Mathematical Models for Optimal Dynamic Planning of Multi-Component Water Resources Systems ۱. A Linear-Integer Screening Model, ۲. A Groundwater Parameter Estimation Model

Water resources planning is a multi-disciplinary and dynamic process. For large multi-component and multi-basin systems, this process becomes rather complicated because of the number of options that the planners must consider. Systems analysis technology can play a major role in screening the number of options which the planners have to deal with, and in making the planners capable of repeating the planning process consistently. The process of modern water resources planning is complicated even more by the demands that government and funding authorities put on the planners to justify the purpose, scale and construction time requirements of water resources systems. Traditionally, water resources planners have dealt with these difficulties by proposing individual projects with different scales, and depending on the urgency of the project, they have managed to obtain funding for one or more options. With the development of powerful computational hardware and software. it is now feasible to analyze several components conjunctively, and thus justify the options more rationally. In this paper, a mathematical model based on a linear-integer programming technique is formulated to optimize the scale, date of readiness, and the present worth of the total cost (capital costs, CC, plus operation, maintenance, and replacement costs, OMR) of a multi-component water resources system over several operation periods. The system includes surface and sub-surface reservoirs as well as pipe lines, treatment plants, desalinization plants, and demand centers (domestic, industrial, and agricultural). Since the decision variables for the sub-surface reservoirs are highly dependent on the physical properties and boundary conditions which must be entered into a numerical model describing the flow and storage of water in the reservoir, a groundwater parameter estimation model based on the log-likelihood criterion is adopted to estimate these parameters. This criterion is optimized using an iterative nonlinear mathematical programming approach. A multi-dimensional finite element model is used as a tool for the calculation of the hydraulic head as a function of a set of parameters in this iterative process