Summary • Objective Function Sensitivity Analysis • RHS Sensitivity Analysis • Report to Manager

  3. Problem Statement Pg. 76 Problem 5 Each day, workers at the Gotham City Police Department work two 6-hour shift chosen from 12 a.m. to 6 a.m., 6 a.m. to 12 p.m., 12 p.m. to 6 p.m., and 6 p.m. to 12 a.m. The number of workers are needed during each shift are shown at table below. Workers whose two shifts are consecutive are paid $12 per hour; workers whose shifts are not consecutive are paid $18 per hour. Formulate an LP that can be used to minimize the cost of meeting the daily work-force demands of the Gotham City Police Department.

  4. Summary Consecutive Shifts = $12 an hour Not Consecutive Shifts = $18 an hour

  5. Formulation of Problem Decision Variables: Xi= Number of workers whose two shifts are consecutive and start at shift I (Shift i=1,2,3,4) Yj= Number of workers whose two shifts are not consecutive and start at shift j (Shift j=1,2) Xi ≥ 0 Yj ≥ 0

  6. Formulation of Problem Constraints: Objective Function: Minimize Z = 12(X1+X2+X3+X4) + 18(Y1+Y2)

  7. WinQSB Input Consecutive Shift 1 = X1 Consecutive Shift 2 = X2 Consecutive Shift 3 = X3 Consecutive Shift 4 = X4 Not Consecutive Shift 1 = Y1 Not Consecutive Shift 2 = Y2

  8. WinQSB Solution

  9. Solution Summary

  10. Sensitivity Analysis of O.F. • The only possible SA that can be done to the O.F. Is the not consecutive shift 2 because it is the only variable that has an RC value. • Therefore we changed the hourly rate from $18 to $6 based on RC=12

  11. Sensitivity Analysis of O.F.

  12. Sensitivity Analysis of O.F. • Although the Zmin decreases we realize that it is not practical for the hourly wage to decrease by $12.

  13. Sensitivity Analysis of RHS • We choose to decrease the number of workers on shift 3 for a couple reasons: • It has one of the largest SP (SP=9) • More flexibility in the allowable range which will minimize our cost.

  14. Sensitivity Analysis of RHS

  15. Report to Manager • Minimum cost $276 • Decrease hourly wage for non consecutive shift 2 from $18 to $6 • Decrease number of workers in shift 3 from 12 to 11 which is within the range

  16. QUESTIONS?

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