Random Boundary Interval Research Articles

Risk-based agricultural water allocation under multiple uncertainties

A risk-based interval-stochastic optimization modelling approach is developed for agricultural water allocation in response to the complexity arising from uncertainties and risk in agricultural water management systems. The approach comprises conditional-value-at-risk (CVaR) model, inexact two-stage stochastic programming (ITSP) model with imprecise probabilities (IPs), and random-boundary intervals (RBIs) within a general framework. The approach can simultaneously balance expected benefits, penalties, and risks from agricultural water allocation, and can address uncertainties of agricultural water supply and demand in the form of probability distributions and intervals with random boundaries. As demonstrated in Hulan River irrigation area, northeast China, the objective of the approach is to allocate limited agricultural water resources to make a trade-off between various subareas under different risk-aversion levels and possible runoff discharges. Most inputs to the approach are expressed as interval numbers that are generated by statistical simulation, based on which various agricultural water allocation schemes are obtained. Irrigation water performance based on the optimal results are also analyzed. Results validate the applicability of the approach incorporating multiple uncertainties and risk-aversion measures in optimization models, and generating agricultural water allocation schemes in the form of interval numbers.

Stochastic multi-objective modeling for optimization of water-food-energy nexus of irrigated agriculture

Irrigated agriculture is the primary user of world's fresh water resources on one hand and the producer of food to feed the world's growing population on the other hand. Water, food, and energy are intertwined in irrigated agricultural systems and an effective and coordinated management of the water-food-energy nexus is needed for the sustainable development of agriculture which is challenging because of large uncertainties involved therein. This paper developed an optimization model for the allocation of resources toward the sustainable management of agricultural water, food, and energy nexus under uncertainty. The model is capable of providing policy makers with the ability to determine optimal policy options among water, energy, and land resources to obtain the maximum system economic benefit and simultaneously minimize environmental impacts. The model is also capable of handling complex uncertainties of random boundary intervals. The model is demonstrated to solve a real-world nexus management problem in an irrigation district in northeast China. Results highlight the sensitivity of food production and environmental pollution to the utilization of water, energy, and land resources. The model is applicable for similar agriculture-centered regions with limited resources.

A risk-based interactive multi-stage stochastic programming approach for water resources planning under dual uncertainties

In this study, a risk-based interactive multi-stage stochastic programming (RIMSP) approach is proposed through incorporating the fractile criterion method and chance-constrained programming within a multi-stage decision-making framework. RIMSP is able to deal with dual uncertainties expressed as random boundary intervals that exist in the objective function and constraints. Moreover, RIMSP is capable of reflecting dynamics of uncertainties, as well as the trade-off between the total net benefit and the associated risk. A water allocation problem is used to illustrate applicability of the proposed methodology. A set of decision alternatives with different combinations of risk levels applied to the objective function and constraints can be generated for planning the water resources allocation system. The results can help decision makers examine potential interactions between risks related to the stochastic objective function and constraints. Furthermore, a number of solutions can be obtained under different water policy scenarios, which are useful for decision makers to formulate an appropriate policy under uncertainty. The performance of RIMSP is analyzed and compared with an inexact multi-stage stochastic programming (IMSP) method. Results of comparison experiment indicate that RIMSP is able to provide more robust water management alternatives with less system risks in comparison with IMSP.

Inexact Probabilistic Optimization Model and Its Application to Flood Diversion Planning in a Dynamic and Uncertain Environment

AbstractFlood management systems involve a variety of complexities, such as multiple uncertainties and their interdependences, as well as multiregion and dynamic features. This paper thus presents an inexact two-stage mixed-integer programming with random coefficients (ITMP-RC) model for flood management in a dynamic and uncertain environment. ITMP-RC is capable of addressing dual uncertainties expressed as random boundary intervals that exist in the coefficients of the objective function. A case study of flood diversion planning is used to demonstrate the applicability of the proposed methodology. Results indicate that total system costs would be rising gradually with increased probabilities of occurrence, implying a trade-off between economic objective and system safety. A variety of decision alternatives can be obtained under different policy scenarios, which are useful for decision makers to formulate appropriate flood management policies according to practical situations. The performance of ITMP-RC i...

An inexact programming approach for urban electric power systems management under random-interval-parameter uncertainty

In electric power management problems, a number of system parameters are subjected to many powerful and unpredictable influences (e.g. economic situation, technologies in energy conservation). This leads to the difficulty in accurately qualifying them through conventional approaches. In this paper, a concept of random-boundary interval (RBI) whose upper and lower bounds are random variables is introduced to account for the high-uncertain components, like electricity demand, in electric power systems. A fuzzy integer programming model with RBI parameters is developed to support effective planning of urban electric power systems (UEPS). A case study is then provided for demonstrating the applicability of the proposed model. The obtained solutions can be used for generating efficient electricity-supply and capacity-expansion schemes under various situations. Compared with the existing methods, the proposed model could tackle the complex parameter uncertainty in electric power systems, and the potential system-failure risks arising from such uncertainty could be quantified by means of violation levels and satisfaction levels.

