Inexact Fuzzy Chance-constrained Programming Research Articles

Total consumption controlled water allocation management for multiple sources and users with inexact fuzzy chance-constrained programming: a case study of Tianjin, China

Environmental and ecological issues caused by water resources crisis have brought enormous challenges to the sustainable development of water-deficient area. Water resources allocation management balancing the relationship between the social-economic development and the ecological environment has become a hot topic in recent years. In this paper, an inexact fuzzy chance-constrained programming (IFCCP) approach is proposed for regional water resource allocation optimization with the aim of promoting the harmonious development of the social economic and the ecological environment, improving water utilization efficiency, and realizing water resources consumption control under uncertainties. The method is incorporated with interval parameter programming, fuzzy programming, and chance-constrained programming, for handling system uncertainties and balancing the optimal objectives with the risk of violating system constraints. Under this framework, an IFCCP model for water resources allocation management was successfully formulated and applied to a typical water-deficit area, Tianjin, China, for obtaining a better water resources plan among multiple users under resources and environmental limitation. Different total water consumption control policies are designed for assessing regional water allocation schemes. The results indicated that the gap of supply and demand will only be solved by foreign water, the transferred water from Luan River and Changjiang River would still be the main supplier in planning horizon. Moreover, the strict total water consumption control policy would guarantee the water requirement of ecological environment, lead to changes in the structure of water supply, actively guide on water conservation, and promote the large-scale utilization of desalted water and recycle water.

Inexact fuzzy chance-constrained programming for community-scale urban stormwater management

Abstract Due to frequent and serious waterlog and environmental pollution in cities in recent years, urban stormwater management (USM) has become an essential issue of urban sustainable development in China. Low Impact Development (LID) technologies are effective and popular measures of USM, and can be used to reduce urban waterlog and the associated environmental pollution. In this paper, in order to identify an optimal strategy of LID technologies based on economic efficiencies and environmental performances, the construction costs and environmental benefits of the four LID technologies (including grass swales, bioretention cells, green roofs, and permeable pavement) were analyzed. Then, due to the uncertain feature of rainfall, concentration of pollutants and many social-economic factors, an inexact fuzzy chance-constrained programming (IFCCP) model was developed. Multiple uncertainties that can be expressed as interval parameters, fuzzy sets, and stochastic distribution can be addressed effectively and incorporated directly into the modeling process. Based on the analysis of the precipitation probability distribution and land use data, the developed model was applied to a university campus with relatively high building density and plot ratio in Beijing. Then, optimal solutions of multiple precipitation probabilities ( p m ) under varying USM goals were obtained. The four LID technologies were chosen to meet multiple USM goals based on multiple p m values. When p m = 0.1 , 0.05 , 0.02 and 0.015 , the total construction investments would be 1.46 to 4.66, 1.46 to 5.25, 2.31 to 8.54 and 3.95 to 12.7 million yuan, respectively. The relationship between construction costs and p m represented the relationship between economic benefit and system risk. The results indicated that USM was influenced by the rainfall capacity, construction costs would increase with the increase of precipitation, and the risks of constraint violation would decrease as the construction costs increase. When considering the four LID technologies during the planning stage of USM, the preferred selection order would be bioretention cells, permeable pavements, grass swales and green roofs. Therefore, the solutions under each p m level could provide the references for desired USM plans.

Uncertain and multi-objective programming models for crop planting structure optimization

Crop planting structure optimization is a significant way to increase agricultural economic benefits and improve agricultural water management. The complexities of fluctuating stream conditions, varying economic profits, and uncertainties and errors in estimated modeling parameters, as well as the complexities among economic, social, natural resources and environmental aspects, have led to the necessity of developing optimization models for crop planting structure which consider uncertainty and multi-objectives elements. In this study, three single-objective programming models under uncertainty for crop planting structure optimization were developed, including an interval linear programming model, an inexact fuzzy chance-constrained programming (IFCCP) model and an inexact fuzzy linear programming (IFLP) model. Each of the three models takes grayness into account. Moreover, the IFCCP model considers fuzzy uncertainty of parameters/variables and stochastic characteristics of constraints, while the IFLP model takes into account the fuzzy uncertainty of both constraints and objective functions. To satisfy the sustainable development of crop planting structure planning, a fuzzy-optimizationtheory-based fuzzy linear multi-objective programming model was developed, which is capable of reflecting both uncertainties and multi-objective. In addition, a multiobjective fractional programming model for crop structure optimization was also developed to quantitatively express the multi-objective in one optimization model with the numerator representing maximum economic benefits and the denominator representing minimum crop planting area allocation. These models better reflect actual situations, considering the uncertainties and multi-objectives of crop planting structure optimization systems. The five models developed were then applied to a real case study in Minqin County, north-west China. The advantages, the applicable conditions and the solution methods of each model are expounded. Detailed analysis of results of each model and their comparisons demonstrate the feasibility and applicability of the models developed, therefore decision makers can choose the appropriate model when making decisions.

Optimization of the industrial structure facing sustainable development in resource-based city subjected to water resources under uncertainty

An inexact stochastic fuzzy programming (ISFP) approach has been developed for the optimization of the industrial structure in resource-based city subjected to water resources under uncertainty in present study. The ISFP method incorporates the techniques of inexact stochastic programming and inexact fuzzy chance-constrained programming, where the uncertainties are expressed as interval, fuzzy sets, and probability distribution, respectively. Moreover, it can also examine the risk of violating fuzzy tolerance constraints. The developed method is subsequently employed in a realistic case for industrial development in the Jinchang city, Gansu province, China. The result can help to analyze whether the water resources carrying capacity of Jinchang can meet the need of local economic development plan under uncertainty and help decision maker to optimize the industry structure under water resource constraints to meet the maximum economic efficiency.

Dual inexact fuzzy chance-constrained programming for planning waste management systems

This study develops a dual inexact fuzzy chance-constrained programming (DIFCCP) method for planning municipal solid waste (MSW) management systems. The concept of random boundary interval (RBI) is introduced to address the high uncertain parameters in the studied system. Fuzzy flexible programming and chance-constrained programming are also introduced to take into account the uncertainties of RBIs and various uncertainties in MSW management system. Compared with the existing methods, the developed method could deal with the uncertainty without simplification and thus is more robust. Moreover, the potential system-failure risks in MSW management system due to the existing uncertainties could be quantified by means of violation levels and satisfaction levels in DIFCCP. The developed method then is applied to a MSW management system. The obtained solutions could be used for generating efficient management schemes. The values of violation and satisfaction levels could help decision makers understand the tradeoffs between system cost and system-failure risk, and identify desired strategy according to the practical economic and environmental situation.