**1. Introduction**

Water resources are the lifeline of social progress and economic development. However, in today's world, social development and progress, population expansion, and overexploitation of water resources have caused a shortage of fresh water resources [1]. The optimal allocation of water resources is an important means to coordinate the relationship between supply and demand of water resources, improve the utilization of water resources, and coordinate the conflicts among water consuming departments, particularly in areas with water shortages [2–4]. Therefore, it is necessary to optimize the allocation of water resources in water-scarce areas. With the increasing demand for water quality improvement, water demand has become important for regional water resource optimization and allocation [5,6]. However, the value created by the water ecosystem cannot be presented intuitively, the conventional optimal allocation of urban water resources pays more attention to the economic output of water consumption and does not fully consider the ecological value, which is not conducive to the synergistic efficiency of socio-economic and ecological water consumption. Therefore, it is necessary to increase the direct consideration of ecological value factors while considering the optimal allocation of water resources. In addition, there are many uncertainties in the optimal allocation of water resources, such as variable

**Citation:** Zhang, J.; Meng, C.; Hu, S.; Li, W. Optimal Allocation Model for Water Resources Coupled with Ecological Value Factors—A Case Study of Dalian, China. *Water* **2022**, *14*, 266. https://doi.org/10.3390/ w14020266

Academic Editors: Alban Kuriqi and Luis Garrote

Received: 14 December 2021 Accepted: 15 January 2022 Published: 17 January 2022

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availability of water resources, demand, and development of water treatment technologies, which make it difficult to select the optimal allocation method. Therefore, under the background of promoting the construction of urban ecological civilization, the optimal allocation of water resources presents challenges in coordinating the ecological value and dealing with various uncertain factors [7].

Interval-parameter programming, fuzzy programming, and stochastic programming are common methods for water resources allocation under uncertainty [8–12]. For example, Huang and Locks [13] were the first to propose the inexact two-stage stochastic programming (ITSP) to deal with uncertain information in interval-valued and random variable representations. Under the framework of the ITSP method, various advanced models are proposed and applied to water resources management [14]. Maqsood [15] presented an interval-parameter fuzzy two-stage stochastic programming (IFTSP) method for the planning of water resource management systems under uncertainty; Li et al. [16] selected an interval-fuzzy two-stage stochastic quadratic programming model with the objective of maximum benefits to have the best irrigation water allocation scheme. Xie [13] developed an inexact, two-stage, water resources management model for multi-regional water resources planning in the Nansi Lake Basin, China. In the ITSP, an initial decision is made before the random events. After future uncertainties are resolved and the values of the random variables are revealed, a second decision is made that minimizes penalties due to any infeasibilities [17]. It can be seen that ITSP is an effective method for optimal allocation of water resources under uncertain conditions.

As the leading revitalization and famous coastal industrial city in Northeast China, Dalian lacks freshwater resources. With the development of the urban social economy and the improvement of the ecosystem, the demand for water resources continues to grow rapidly and presents intensified competition. It is difficult to coordinate water use among industrial, municipal, and ecological environment sectors [18]. Under the overall objective of coordinating urban social and economic development and improving the living environment, this study intended to reflect different probabilities of water resource availability and environmental carrying capacity in different flow scenarios. An ITSP model was constructed by coupling the ecological value factors, which was more comprehensively considering the impact of ecological value factors on the optimal allocation results of water resources. The four major urban water departments in Dalian, including the industry, urban community, agriculture, and ecological environment, were studied to discuss the optimal allocation mode and method for urban water resources, coordinate the needs and value factors for the improvement of the ecosystem, and realize the coordinated development of ecological value and social and economic benefits.

Therefore, aiming at the dual constraints of water resource shortage and water environment quality and based on the principle of achieving the coordination of ecological value and social and economic benefits, a general framework for establishing an ITSP for the optimal allocation of water resources in Dalian under uncertain conditions is proposed (Figure 1). The model considers constraints such as ecological area and water consumption, as well as available water resources and water environment capacity, and combines ecological value benefits with water resource management to provide Dalian with a relatively reasonable water resource allocation plan. Our study findings are of great significance for establishing a rational water resource management system for water resource exploitation and utilization, as well as water ecosystem protection, and provide a basis for realizing the coordinated development of Dalian's socio-economic development goals, water resource utilization, and environmental quality improvement.

**Figure 1.** Framework for the inexact two-stage stochastic programming (ITSP) model.
