Engineering Optimization

40Case Study 5: Reservoir

40.1 The Process and Analysis

There is a Monte Carlo function in the 2‐D Optimization Examples VBA program that simulates the stochastic outcome of a reservoir—Function 18. Reservoir capacity and nominal level are the decision variables. The models are described in Appendix E.

The larger the reservoir and associated dam, the greater the initial cost. Cost is the objective function. So, superficially, the solution is to build a small dam to reduce cost.

However, if the reservoir is too small, and/or it is maintained nearly full, it does not have enough capacity to absorb a flood due to exceptionally heavy upstream rainfall and it will transmit the flood downstream. Downstream flooding incurs a cost of damaged property. But the chance of a flood and the magnitude of the flood depend on the upstream rainfall. So, the simulator models a day‐to‐day status with a lognormal rainfall distribution for a time period. I set it to 20 years, but you can change it.

Contrasting flooding conditions are drought conditions. If the reservoir is too small, and/or maintained with little reserve of water, an upstream drought will require stopping the water release, which stops downstream river flow. Downstream dwellers, recreationists, or water users will not like this. There is also a cost related to zero downstream flow.

There is a fixed cost of the structure and a probabilistic or stochastic penalty cost of extreme events.

Since one 20‐year simulation will not reveal ...