5.4. Example of a Sensitivity
Analysis of the MD River Basin
Model
137
Failure to meet irrigation demands was introduced by a linear loss
function that penalized large violations of the demand constraints. The
penalty function associated with arc (5, 2), PFt t2 ,
took the following
form:
PF6,2
= 20,000(^/5,2 -
fVO
where HI is the capacity of the arc, and F is the flow in the arc. The penalty
function reflects the increasing damage to unirrigated and fallow lands.
Similar penalty functions were associated with the other irrigation arcs
and may be incorporated in the return function.
The results of the sixteen sets of trials are summarized in Tables 5.2 and
5.3.
In eleven of the cases, the dam construction schedule was insensitive to
perturbations of the inputs and parameters. In each of the eleven cases,
two irrigation reservoirs were constructed first and then a hydroelectric
reservoir was built. However, when the interest rate and the demand
schedules were both simultaneously at their lower levels, the scheduling
sequence was changed. The significant change that took place was that the
hydroelectric dam was assigned second priority rather than third because
there was a satisfactory trade-off between increased energy revenues and
the irrigation losses caused by the delay in constructing another irrigation
dam. However, over the short term the same dam (number 9) was chosen
to be built first. The decision maker thus could wait until additional information was available on demand profiles before deciding which dam to
build next.
Table 5.2
Variation of Net Return
0 / with Different Combinations of Inputs
Demand profile
Reservoir
costs
tf>P)l
Interest rate
(DP),
Hydrology
Reservoir
costs
η
r 2
η
η
HYi
Rd
RC2
150.43
146.34
139.72
No Solution
151.03
146.65
140.24
No Solution
HY 2
RCi
143.44
138.98
133.06
No Solution
143.64
139.21
133.28
No Solution
α Return is in millions of dollars.
Analysis of the MD River Basin
Model
137
Failure to meet irrigation demands was introduced by a linear loss
function that penalized large violations of the demand constraints. The
penalty function associated with arc (5, 2), PFt t2 ,
took the following
form:
PF6,2
= 20,000(^/5,2 -
fVO
where HI is the capacity of the arc, and F is the flow in the arc. The penalty
function reflects the increasing damage to unirrigated and fallow lands.
Similar penalty functions were associated with the other irrigation arcs
and may be incorporated in the return function.
The results of the sixteen sets of trials are summarized in Tables 5.2 and
5.3.
In eleven of the cases, the dam construction schedule was insensitive to
perturbations of the inputs and parameters. In each of the eleven cases,
two irrigation reservoirs were constructed first and then a hydroelectric
reservoir was built. However, when the interest rate and the demand
schedules were both simultaneously at their lower levels, the scheduling
sequence was changed. The significant change that took place was that the
hydroelectric dam was assigned second priority rather than third because
there was a satisfactory trade-off between increased energy revenues and
the irrigation losses caused by the delay in constructing another irrigation
dam. However, over the short term the same dam (number 9) was chosen
to be built first. The decision maker thus could wait until additional information was available on demand profiles before deciding which dam to
build next.
Table 5.2
Variation of Net Return
0 / with Different Combinations of Inputs
Demand profile
Reservoir
costs
tf>P)l
Interest rate
(DP),
Hydrology
Reservoir
costs
η
r 2
η
η
HYi
Rd
RC2
150.43
146.34
139.72
No Solution
151.03
146.65
140.24
No Solution
HY 2
RCi
143.44
138.98
133.06
No Solution
143.64
139.21
133.28
No Solution
α Return is in millions of dollars.