Solving linear programming problems under fuzziness and randomness environment using attainment values

In this paper, the author presents a model to measure attainment values of fuzzy numbers/fuzzy stochastic variables. These new measures are then used to convert the fuzzy linear programming problem or the fuzzy stochastic linear programming problem into the corresponding deterministic linear programming problem. Numerical comparisons are provided to illustrate the effectiveness of the proposed method.     

A note on “Solving linear programming problems under fuzziness and randomness environment using attainment values”

This paper is an amendment to Hop’s paper [N.V. Hop, Solving linear programming problems under fuzziness and randomness environment using attainment values, Information Sciences 177 (2007) 2971-2984], in solving linear programming problems under fuzziness and randomness environments. Hop introduced a new characterization of relationship, attainment values, to enable the conversion of fuzzy (stochastic) linear programming models into corresponding deterministic linear programming models. The purpose of this paper is to provide a correction and an improvement of Hop’s analytical work through rationalization and simplification. More importantly, it is shown that Hop’s analysis does not support his demonstration or the solution-finding mechanism; the attainment values approach as he had proposed does not result in superior performance as compared to other existing approaches because it neglects some relevant and inevitable theoretical essentials. Two numerical examples from Hop’s paper are also employed to show that his approach, in the conversion of fuzzy (stochastic) linear programming problems to corresponding problems, is questionable and can neither find the maximum nor the minimum in the examples. The models of the examples are subsequently amended in order to derive the correct optimal solutions.     

Chance measure for hybrid events with fuzziness and randomness

In many cases, fuzziness and randomness simultaneously appear in a system. Hybrid variable is a tool to describe this phenomena. Fuzzy random variable and random fuzzy variable are instances of hybrid variable. In order to measure hybrid event, a concept of chance measure is proposed in this paper. Furthermore, several useful properties about this measure are proved such as self-duality, subadditivity and semicontinuity. Some concepts are also presented such as chance distribution, expected value, variance, moments, critical values, entropy, distance and sequence convergences.     

Fuzzy two-stage quadratic programming for planning solid waste management under uncertainty

In this study, a fuzzy two-stage quadratic programming (FTSQP) method is developed for planning waste-management systems under uncertainty. It incorporates approaches of fuzzy quadratic programming and two-stage stochastic programming within a general optimization framework, to better reflect uncertainties expressed as probability-density and fuzzy-membership functions. The FTSQP can be used for analyzing various policy scenarios that are associated with different levels of economic penalties when the promised policy targets are violated. Moreover, using fuzzy quadratic terms rather than linear ones, the proposed method can improve upon the existing fuzzy linear programs through (a) more effectively optimizing the general satisfaction of the objective and constraints, (b) minimizing the variation of satisfaction degrees among the constraints and leading to more robust solutions, and (c) reflecting the trade-off between the system cost and the constraint-violation risk. The developed method is applied to a case study of municipal solid waste management. The results indicate that reasonable solutions have been generated. They will allow in-depth analyses of trade-offs between environmental and economic objectives as well as those between system cost and decision-maker's satisfaction degree.     

A two-stage stochastic programming approach for project planning with uncertain activity durations

This paper investigates the problem of setting target finish times (due dates) for project activities with random durations. Using two-stage integer linear stochastic programming, target times are determined in the first stage followed by the development of a detailed project schedule in the second stage. The objective is to balance (1) the cost of project completion as a function of activity target times with (2) the expected penalty incurred by deviating from the specified values. It is shown that the results may be significantly different when deviations are considered, compared to when activities are scheduled as early as possible in the traditional way. For example, the optimal target completion time for a project may be greater than the makespan of the early-start schedules under any scenario. To find solutions, an exact algorithm is developed for the case without a budget constraint and is used as a part of a heuristic when crashing is permitted. All computational procedures are demonstrated on a set of 150 benchmark problems consisting of 90 activities each.     

Railway freight transportation planning with mixed uncertainty of randomness and fuzziness

The railway freight transportation planning problem under the mixed uncertain environment of fuzziness and randomness is investigated in this paper, in which the optimal paths, the amount of commodities passing through each path and the frequency of services need to be determined. Based on the chance measure and critical values of the random fuzzy variable, three chance-constrained programming models are constructed for the problem with respect to different criteria. Some equivalents of objectives and constraints are also discussed in order to investigate mathematical properties of the models. To solve the models, a potential path searching algorithm, simulation algorithms and a genetic algorithm are integrated as a hybrid algorithm to solve an optimal solution. Finally, some numerical examples are performed to show the applications of the models and the algorithm.     

