Hindawi Mathematical Problems in Engineering Volume 2020, Article ID 6273513, 13 pages https://doi.org/10.1155/2020/6273513 Research Article An Inexact Inventory Theory-Based Water Resources Distribution Model for Yuecheng Reservoir, China Meiqin Suo ,1 Fuhui Du,1 Yongping Li,2 Tengteng Kong,1 and Jing Zhang1 1School of Water Conservancy and Hydroelectric Power, Hebei University of Engineering, Handan 056038, China 2School of Environment, Beijing Normal University, Beijing 100875, China Correspondence should be addressed to Meiqin Suo; [email protected] Received 11 August 2020; Revised 11 September 2020; Accepted 11 October 2020; Published 31 October 2020 Academic Editor: Huiyan Cheng Copyright © 2020 Meiqin Suo et al. %is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this study, an inexact inventory theory-based water resources distribution (IIWRD) method is advanced and applied for solving the problem of water resources distribution from Yuecheng Reservoir to agricultural activities, in the Zhanghe River Basin, China. In the IIWRD model, the techniques of inventory model, inexact two-stage stochastic programming, and interval-fuzzy mathematics programming are integrated. %e water diversion problem of Yuecheng Reservoir is handled under multiple uncertainties. Decision alternatives for water resources allocation under different inflow levels with a maximized system benefit and satisfaction degree are provided for water resources management in Yuecheng Reservoir. %e results show that the IIWRD model can afford an effective scheme for solving water distribution problems and facilitate specific water diversion of a reservoir for managers under multiple uncertainties and a series of policy scenarios. 1. Introduction resources management under uncertainty [2–19]. Among them, inexact two-stage stochastic programming (ITSP) is %e economic development of a region depends heavily on effective for analyzing policy scenarios, and taking corrective the water distribution of its large reservoirs. However, actions after a random event has taken place in order to reservoir water resource management is complex that in- minimize “penalties” that may appear due to incorrect policy volves many factors and processes. For example, it is related [11]. Meanwhile, ITSP can reflect the random uncertainty with the local natural conditions, the adjustable water di- quantified as probability density functions (PDFs) and version from upstream in case of drought, the storage ca- handle uncertain parameters or variables with variable pacity and maintaining condition under different inflow ranges in programming problems by interval numbers. levels, the laying of channels/pipes and the loss in the process Interval-fuzzy mathematics programming is useful for de- of water diversion and supply, and different demands of cision problems of fuzzy goals and constraints with fuzziness various water users. Each factor/process has many uncer- by establishing fuzzy sets and fuzzy functions under interval tainties, which become more complex depending on the uncertainty [20]. quality of the obtained data [1]. In addition, with the dif- However, many parameters in actual problem have no ferent levels of economic development, water demand will information of probability distribution and change with the change dynamically with various temporal and spatial scales. different temporal and spatial scales and may be presented as %erefore, effectively optimizing the water distribution of a intervals. In addition, these intervals have no determined reservoir under uncertainty would be helpful to realize the boundaries at sometimes, such as the system cost, and its sustainable development of the region, especially reducing boundary is difficult to ascertain associated with the vola- the risk of water shortage under severe drought. tility of the market and the change in supply and demand Over the past decades, a number of simulation and and thus shown with fuzziness. It is noted that when the optimization methods were developed for reservoir water range of interval parameter is so wide that the final result of 2 Mathematical Problems in Engineering the model has a wide interval solution, the manager would 2. Water Resources Distribution in feel difficult to make decision by ITSP. According to the past Yuecheng Reservoir studies [21–24], it is known that the interval-fuzzy mathe- matics programming (IFMP) could well indicate the fuzzy %e Yuecheng Reservoir is a superlarge reservoir directly uncertainty by fuzzy number and membership degree and under the administration of the state, located in Ci County of provides interval solution with a certain satisfaction degree Handan City, Hebei Province, controlling a river basin area under flexible constraints, to avoid the trouble of making of 18.1 × 103 km2. Its main task is flood control, irrigation, decision resulting from the wide interval solution. Ac- urban water supply, and electricity generation. Its total cordingly, multiple uncertainties would be handled by in- capacity is 1.3 ×109 m3 