A Three-Dimensional Optimization Problem in Water-Resources Engineering

The problem under consideration is related to a system consisting of two storage facilities in series. Part of the water reaching the upstream reservoir may be diverted for storage in the downstream facility. However, there is a certain lag between the time when water is released from the upper reservoir and the time when it is available for utilization in the lower one. Thus the vector describing the state of the system at any one time consists of three elements:

1. a)
   amount of water stored in the upstream reservoir;
    
2. b)
   amount of water stored in the downstream reservoir;
    
3. c)
   amount of water in transit.
    

An optimum operating policy for the system had to be derived.The method of dynamic programming was applied in the analysis of this problem. The algorithm obtained was programmed for solution on an IBM 7090 digital computer. Optimal policies were obtained for each admissible state of the system.