A Problem of Optimizing a Collecting Reservoir System

The paper deals with the design of a collecting reservoir system on the lower reaches of a river. The daily input into the reservoir is approximated by the negative exponential distribution and the output is continuous, the water being pumped to another existing reservoir. The problem is how big a reservoir to build and what should the pumping capacity be, such that the cost per cubic meter of water pumped is a minimum. A solution, subject to local cost considerations, is given for any feasible quantity of water exploited. The model described and analyzed here can also be used as an inventory model.