140
5. Sensitivity
of Planning Decisions in River Basin
Management
possible ways in which various future system inputs might occur, 30 or 40
sequences may be barely adequate, and much larger number of sequences,
say 200, is likely to be needed for statistical reliability. Thus, as straightforward as method 2 may seem, it is usually too costly and may even be
infeasible from a computational standpoint.
Method 3 differs from method 2 in that one tries to restrict the extent
of the simulation somewhat by intermediate optimization for the operation
policy rather than supplying an operation policy and examining the result.
A general outline of method 3 is:
1. Simulate a possible future set of stochastic data.
2. Find the optimal operating policy for that set of data.
3. Repeat steps 1 and 2 several times.
4. Carry out a regression analysis on the results to estimate an operating
policy that is optimal given that there are several possible future sets of
data for stream flow, runoff, and so on. The approach of method 3 was
also pioneered at Harvard University by Young and Fiering who developed
reservoir operating rules using forward dynamic programming in step 2.
They christened their technique Monte Carlo Dynamic Programming
(Young, 1967).
Figure 5.3 illustrates one way to select the stochastic sequences to be used.
The same model and algorithm described in Chapters 2 and 3 may be
used for determination of capital investment strategies and the degree of
associated risk for systems with stochastic inputs by method 3 as follows.
For the planning problem, including stochastic parameters, the capital
investment optimization algorithm is combined with Monte Carlo experimentation and duality analysis to determine the optimum river basin
management strategy and the risks involved. A river basin can be chosen
to have a current configuration of unregulated streams and rivers, of
reservoirs, of canals, and of sites for future additional construction. From
the hydrological record a series of representative synthetic flow sequences
can be generated by an equation such as the Thomas-Fiering equation
[Fiering, 1966] and used as inputs to the model. Given a unique set of
costs, interest rates, and future profiles of demand and pollution load, an
optimal solution can be found for each hydrological sequence, as well as
(1) the expected return from operating the system, (2) the risk of not
meeting the demands on the system, (3) the sensitivity of construction
schedules to variations in the hydrological flow sequences, and (4) whether
the sizes of the structure built were truly optimal, as ascertained through a
duality analysis.
5. Sensitivity
of Planning Decisions in River Basin
Management
possible ways in which various future system inputs might occur, 30 or 40
sequences may be barely adequate, and much larger number of sequences,
say 200, is likely to be needed for statistical reliability. Thus, as straightforward as method 2 may seem, it is usually too costly and may even be
infeasible from a computational standpoint.
Method 3 differs from method 2 in that one tries to restrict the extent
of the simulation somewhat by intermediate optimization for the operation
policy rather than supplying an operation policy and examining the result.
A general outline of method 3 is:
1. Simulate a possible future set of stochastic data.
2. Find the optimal operating policy for that set of data.
3. Repeat steps 1 and 2 several times.
4. Carry out a regression analysis on the results to estimate an operating
policy that is optimal given that there are several possible future sets of
data for stream flow, runoff, and so on. The approach of method 3 was
also pioneered at Harvard University by Young and Fiering who developed
reservoir operating rules using forward dynamic programming in step 2.
They christened their technique Monte Carlo Dynamic Programming
(Young, 1967).
Figure 5.3 illustrates one way to select the stochastic sequences to be used.
The same model and algorithm described in Chapters 2 and 3 may be
used for determination of capital investment strategies and the degree of
associated risk for systems with stochastic inputs by method 3 as follows.
For the planning problem, including stochastic parameters, the capital
investment optimization algorithm is combined with Monte Carlo experimentation and duality analysis to determine the optimum river basin
management strategy and the risks involved. A river basin can be chosen
to have a current configuration of unregulated streams and rivers, of
reservoirs, of canals, and of sites for future additional construction. From
the hydrological record a series of representative synthetic flow sequences
can be generated by an equation such as the Thomas-Fiering equation
[Fiering, 1966] and used as inputs to the model. Given a unique set of
costs, interest rates, and future profiles of demand and pollution load, an
optimal solution can be found for each hydrological sequence, as well as
(1) the expected return from operating the system, (2) the risk of not
meeting the demands on the system, (3) the sensitivity of construction
schedules to variations in the hydrological flow sequences, and (4) whether
the sizes of the structure built were truly optimal, as ascertained through a
duality analysis.