Benefit Allocation in Shared Water-Saving Management Contract Projects Based on Modified Expected Shapley Value
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Benefit Allocation in Shared Water-Saving Management Contract Projects Based on Modified Expected Shapley Value Xinxin Liu1 · Xiaosheng Wang1
· Haiying Guo1 · Xiaojie An1
Received: 2 April 2020 / Accepted: 28 October 2020 / © Springer Nature B.V. 2020
Abstract Water-Saving Management Contract (WSMC) is an innovative business model to reduce water consumption and improve water-use efficiency. The Shared Water-Saving Model, as a primary operating model in WSMC projects, is relatively widely used compared with other patterns. However, the lack of a water-saving benefit allocation scheme is one of the critical obstacles frustrating the implementation and promotion of the Shared Water-Saving Model. To correct this deficiency, a modified expected Shapley value method is developed, in which alliance revenues are characterized as uncertain variables due to the lack of historical data. Firstly, risk, input and effort are identified as key influencing factors to improve the deficiencies in the distribution of benefits based on the contribution. Secondly, equity criteria, including symmetry, efficiency and additivity, are redefined based on correction factors to measure the fairness of the allocation scheme. Thirdly, we prove that the allocation result obtained by the proposed method satisfies the equity criteria and is unique. Finally, a watersaving project launched by Handan City located in North China is studied to illustrate the applicability of the proposed method. The result shows that the modified expected Shapley value method significantly enhances the cooperative relationship and can therefore be used as an effective tool for the fair and reasonable distribution of benefits in Shared WSMC projects. Keywords Water-Saving Management Contract · Shared Water-Saving Model · Benefit allocation · Modified expected Shapley value
1 Introduction With rapidly increasing populations (Wang et al. 2020), climate change (Zheng et al. 2020) and accelerated urbanization (Cai et al. 2019), a multitude of regions of the world are confronted with severe water shortages, especially in developing countries such as China and
Xiaosheng Wang
[email protected] 1
School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China
X. Liu et al.
India (V¨or¨osmarty 2000; V¨or¨osmarty et al. 2010; Liu et al. 2019b; Sharma et al. 2019). Moreover, poor management of water resources has been recognized as one of the important causes of water losses, exacerbating water scarcity issues (Cosgrove and Loucks 2015). In particular, leakage accounts for the majority of the total water losses in water distribution networks, usually more than 70% (Samir et al. 2017; Jang et al. 2018). Recent estimates indicate that the global water deficit will reach 40% by 2030, which may cause more than half of the world’s population to suffer from water shortages (Zhuang 2016; Sinha et al. 2020). Therefore, new water-saving measures should be implemented by governments and other societal stakeholders to ensure sustainable water resources m
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