A chance-constrained multi-period model for a special multi-reservoir system

We develop a model for optimal multi-period operation of a multi-reservoir system for a basin operating under a conjunctive use of ground and surface water. The inflows to the main reservoir as well as the irrigation demands are stochastic. The ground stock suffers from severe overdrafts increasing the risk of the total depletion of the aquifer in addition to the quality degradation and the threat of seawater intrusion. We treat the uncertainties in the inflows through chance constraints and penalties of failure to release the planned amounts of surface water from the main reservoir. However, we reflect uncertainties in irrigation demands by opting for deficit irrigation and using adequate production functions to estimate the expected crop yields. We attempt in the model to avoid large deficits except perhaps for periods where crop yields are relatively insensitive to water shortage. The objective is to maximize the total expected profit of the entire region. We illustrate the model through an example partially based on some hypothetical data.