|Ph.D Student||Housh Mashor|
|Subject||Optimal Multi-Year Management of Regional Water Resources|
Systems under Uncertainty
|Department||Department of Civil and Environmental Engineering||Supervisors||Professor Avi Ostfeld|
|Professor Emeritus Uri Shamir|
|Full Thesis text|
This thesis deals with management of water resources systems under uncertainty, concentrating on seasonal multi-year management of water quantities and salinities in regional water supply systems (WSS), where water is taken from sources, which include aquifers, reservoirs, and desalination plants, and delivered through a distribution system to consumers who require prescribed quantities of water under salinity constraints. Within this framework the natural replenishment into the aquifers is uncertain, while the desalination plants can produce a large and reliable amount of water, but at greater cost. A deterministic optimization model has been developed. In which the uncertain variables are represented by some deterministic values. The objective function and some of the constraints in this model are non-linear and therefore a non-linear optimization method was used. The model determines the optimal operational plan of the supply system of reservoirs, aquifers, desalination plants and the conveyance system.
A number of approaches for optimization under uncertainty of the aquifers' recharge have been developed and applied, including: (a) probabilistic (stochastic) approaches in which the aquifers recharge is modeled as a stochastic process and (b) non-probabilistic approaches in which no probabilistic assumption is made about the aquifers' recharge.
A key issue when formulating stochastic models is the sequence in which decisions alternate with observations. Various stochastic models were developed in this thesis, which considered different alternations between decisions and observations of the recharge stochastic process. These models include two-stage and multi-stage stochastic programming along with the two extreme cases: a) the Wait-and-See approach, in which decisions are made after all the realizations are known b) the Here-and-Now approach, in which decisions are made before the realizations are known.
In addition to these approaches a Limited Multi-stage Stochastic Programming (LMSP) approach was developed. The LMSP is an approximation of the Multi-stage Stochastic Programming (MSP) approach which was developed in the current work. The Robust Optimization (RO) methodology and the Info-Gap decision theory (non-probabilistic approaches) were applied.
A small "made up" system was used for testing the algorithms and for demonstrating and explaining the results; a real scaled system which represents the central part of the Israeli National Water System (INWS) was solved by all models, and the results are presented to demonstrate the efficacy of the tools used and efficiency of the models as proof of their practicality. The results of the large system show the importance for models with uncertainty incorporation over deterministic models.