If reservoirs are located close to one another on the same river, sometimes they can be treated as one large reservoir with a capacity equal to the sum of the individual reservoir capacities. For example, to provide the required safe yield for water supply, a total capacity of 40 million acre-Feet (maf) might be required. Three potential sites for reservoirs exist along a short stretch of river. Cost data are provided in the accompanying table. It is desired to achieve the required total storage at least cost. Further development of this problem can be found in Wathne et al. (1975).
(a) Write the mathematical programming model for the problem.
(b) Write the dynamic programming recursive equation for the problem and define terms.
(c) Construct tables and calculate the optimal cost and associated optimal reservoir size at each site to achieve a total storage of from 0 to 50 maf (in increments of 5 maf).
(d) Plot optimal cost versus total system storage.
Reservoir Site | Reservoir Size (maf) | Reservoir Total Cost ($ million) |
1 | 5 | 3 |
| 10 | 5 |
| 15 | 11 |
2 | 5 | 5 |
| 10 | 7 |
| 15 | 16 |
3 | 5 | 6 |
| 10 | 9 |
| 15 | 12 |
| 20 | 20 |
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