A dual-inexact fuzzy stochastic model for water resources management and non-point source pollution mitigation under multiple uncertainties

Abstract. In this research, a dual-inexact fuzzy stochastic programming (DIFSP) method was developed for supporting the planning of water and farmland use management system considering the non-point source pollution mitigation under uncertainty. The random boundary interval (RBI) was incorporated into DIFSP through integrating fuzzy linear programming (FLP) and chance-constrained programming (CCP) approaches within an interval linear programming (ILP) framework. This developed method could effectively tackle the uncertainties expressed as intervals and fuzzy sets. Moreover, the lower and upper bounds of RBI are continuous random variables, and the correlation existing between the lower and upper bounds can be tackled in RBI through the joint probability distribution function. And thus the subjectivity of decision making is greatly reduced, enhancing the stability and robustness of obtained solutions. The proposed method was then applied to solve a water and farmland use planning model (WFUPM) with non-point source pollution mitigation. The generated results could provide decision makers with detailed water supply–demand schemes involving diversified water-related activities under preferred satisfaction degrees. These useful solutions could allow more in-depth analyses of the trade-offs between humans and environment, as well as those between system optimality and reliability. In addition, comparative analyses on the solutions obtained from ICCP (Interval chance-constraints programming) and DIFSP demonstrated the higher application of this developed approach for supporting the water and farmland use system planning.

A robust optimization modelling approach for managing water and farmland use between anthropogenic modification and ecosystems protection under uncertainties

In this study, a dual inexact fuzzy radial chance-constrained programming (DIFRCCP) method was developed for planning water and farmland use management system with the consideration of the conflicts between anthropogenic modification and ecosystems protection. This method can effectively reflect and tackle the multiple uncertainties existing in water and farmland use activities and eco-environmental management, which can be expressed as regular and radial intervals, random boundary interval (RBI) and fuzzy sets. Particularly, it could ensure solutions feasible and near optimal with high probability when the data changes within a certain bound radii of ecological parameters. Meanwhile, the correlation consisting between the lower and upper bounds of RBI (i.e., water supply parameters) can get solved by the joint probability distribution function, further strengthening the robustness of developed model. Through computing the proposed model, the generated solutions could provide detail water and farmland use management plans between anthropogenic modification and ecosystems protection for decision makers, including farmland use arrangement, water allocations to various consumers, as well as ecological and environmental pollution control through balancing the tradeoffs among system profits, the probability of constraints violation and system reliability under reasonable protection levels and satisfaction degrees.

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.

Integer programming with random-boundary intervals for planning municipal power systems

Abstract Uncertainty attached to municipal power systems has long been crucial considerations for the related planners. Such an uncertainty could be expressed as random-boundary intervals (RBIs). In this study, an integer programming with random-boundary intervals (IPRBI) approach was developed for municipal electricity-supply management under uncertainty. A concept of random-boundary interval (RBI) was introduced to reflect dual uncertainties that exist in many system components. A solution method named two-boundary approach (TBA) was proposed to solve the IPRBI model. A case study was provided for demonstrating applicability of the developed method. The results indicated that the RBI and integer-interval concepts were effective in dealing with highly uncertain parameters. The IPRBI method solutions could be used for generating efficient electricity-supply schemes under various complexities. They can also be used for analyzing tradeoffs between system cost and electricity-shortage risk. Compared with the existing methods, IPRBI was advantageous in reflecting the complexities of system uncertainties that were presented as RBIs, integer-intervals and intervals.

A Superiority-Inferiority-Based Inexact Fuzzy Stochastic Programming Approach for Solid Waste Management Under Uncertainty

A superiority–inferiority-based inexact fuzzy stochastic programming (SI-IFSP) model was developed for planning municipal solid waste management systems under uncertainty. The SI-IFSP approach represents a new attempt to tackle multiple uncertainties in objective function coefficients which are beyond the capabilities of existing inexact programming methods. Through introducing the concept of fuzzy random boundary interval, SI-IFSP is capable of reflecting multiple uncertainties (i.e., interval values, fuzzy sets, probability distributions, and their combinations) in both the objective function and constraints, leading to enhanced system robustness. The developed SI-IFSP method was applied to a case study of long-term municipal solid waste management. Useful solutions were generated. A number of decision alternatives could be generated based on projected applicable conditions, reflecting the compromise between system optimality and reliability as well as the tradeoffs between economic and environmental objectives. Moreover, the consequences of system violations could be quantified through introducing a set of economic penalties, reflecting the relationships between system costs and constraint violation risks. The results suggest that the proposed SI-IFSP method can explicitly address complexities in municipal solid waste management systems and is applicable to practical waste management problems.

Planning of municipal solid waste management systems under dual uncertainties: a hybrid interval stochastic programming approach

In this study, a random-boundary-interval linear programming (RBILP) method is developed and applied to the planning of municipal solid waste (MSW) management under dual uncertainties. In the RBILP model, uncertain inputs presented as interval numbers can be directly communicated into the optimization process; besides, intervals with uncertain lower and upper bounds can be handled through introducing the concept of random boundary interval. Consequently, robustness of the optimization process can be enhanced. To handle uncertainties with such complex presentations, an integrated chance-constrained programming and interval-parameter linear programming approach (ICCP) is proposed. ICCP can help analyze the reliability of satisfying (or risk of violating) system constraints under uncertainty. The applicability of the proposed RBILP and ICCP approach is validated through a case study of MSW management. Violations for capacity constraints are allowed under a range of significant levels. Interval solutions associated with different risk levels of constraint violation are obtained. They can be used for generating decision alternatives and thus helping waste managers to identify desired policies under various environmental, economic, and system-reliability constraints.