The MOSEK Python optimizer API manual Version 7.0 (Revision 141)

15.4. SENSITIVITY ANALYSIS FOR LINEAR PROBLEMS 191
Basis type
Con. β 1 β 2 σ 1 σ 2
1 −300.00 0.00 3.00 3.00
2 −700.00 +∞ 0.00 0.00
3 −500.00 0.00 3.00 3.00
4 −0.00 500.00 4.00 4.00
5 −0.00 300.00 5.00 5.00
6 −0.00 700.00 5.00 5.00
7 −500.00 700.00 2.00 2.00
Var. β 1 β 2 σ 1 σ 2
x 11 −∞ 300.00 0.00 0.00
x 12 −∞ 100.00 0.00 0.00
x 23 −∞ 0.00 0.00 0.00
x 24 −∞ 500.00 0.00 0.00
x 31 −∞ 500.00 0.00 0.00
x 33 −∞ 500.00 0.00 0.00
x 34 −0.000000 500.00 2.00 2.00
Optimal partition type
Con. β 1 β 2 σ 1 σ 2
1 −300.00 500.00 3.00 1.00
2 −700.00 +∞ −0.00 −0.00
3 −500.00 500.00 3.00 1.00
4 −500.00 500.00 2.00 4.00
5 −100.00 300.00 3.00 5.00
6 −500.00 700.00 3.00 5.00
7 −500.00 700.00 2.00 2.00
Var. β 1 β 2 σ 1 σ 2
x 11 −∞ 300.00 0.00 0.00
x 12 −∞ 100.00 0.00 0.00
x 23 −∞ 500.00 0.00 2.00
x 24 −∞ 500.00 0.00 0.00
x 31 −∞ 500.00 0.00 0.00
x 33 −∞ 500.00 0.00 0.00
x 34 −∞ 500.00 0.00 2.00
Table 15.1: Ranges and shadow prices related to bounds on constraints and variables. Left: Results
for the basis type sensitivity analysis. Right: Results for the optimal partition type sensitivity analysis.
x 11 + x 12 ≤ 400,
x 23 + x 24 ≤ 1200,
x 31 + x 33 + x 34 ≤ 1000,
x 11 + x 31 = 800,
x 12 = 100,
x 23 + x 33 = 500,
x 24 + x 34 = 500,
x 11 , x 12 , x 23 , x 24 , x 31 , x 33 , x 34 ≥ 0.
(15.3)
The basis type and the optimal partition type sensitivity results for the transportation problem are
shown in Table 15.1 and 15.2 respectively. Examining the results from the optimal partition type
sensitivity analysis we see that for constraint number 1 we have σ 1 ≠ σ 2 and β 1 ≠ β 2 . Therefore, we
have a left linearity interval of [−300, 0] and a right interval of [0, 500]. The corresponding left and
right shadow prices are 3 and 1 respectively. This implies that if the upper bound on constraint 1
increases by
β ∈ [0, β 1 ] = [0, 500]
then the optimal objective value will decrease by the value
σ 2 β = 1β.
Correspondingly, if the upper bound on constraint 1 is decreased by