CHAPTER 4
LINEAR PROGRAMMING SENSITIVITY ANALYSIS
S
OLUTIONS TO
D
ISCUSSION
Q
UESTIONS
4-1.
In most real world situations that are modeled using LP, conditions are dynamic and changing.
Hence, input data such as resource availabilities, prices, and costs used in the LP model are
estimated
,
rather than known with certainty. In such environments, sensitivity analysis can be used to identify the
ranges of values of these input data for which the current LP solution remains optimal.
This is done
without solving the problem again each time we need to examine a change in an input data’s value. When
all model values are deterministic, that is, known with certainty, sensitivity analysis may not be needed
from the perspective of evaluating data accuracy. This may be the case in a portfolio selection model in
which we select from among a series of bonds whose returns and cash-in values are set for long periods of
time.
4-2.
Sensitivity analysis is important in all decision modeling techniques. For example, it is important in
breakeven analysis to test the model’s sensitivity to selling price, fixed cost, and variable cost. Likewise,
it is important in inventory models in which we test the result’s sensitivity to changes in demand, lead-
time, costs, and so on.
4-3.
A change in a resource’s availability (right-hand-side) changes the size of a feasible region. An
increase means more units of that resource are available, causing the feasible region to increase in size. A
decrease means fewer units are available. Obviously, if more units of a
binding
resource are available, it
may be possible for the optimal objective value to improve. In contrast, if more units of a
non-binding
resource are available, the additional units would just contribute to more slack and there would be no
improvement in the optimal objective value.
4-4.
A change in an objective function coefficient changes the slope of the objective function, with
respect to that variable. The change in the slope may be sufficient to make a different corner point
become the new optimal solution to the LP model.
4-5.
Simultaneous changes in input data values are extremely logical in many contexts. For example, it
may be possible to trade one type of resource for another, causing a decrease in the availability of one
resource and an increase in the other’s availability. Likewise, market conditions may cause us to
simultaneously reduce the price of all our products, not just in a single product.
4-6.
We use the 100% rule to verify if the shadow prices in the current Sensitivity Report are still valid to
analyze the impact of a proposed simultaneous change in input data values. To analyze a simultaneous
change, we compute the ratio of each proposed change in a parameter’s value to the maximum allowable
change in its value, as given in the Sensitivity Report. The sum of these ratios must not exceed 1 (or
100%) in order for the information given in the current Sensitivity Report to be valid. If the sum of the