122
4. Application
of the Optimization
Algorithm
In this case
%i = $7,350,000, T m&x = 50 yr, r = 4.625%
Upon substituting these values one obtains
CRx + TR 2 = $142,346,000
The values for the OR terms are found in the PVBAR matrix in Appendix
B:
OR lt2 = $8,278,000, ORn t z = $1,415,000, OR 9A = $561,000
Therefore
B 7t2 = 142,346,000 + 8,278,000 + 1,415,000 + 561,000 = $152,600,000
In Figure 4.4 the value of #7,2 is truncated to the first 5 significant figures
of $152.60 million.
4.5. Results of the Optimization
The detailed results obtained from the overall optimization algorithm are
listed in Appendix B. It took 6.138 sec on a CDC 6600 to generate a first
solution and 297.12 sec to backtrack completely through the decision tree.
In the backtracking procedure, 124 alternative solutions were examined;
of these, eleven had a higher return than the first solution. Only those
alternative solutions whose bounds at the time of examination were higher
than the best solution were considered. The efficacy of the heuristic procedure employed in finding a first feasible solution to the optimization
problem is demonstrated by the fact that the return from the first solution
was within 3.3% of the final optimum.
Irrigation demands were never fully met in any year in the optimal solution because there were insufficient surface waters available to meet the
simultaneous depletion of ground-water resources and the overall increase
in irrigation acreage. Note that the first solution scheduled first the construction of the irrigation reservoirs 9 and 12 and the hydroelectric dam 8,
while the optimal solution reversed this order and also scheduled the construction of the first dam at a later date.
The situation of constructing the irrigation reservoirs first would be
achieved by using a penalty function related to the failure to meet irrigation demands. Another advantage would also accrue from using a penalty
function: many solutions whose bounds heretofore were higher than the
4. Application
of the Optimization
Algorithm
In this case
%i = $7,350,000, T m&x = 50 yr, r = 4.625%
Upon substituting these values one obtains
CRx + TR 2 = $142,346,000
The values for the OR terms are found in the PVBAR matrix in Appendix
B:
OR lt2 = $8,278,000, ORn t z = $1,415,000, OR 9A = $561,000
Therefore
B 7t2 = 142,346,000 + 8,278,000 + 1,415,000 + 561,000 = $152,600,000
In Figure 4.4 the value of #7,2 is truncated to the first 5 significant figures
of $152.60 million.
4.5. Results of the Optimization
The detailed results obtained from the overall optimization algorithm are
listed in Appendix B. It took 6.138 sec on a CDC 6600 to generate a first
solution and 297.12 sec to backtrack completely through the decision tree.
In the backtracking procedure, 124 alternative solutions were examined;
of these, eleven had a higher return than the first solution. Only those
alternative solutions whose bounds at the time of examination were higher
than the best solution were considered. The efficacy of the heuristic procedure employed in finding a first feasible solution to the optimization
problem is demonstrated by the fact that the return from the first solution
was within 3.3% of the final optimum.
Irrigation demands were never fully met in any year in the optimal solution because there were insufficient surface waters available to meet the
simultaneous depletion of ground-water resources and the overall increase
in irrigation acreage. Note that the first solution scheduled first the construction of the irrigation reservoirs 9 and 12 and the hydroelectric dam 8,
while the optimal solution reversed this order and also scheduled the construction of the first dam at a later date.
The situation of constructing the irrigation reservoirs first would be
achieved by using a penalty function related to the failure to meet irrigation demands. Another advantage would also accrue from using a penalty
function: many solutions whose bounds heretofore were higher than the