Carbon and air pollutants constrained energy planning for clean power generation with a robust optimization model—A case study of Jining City, China

A Stochastic Inexact Robust Model for Regional Energy System Management and Emission Reduction Potential Analysis—A Case Study of Zibo City, China

“…However, Model (1) could not effectively reflect the system risk introduced by random information, that directly affect the feasibility and reliability of the proposed model. SRO is an effective choice for solving such problems, and it can be introduced into Model 1, that leads to a multistage stochastic inexact robust programming (MSIRP) as follows [32]:…”

“…jt , the first-stage variable x jt = x − jt + µ jt ∆x jt , and µ jt are intermediate decision variables for obtaining an optimized target values of the first-stage to support the related policy analyses [32]. According to [37], the MSIRP model can be transformed into two linear submodels, and the submodel corresponding to f − can be firstly transformed as follows (assume that c ± jt ≥ 0,ŵ + itk > 0, b ± rt > 0, and f ± > 0 ):…”

“…For example, Chen et al (2013) developed an interval robust-optimization model for CO 2 emission reduction management in energy systems, where the robustness measures were introduced to examine whether the second-stage cost variability could meet the expected levels or not [31]. Xie et al (2014) proposed an inexact stochastic risk-aversion model for electric-power structure adjustment and pollutant emission management, where interval-parameter programming, stochastic robust optimization, and multistage stochastic programming were integrated to address system uncertainties [32].…”

Development of a fuel management model for a multi-source district heating system under multi-uncertainty and multi-dimensional constraints

“…To overcome the data-driven uncertainty problems, the interval linear programming (ILP) developed by Huang et al has attracted great attention in the past two decades due to its benign capability to deal with discrete intervals [31]. In addition to the advantage of less data requirement, its effective two-step interactive solution algorithm and the subsequent interval solutions with low uncertain degree contribute to the widespread acceptance and application of ILP in EMS [32][33][34]. These merits may provide an opportunity to handle multiple uncertainties lying in FM of a MSDHS.…”

An Integrated Air Quality Model and Optimization Model for Regional Economic and Environmental Development: A Case Study of Tangshan, China

“…For example, Li et al (2006) proposed a hybrid two-stage fuzzy-stochastic robust programming (TFSRP) model for the planning of an air-quality management system. Xie et al (2014) combined interval parameter programming (IPP), stochastic robust optimization (SRO), and multistage stochastic programming (MSP) in their robust optimization model for regional energy system management and gained different electricity generation schemes with varied system cost and system-failure risk.…”