Two-stage programming (TSP) is popular in resources planning management, especially for limited and precious resources. Remarkable study has been done to improve the model performance. However, one of the biggest obstacle is lack of objectivity when it comes to penalty quantification derived from recourse behavior. Besides, much attention has been paid in the resources deficiency penalty but little in resources residual, which may lead to wasting. In order to clarify the physical meaning of mathematical equation for recourse penalty from both resources scarcity and surplus, the production frontier was estimated and the technical efficiency and shadow prices of resources were introduced into TSP to characterize the resources deficiency and residual penalty, respectively. Then, an intuitionist fuzzy interval two-stage stochastic programming (IFITSP) was generated integrating the uncertainty of fuzzy membership and traditional TSP. An integrated solving approach was proposed coupling several previous uncertain programming methods and an improved robust interval TSP method. A case study was conducted in an arid area of northwest China to schedule agricultural cultivation scale based on limited water resources. The inefficiencies were [0.26, 0.49], [0.14, 0.37] and [0, 0.03] for GZ, LZ, and GT. The shadow prices of GZ, LZ, and GT in 2015 were 12.94, 2.61, 2.67 Yuan/m3 respectively, indicating the sever water crisis of GZ. The relatively unbiased and abundant decision could be generated by the developed IFITSP to help decision makers with various preferences make tradeoff between benefits and basic crop production requirement as well as balance resources deficiency and surplus. The results also show that the developed model could unveil the uncertainty influence of model inputs on decision strategies and trigger managers to deeply analyze subjective effect and associated risk. By comparison, the proposed methodology can not only clarify the physical meaning of penalty but deal with more complex uncertainty than previous methods. Therefore, the established model can provide reliable and scientific support for resources planning with recourse.
Resources scarcity is threatening human sustainable development around the world. Climate change, population growth, environmental contamination and industrial expansion have worsened the resources crisis which urges managers to develop high-efficient resources management approaches (Singh, 2012). In response to mitigating the resources crisis, the reasonable resources planning is among the most popular resources management and has been widely discussed worldwide. Remarkable contributions have been done surrounding the optimal resources planning and one of the achievements is twostage programming (TSP), which is capable of modifying the predetermined targets (called first-stage decision) based on the overall influence of uncertain events and generating corresponding decision (called second-stage decision) after the uncertain events happen. Resources planning optimization research on TSP covers all walks of life, ranging from agriculture (Fu et al., 2018; Zhang et al., ۲۰۱۷), hydrology (Ding et al., 2017; Hu et al., 2016; Yu et al., 2016), environment (Han et al., 2012; Han et al., 2013; Han and LEE, 2011), energy (Yun et al., 2017), and transportation (Barbarosoglu and Arda, 2004) to medicine (Dillon et al., 2017), manufacture (Alfieri et al., 2012), and networks (Wu and Kucukyavuz, 2018). A highlighted part in TSP is penalty quantification caused by uncertain events, which is usually expressed as benefits loss from resources deficiency according to previous studies. However, the previous achievements share two problems.