*Article* **A Fuzzy-Interval Dynamic Optimization Model for Regional Water Resources Allocation under Uncertainty**

**Meiqin Suo 1,2,\*, Feng Xia 1,2 and Yurui Fan <sup>3</sup>**


**Abstract:** In this study, a fuzzy-interval dynamic programming (FIDP) model is proposed for regional water management under uncertainty by combining fuzzy-interval linear programming (FILP) and dynamic programming (DP). This model can not only tackle uncertainties presented as intervals, but also consider the dynamic characteristics in the allocation process for water resources. Meanwhile, the overall satisfaction from users is considered in the objective function to solve the conflict caused by uneven distribution of resources. The FIDP model is then applied to the case study in terms of water resources allocation under uncertainty and dynamics for the City of Handan in Hebei Province, China. The obtained solutions can provide detailed allocation schemes and water shortage rates at different stages. The calculated comprehensive benefits of economy, water users' satisfaction and pollutant discharge (i.e., COD) are [2264.72, 2989.33] <sup>×</sup> <sup>10</sup><sup>8</sup> yuan, [87.50, 96.50] % and [1.23, 1.65] <sup>×</sup> <sup>10</sup><sup>8</sup> kg respectively with a plausibility degree (i.e., *λ* ± *opt*) ranging within [0.985, 0.993]. Moreover, the benefit from FIDP model under consideration of dynamic features is more specific and accurate than that of FILP model, whilst the water shortage rate from FIDP is [5.10, 9.10] % lower than that of FILP model.

**Keywords:** optimal allocation; interval; fuzzy; dynamic programming; water resources
