3..?· The Operational
Policy Problem (Problem
III)
83
Thus Bj t is defined by
B jt = CR t -! + TR t + 0R jt + ORj,,^ + ORy.** + Οβ/ν ΜΧ
(3.4)
where /,j", .. . , j
m are the ranking of the 0R 3t for the remaining alternatives in the respective time periods.
We should note that when Bj t is calculated, all the projects incompatible
with project j are not considered. For example, if project Ν + 1 is incompatible with two other projects Ν + 2 and Ν + 3 [refer to constraint
(2.4) of the problem formulation in Chapter 2], B Jt is calculated without
consideration of project Ν + 1 or Ν + 2.
(c)
PROCEDURE FOR SEARCHING THROUGH THE TREE
For month (period) 1 the bounds for every node are calculated and
ranked in the order of their maximum return. The node with the highest
bound that meets the budgetary contraint is selected and the operational
policy (OP) problem is solved for 12 periods (1 year) with a new dam added
at the beginning of year 1. The OP problem is also solved for 12 periods
(1 yr) for the case in which no dam is added. If and only if the solution of
the former OP problem gives a higher return than the solution of the latter
OP problem should a new dam be constructed in year 1.
Branching takes place from the node corresponding to the higher OP
return. All other nodes with bounds lower than the return from the branching node are eliminated.
This procedure is repeated for each subsequent year. On termination of
branching at T m£LX or when all the dams have been built that can be, the
next step is to backtrack up the tree to examine any remaining intermediate
nodes and to branch from them until they are either eliminated or replace
the current feasible solution. The optimal solution is found when all the
feasible nodes have either been searched or eliminated.
3.3. The Operational Policy Problem (Problem III)
Once it has been decided that a new dam may be added, its feasibility
must be tested with respect to the river basin model. The water resources
system can be regarded as a three-dimensional network one with one axis
corresponding to the variable time and the other two axes corresponding
to the physical flow in two-dimensional space through the system for each
month. Figure 3.9 is a sketch of the information flow for a typical year of
12 periods (months). Any of the optimization techniques described in
Policy Problem (Problem
III)
83
Thus Bj t is defined by
B jt = CR t -! + TR t + 0R jt + ORj,,^ + ORy.** + Οβ/ν ΜΧ
(3.4)
where /,j", .. . , j
m are the ranking of the 0R 3t for the remaining alternatives in the respective time periods.
We should note that when Bj t is calculated, all the projects incompatible
with project j are not considered. For example, if project Ν + 1 is incompatible with two other projects Ν + 2 and Ν + 3 [refer to constraint
(2.4) of the problem formulation in Chapter 2], B Jt is calculated without
consideration of project Ν + 1 or Ν + 2.
(c)
PROCEDURE FOR SEARCHING THROUGH THE TREE
For month (period) 1 the bounds for every node are calculated and
ranked in the order of their maximum return. The node with the highest
bound that meets the budgetary contraint is selected and the operational
policy (OP) problem is solved for 12 periods (1 year) with a new dam added
at the beginning of year 1. The OP problem is also solved for 12 periods
(1 yr) for the case in which no dam is added. If and only if the solution of
the former OP problem gives a higher return than the solution of the latter
OP problem should a new dam be constructed in year 1.
Branching takes place from the node corresponding to the higher OP
return. All other nodes with bounds lower than the return from the branching node are eliminated.
This procedure is repeated for each subsequent year. On termination of
branching at T m£LX or when all the dams have been built that can be, the
next step is to backtrack up the tree to examine any remaining intermediate
nodes and to branch from them until they are either eliminated or replace
the current feasible solution. The optimal solution is found when all the
feasible nodes have either been searched or eliminated.
3.3. The Operational Policy Problem (Problem III)
Once it has been decided that a new dam may be added, its feasibility
must be tested with respect to the river basin model. The water resources
system can be regarded as a three-dimensional network one with one axis
corresponding to the variable time and the other two axes corresponding
to the physical flow in two-dimensional space through the system for each
month. Figure 3.9 is a sketch of the information flow for a typical year of
12 periods (months). Any of the optimization techniques described in