and can partially solve the industrial corporating ITSP and IFMP within a general framework. and living water of Handan City and Anyang City. On the contrary, in reservoir water resource manage- According to historical statistics, the accumulated water ment system, there is a series of process that needs to be supply of the reservoir was 17.17 ×109 m3 from 1962 to 2005, considered besides the above described uncertainties. In and the total water supply to Hebei Province and Henan particular, when the drought is severe and the reservoir is Province was 11.73 ×109 m3 and 5.44 ×109 m3 [36], re- insufficient, the water diversion would be necessary to satisfy spectively. In addition, it can irrigate a farmland of the local water demand. In this case, a scheme of water 1.47 ×105 ha through Minyou Canal in Hebei Province and diversion needs to be established according to the adjustable Zhangnan Canal in Henan Province. %e irrigated areas of water diversion from upstream, the local water demand, and Minyou and Zhangnan refer to 15 counties, with many kinds the reservoir storage limit, including total diversion quan- of crops, but mainly wheat, corn, and cotton. tity, diversion batch size, and period per time. %e past Recently, due to the rainfall decrease and the building of models for water diversion of reservoirs mainly focused on water diversion channels in the upstream river basin, the the total quantity of water diversion, but few studied the incoming runoff of Yuecheng Reservoir is reducing year by specific diversion batch and period [25–29]. As an economic year, resulting in serious irrigation water shortage and model, the inventory model can effectively tackle the critical water supply problems, especially in the Zhangnan problem of supply and demand and provide the most irrigation area. For example, the average annual water economical material purchase batch and period. But the past supply of Zhangnan irrigation area from the reservoir was inventory models rarely studied the planning problems for 51.7 ×106 m3 from 1981 to 1986, and from 1991 to 1996, it water resources [30–35]. Since water as a resource has been was 30.5 ×106 m3, but from 2001 to 2006, it was only gradually marketized, the combination of inventory model 7.0 ×106 m3 [37]. Moreover, in order to ensure the safe flood and other uncertain optimization technologies would un- of the reservoir, the water of the reservoir on the level of doubtedly make the research studies on the planning of 132 m would be leaked before the main flood period, about water resources system more rich and perfect and has better 85 ×106 m3. After entering the flood period, because the applicability. rainfall in the Zhangwei River Basin is small, the river flow %erefore, the objective of this study is to develop an and runoff are few, and the water storage of the reservoir inexact inventory theory-based water resources distribu- would be not enough. As the important water sources of tion (IIWRD) method through incorporating inventory industry and agriculture for Handan City and Anyang City, theory, ITSP, and IFMP within a general framework. %e Yuecheng Reservoir plays a significant role in the economic IIWRD method will be helpful for quantitatively analyzing life in the two cities and bear a huge pressure of water supply a series of policy scenarios under multiple uncertainties; [38]. more importantly, it can afford the specific scheme for %ere are three large reservoirs in the upstream that can water diversion associated with different policy scenarios, divert water to Yuecheng Reservoir, namely, Guanhe, Back including the total water diversion, diversion batch, and bay, and Zhangze. According to the data, from 1960 to 2004, period per time. %en, IIWRD is applied to planning water the average annual abandoned water of Zhangze Reservoir resources distribution of Yuecheng Reservoir that is located was 112 ×106 m3, the average annual leaked water from in Zhanghe River Basin, China. %e results will help to Guanhe and Back bay was 23 ×106 m3 and 37 ×106 m3. identify desired schemes of water diversion and water al- Under this condition, if continuous rainfall occurs in the location under different inflow levels with maximized Zhanghe River Basin and the upstream reservoirs store water system benefit and satisfaction degree. Furthermore, the fully, it could be considered transferring water from them to system benefit and total water diversion under different Yuecheng Reservoir to relieve the local drought [38]. Since scenarios of inflow levels and unit diversion costs are the water allocation of Yuecheng Reservoir to Handan City analyzed to help managers make decision. Comprehen- and Anyang City is generally preferred to meet municipal sively, three special characteristics of IIWRD make it and industrial use, the agricultural water often appears in- unique after comparing with the existing methods: (i) it can sufficient, having to take the high cost of groundwater to effectively handle multiple forms of uncertainties, (ii) it is solve water shortage problems.