Chance Constrained Model of Water Reservoir: Bounds on the Long-Run Distribution of the Water Stock

In this model, treating water release as a deterministic decision variable facilitated the transformation of the chance constraints into deterministic form. This was done for a fairly generalized profit function and without assuming an a priori specific form for the decision rule. Moreover, an approximation for the long-run distribution of the stock of water in the reservoir was derived that provided reasonable bounds for the expected value of the distribution. Such an approximation facilitates the design of an insurance scheme that internalizes the risk from the inflow's uncertainty. It also provides a rule of thumb against which a judgment as to whether too much or too little water is being stored.