Optimization and Allowable Value

Topics: Optimization, Operations research, Linear programming Pages: 3 (950 words) Published: November 2, 2014
Solution to Chapter 4

2.

See file: Prb4_2.xlsm
Microsoft Excel Sensitivity Report
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell
Name
Value
Cost
Coefficient Increase Decrease
$C$4 Value: X1
12
0
2
1E+30
0
$D$4 Value: X2
0
0
4
0
1E+30
Constraints
Cell
Name
$E$10 Used:
$E$8 Used:
$E$9 Used:
a.
b.

c.

d.
e.

4.

a.

Final Shadow Constraint Allowable Allowable
Value
Price
R.H. Side
Increase Decrease
12
0
2
10
1E+30
-12
0
8
1E+30
20
12
2
12
1E+30
10

Constraint 2 is binding.
There is an alternate optimal solution. Variable X2 is at its lower bound (of zero) but also has a reduced cost of zero. This indicates that the value of X2 could be increased while having zero impact on the optimal objective function value.

There is no way to answer this question directly from the sensitivity report. We know that the optimal solution would change since the allowable decrease in the objective function value of X1 is zero, but we cannot tell what the new optimal solution would be. If we re-solve the revised model the solution is X1=2, X2=5.

It can decrease by any amount without changing the solution. Constraint 2 is the only binding constraint. Therefore, we would want to increase its RHS value before any other.
MIN: 260X13 + 220X14 + 290X15 + 230X23 + 240X24 + 310X25
S.T.:
X13 + X14 + X15 ≤ 20
X23 + X24 + X25 ≤ 20
X13 + X23 ≥ 10
X14 + X24 ≥ 15
X15 + X25 ≥ 10
Xij ≥ 0

b. See file: Prb4_4.xlsm
c. See below
Microsoft Excel Sensitivity Report
Adjustable Cells
Cell
$C$10
$D$10
$E$10
$C$11
$D$11
$E$11

Final Reduced Objective Allowable Allowable
Name
Value
Cost
Coefficient Increase Decrease
Eustis Miami
0
50
260
1E+30
50
Eustis Orlando
10
0
220
20
0
Eustis Tallahassee
10
0
290
0
310
Clermont Miami
10
0
230
50
230
Clermont Orlando
5
0
240
0
20
Clermont Tallahassee
0
0
310
1E+30
0

Constraints
Cell
$C$12
$D$12
$E$12
$F$10
$F$11
d....
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