4.4. Solving the Capital Budgeting
Problem
117
Limits
Arc
Cost
number
Nodes
coefficient
High
Low
Comments
12
239-4
0
15
15
Initial condition for
period 1
56
4-44
0
15
15
Initial condition for
period 2
110
44-240
0
15
15
Final condition for
period 2
Indirectly the hydrology affects the optimal answer insofar as the OKA
distributes optimally the supplied water through the network.
The notation used in the statement of the OP problem is not completely
compatible with that of the OKA used in Sections 3.3.1-3.3.5 for two
reasons:
1. Once the network has been set up, the OKA does not distinguish
between water flows that are used for different purposes (e.g., energy
generation and irrigation); on the contrary, it uses a common coefficient
and flow notation for all arcs. (Refer to Table 3.1.)
2. Similarly, the network notation does not differentiate between the
different time periods. The record of inputs and coefficients for the different
time periods is maintained by the bookkeeping of the user of the OKA.
4.4. Solving the Capital Budgeting Problem
For these reasons all network flows and coefficients have been designated
by the notation of Table 3.1. In this notation an example of the capital
budgeting problem objective function, Eq. (2.1), would be as follows.
(Only the nonzero cost coefficients are included; the nodes are designated
by the subscripts on the 6's.)
Maximize
Σ
a (67,6/7,6
+ 69,1θ/9,10 +
* * * + 6δ3,52/63,52)
net operating return from the present set of
subsystems over the planning period