Towards sustainable water resources planning and pollution control: Inexact joint-probabilistic double-sided stochastic chance-constrained programming model.

This study presents an inexact joint-probabilistic double-sided stochastic chance-constrained programming (IJDSCCP) model for sustainable water resources planning and pollution control in water quality management systems under uncertainty. Techniques of interval parameter programming (IPP), joint-probabilistic programming (JPP) and double-sided stochastic chance-constrained programming (DSCCP) are incorporated into a modeling framework. The IJDSCCP can not only address uncertainties presented as interval parameters and double-sided randomness (i.e. both left-hand and right-hand sides) that are characterized as normal distributions, but also examine the reliability level of satisfying the entire system constraints. It further improves upon conventional stochastic chance-constrained programming for handing random uncertainties in the left-hand and right-hand sides of constraints. Moreover, a non-equivalent but sufficient linearization form of the IJDSCCP is presented to solve such a problem. Then, the model is applied to a representative case for water resources planning and pollution control. The results including water resources planning solutions, pollution control plans and system benefits under the combinations of different joint and individual probability levels will be obtained. The solutions are expressed as combinations of deterministic, interval and distributional information, which can facilitate analysis of different forms of uncertainties. After investigating and comparing the variations of results, it is found that an increasing joint probability level can lead to higher system benefits, i.e., [13,841.68, 21,801.81] × 106 Yuan (p = 0.01, p1  = 0.0033, p2  = 0.0033 and p3  = 0.0033), [14,150.26, 22,260.06] × 106 Yuan (p = 0.05, p1  = 0.0166, p2  = 0.0166 and p3  = 0.0166) and [14,280.55, 22,415.52] × 106 Yuan (p = 0.10, p1  = 0.033, p2  = 0.033 and p3  = 0.033). A set of decreased individual probability levels gives rise to the maximum system benefits at the same joint probability level. Furthermore, the results of the IJDSCCP are compared with a general interval-based optimization framework as well. Therefore, the results from the IJDSCCP are valuable for assisting managers in generating and identifying decision alternatives under different scenarios.