5.1. Sensitivity
Analysis
131
revenue function. For example, a 10% change in the value of a model
input or parameter could have a negligible or significant effect on a constraint or on the return, depending on whether the variable of interest is
insensitive or sensitive to changes in the model input or parameter. Figure
5,1 illustrates how the total system cost (not discounted), i.e., the capital
cost plus operation and maintenance cost, changes as the projected total
requirements for water vary above or below the projected base requirement in the Texas water development plan [Texas Water Development
Board, 1971]. A 10% increase in the water requirements from the base
case (250 million acre-ft) increases the total cost from $9.2 to 10.3 billion,
or approximately 12%. From the opposite viewpoint, Fig. 5.2 shows what
percentage change is required in certain inputs and demands to produce a
10% change in the total system cost. The length of each bar in Fig. 5.2 is
inversely proportional to the importance of the parameter to the system
cost response. If the outputs change very little with perturbations in the
parameters and the inputs, then the coefficients and the inputs in the
equations for these system model may be quite approximate. On the other
hand, if one response shows a high degree of sensitivity to changes in its
Fig. 5.1 Variation of cost of total system with changes in water requirements.
Analysis
131
revenue function. For example, a 10% change in the value of a model
input or parameter could have a negligible or significant effect on a constraint or on the return, depending on whether the variable of interest is
insensitive or sensitive to changes in the model input or parameter. Figure
5,1 illustrates how the total system cost (not discounted), i.e., the capital
cost plus operation and maintenance cost, changes as the projected total
requirements for water vary above or below the projected base requirement in the Texas water development plan [Texas Water Development
Board, 1971]. A 10% increase in the water requirements from the base
case (250 million acre-ft) increases the total cost from $9.2 to 10.3 billion,
or approximately 12%. From the opposite viewpoint, Fig. 5.2 shows what
percentage change is required in certain inputs and demands to produce a
10% change in the total system cost. The length of each bar in Fig. 5.2 is
inversely proportional to the importance of the parameter to the system
cost response. If the outputs change very little with perturbations in the
parameters and the inputs, then the coefficients and the inputs in the
equations for these system model may be quite approximate. On the other
hand, if one response shows a high degree of sensitivity to changes in its
Fig. 5.1 Variation of cost of total system with changes in water requirements.