Linear Programming: Sensitivity analysis and interpretation of solution PDF

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Summary

Professor: Shashi Shahi...

Description

Linear Programming: Sensitivity analysis and interpretation of solution -

Sensitivity Analysis - How changes in the coefficients of an optimization model affect the optimal solution - Changes include - Change in a coefficient of the objective function - Change in the right-hand-side value for a constraint - Importance - Real world problems exist in a changing environment - Prices change - Demand changes - New machinery is purchased - Stock prices fluctuate - Employee turnover - Etc

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Range of optimality - Provides the range of values over which the current solution will remain optimal

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Sensitivity Analysis: Computer solution - Optimal Objective Value = 7668.00000 -

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Variable

Value

Reduced Cost

S

540.00000

0.00000

D

252.00000

0.00000

Optimal Solution and objective value - Optimal solution: S = 540, D = 252 - Maximum profit = 7668 Reduced Cost - On S and D is 0 - This means that the change in S and D by one unit will not have an effect on the optimal solution

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Slack/surplus Constraint

Slack/Surplus

1

0.00000

2

120.00000

3

0.00000

4

18.00000

Dual value Dual Value 4.37500 0.00000 6.93750 0.00000 -

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With an additional 1 hour to constraint 1, the optimal value will increase by $4.37 - With an additional 1 hour to constraint 3, the optimal value increases by $6.94 Objective coefficients

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Variable

Objective Coefficient

Allowable Increase

Allowable Decrease

S

10.00000

3.50000

3.70000

D

9.00000

5.28571

2.33333

Allowable increase or decrease without changing the optimal solution

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Constraints

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Constraint

RHS Value

Allowable Increase

Allowable Decrease

1

630.00000

52.36364

134.40000

2

600.00000

Infinite

120.00000

3

708.00000

192.00000

128.00000

4

135.00000

Infinite

18.00000

Allowable increase or decrease without changing the optimal solution

Limitations of classical sensitivity analysis - Simultaneous changes in input data - Sensitivity analysis is based on the assumption that only one coefficient and everything else remains the same - In the real world, 2 or more coefficients can change simultaneously - Re-run the model with changed coefficients - Changes in constraint coefficients - Sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint - Non-intuitive dual values - Constraints with variables on both left and right sides often lead to dual values that have a no-intuitive explanation...