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# Extra Credit Problem 5 Page 76 Gothams Finest - PowerPoint PPT Presentation

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 CreditProblem 5 Page 76Gothams Finest

Group 3

Saud Aldegaiter

Daniel Bonneville

Tamara Vail

October 18, 2011

IE 416

Dr. Parisay

• Problem Statement

• Summary of Problem

• Formulation of Problem

• WinQSB Inputs and Solution

• Solution Summary

• Objective Function Sensitivity Analysis

• RHS Sensitivity Analysis

• Report to Manager

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.

Consecutive Shifts = \$12 an hour

Not Consecutive Shifts = \$18 an hour

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

Constraints:

Objective Function:

Minimize Z = 12(X1+X2+X3+X4) + 18(Y1+Y2)

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

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

• Although the Zmin decreases we realize that it is not practical for the hourly wage to decrease by \$12.

• 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.

• 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