Sensitivity Analysis
Sensitivity Analysis
• When solving an LP problem we assume that values of all model coefficients are known with certainty.
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• Such certainty rarely exists.
• Sensitivity analysis helps answer questions about how sensitive the optimal solution is to changes in various coefficients in a model.
General Form of a Linear Programming (LP) Problem
MAX (or MIN): c1X1 + c2X2 + … + cnXn
Subject to: a11X1 + a12X2 + … + a1nXn <= b1
ak1X1 + ak2X2 + ... + aknXn <= bk
am1X1 + am2X2 + ... + amnXn = bm
How sensitive is a solution to changes in the ci, aij, and bi? 1-3
Hot Tubs LP Problem, Redux
Hydro- Profit
Unit Profit
$ 350 $ 300
12 16 2880
Optimal Production Levels
Shadow Prices
Amounts by which the objective function value will change given a one-unit change in the right-hand side of the constraint (all other values held constant).
Python PuLP
Microsoft Excel 15.0 Sensitivity Report
Worksheet: [Opt_HotTubs_Sensitivity.xlsx]Model Expanded Report Created: 2/18/2018 10:49:57 AM
Variable Cells
Final Cell Name Value $B$10 Production Level Required 122
Reduced Cost
Objective Allowable Allowable Coefficient Increase Decrease
350 100 20 300 50 40 320 13.33333333 1E+30
Constraint Allowable Allowable R.H. Side Increase Decrease
200 7 26 1566 234 126 2880 1E+30 168
$C$10 Production Level Hydro-Lux $D$10 Production Level Typhoon
Constraints
$F$6 Pumps Used
$F$7 Labor Used
$F$8 Tubing Used
0 -13.33333333
Final Value 200 1566 2712
16.66666667 0
Excel Solver sensitivity report
Shadow Prices
Amounts by which the objective function value will change given a one-unit change in the right-hand side of the constraint (all other values held constant).
Microsoft Excel 15.0 Sensitivity Report
Worksheet: [Opt_HotTubs_Sensitivity.xlsx]Model Expanded Report Created: 2/18/2018 10:49:57 AM
Variable Cells
Final Cell Name Value $B$10 Production Level Required 122
Reduced Cost
Objective Allowable Allowable Coefficient Increase Decrease
350 100 20 300 50 40 320 13.33333333 1E+30
Constraint Allowable Allowable R.H. Side Increase Decrease
200 7 26 1566 234 126 2880 1E+30 168
$C$10 Production Level Hydro-Lux $D$10 Production Level Typhoon
Constraints
$F$6 Pumps Used
$F$7 Labor Used
$F$8 Tubing Used
0 -13.33333333
Final Value 200 1566 2712
16.66666667 0
R lpSolveAPI Excel Solver sensitivity report
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