Optimization of the Parameters of the Water Supply System of a Desert Region Under a Probabilistic Limit

Abstract

The article considers the problem of choosing the parameters of a water supply system in a desert region under a probabilistic constraint. The random activity of the sun is taken into account in the production of water due to the desalination of salt water. A balance equation is derived regarding the cases of company losses when the region's needs for drinking water are not met and regarding the total cost of the system, with the help of which the necessary dependence on the level of probability is subsequently obtained. To which the dichotomy method is then applied to calculate the probability measure. To make sure that the solution is unique, the function is examined for monotonicity with respect to the probability level. Further, to estimate the confidence probability, the problem is solved for average values, where the system cost is estimated and the probability of fulfilling the constraints is calculated. To solve the problem, a confidence method is used, with the help of which the original stochastic poblem is reduced to a linear programming problem. The resulting solution is improved by varying the radius of the confidence ball. One of the possible ways to choose the level of confidence based on the economic balance between the cost of the operation of the water supply system as a whole and the emergency delivery of fresh water is proposed. The choice of the confidence level is made using the initial approximation, which is obtained by solving the problem for average values. An assessment of the reliability of the system used was obtained and a program was implemented to solve this problem.