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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

Extra CreditProblem 5 Page 76Gothams Finest

Group 3

Saud Aldegaiter

Daniel Bonneville

Tamara Vail

October 18, 2011

IE 416

Dr. Parisay


Outline
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


Problem statement
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.


Summary
Summary

Consecutive Shifts = $12 an hour

Not Consecutive Shifts = $18 an hour


Formulation of problem
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


Formulation of problem1
Formulation of Problem

Constraints:

Objective Function:

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


Winqsb input
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




Sensitivity analysis of o f
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



Sensitivity analysis of o f2
Sensitivity Analysis of O.F.

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


Sensitivity analysis of rhs
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.



Report to manager
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



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