Incentive- and compulsion-based cooperative approach in water resources quality management

Simulating control systems for water resources quality is considered. A hierarchical approach to organization of these systems and hierarchical control methods are taken as the basis. Moving from non-cooperative to cooperative relations is proved to be reasonable. A new way to distribute the payoff in the cooperative game is proposed for the problem of water resources quality control. Typical examples are given to illustrate various optimality principles in the cooperative game.     

A two-stage approach for task and resource management in multimedia cloud environment

In recent years, multimedia cloud computing is becoming a promising technology that can effectively process multimedia services and provide quality of service (QoS) provisioning for multimedia applications from anywhere, at any time and on any device at lower costs. However, there are two major challenges exist in this emerging computing paradigm: one is task management, which maps multimedia tasks to virtual machines, and the other is resource management, which maps virtual machines (VMs) to physical servers. In this study, we aim at providing an efficient solution that jointly addresses these challenges. In particular, a queuing based approach for task management and a heuristic algorithm for resource management are proposed. By adopting allocation deadline in each VM request, both task manager and VM allocator receive better chances to optimize the cost while satisfying the constraints on the quality of multimedia service. Various simulations were conducted to validate the efficiency of the proposed task and resource management approaches. The results showed that the proposed solutions provided better performance as compared to the existing state-of-the-art approaches.     

Simulation for queueing systems under fuzziness

The fuzzy arrival rate and fuzzy service rate in a queueing system are proposed in this article. The nonhomogeneous Poisson process with fuzzy intensity function will be taken as the arrival process for this queueing system. The computational procedures for performing simulation in the α-level sense and for obtaining the α-level closed intervals of the system performance measure are also proposed to tackle this kind of model. The numerical results are obtained by using the commercial software MATLAB.     

A two-stage stochastic programming model for transportation network protection

Network protection against natural and human-caused hazards has become a topical research theme in engineering and social sciences. This paper focuses on the problem of allocating limited retrofit resources over multiple highway bridges to improve the resilience and robustness of the entire transportation system in question. The main modeling challenges in network retrofit problems are to capture the interdependencies among individual transportation facilities and to cope with the extremely high uncertainty in the decision environment. In this paper, we model the network retrofit problem as a two-stage stochastic programming problem that optimizes a mean-risk objective of the system loss. This formulation hedges well against uncertainty, but also imposes computational challenges due to involvement of integer decision variables and increased dimension of the problem. An efficient algorithm is developed, via extending the well-known L-shaped method using generalized benders decomposition, to efficiently handle the binary integer variables in the first stage and the nonlinear recourse in the second stage of the model formulation. The proposed modeling and solution methods are general and can be applied to other network design problems as well.     

不确定条件下炼钢-连铸生产调度的两阶段鲁棒优化方法

根据炼钢-连铸生产过程的特点,建立一种考虑加工时间和运输时间不确定性的两阶段鲁棒优化模型,即在第1阶段确定排序和指派变量,在第2阶段确定时间变量.针对两阶段鲁棒优化问题的复杂性和非线性难点,运用线性对偶理论将其转换为最差场景下的网络优化问题.针对简化后的网络优化问题,提出一种基于协方差自适应进化策略(covariance matrix adaptation evolution strategy,CMA-ES)的求解算法,并引入基于瓶颈浇次的重启策略以提升其搜索效率.最后,基于不同规模的测试实例进行模型灵敏度分析及算法对比测试.计算和统计结果验证了所提出的调度模型在不确定性条件下的有效性及改进CMA-ES算法的竞争性.     

A two-stage stochastic programming model for electric energy producers

The bilateral contract selection and bids definition constitute a strategic issue for electric energy producers that operate in competitive markets, as the liberalized electricity ones. In this paper we propose a two-stage stochastic integer programming model for the integrated optimization of power production and trading which include a specific measure accounting for risk management. We solve the model by means of a novel enumerative solution approach that exploits the particular problem structure. Finally, we report some preliminary computational experiments.     

网构软件的随机性资源自适应性的形式化分析与验证

因特网上的资源具有不确定性、随机性,需要考虑如何保证网构软件系统在运行中满足资源需求。使用随机性资源接口自动机对软件构件的行为进行形式化建模,并使用随机性资源接口自动机网络描述构件组装系统的组合行为;在资源不确定的情况下,检验组合系统是否满足资源约束,并提出基于可达图的相应算法。给出了一个实例网上书店系统,并用模型检测工具Spin验证了模型的正确性。     

Risk-averse two-stage stochastic programming with an application to disaster management

Traditional two-stage stochastic programming is risk-neutral; that is, it considers the expectation as the preference criterion while comparing the random variables (e.g., total cost) to identify the best decisions. However, in the presence of variability risk measures should be incorporated into decision making problems in order to model its effects. In this study, we consider a risk-averse two-stage stochastic programming model, where we specify the conditional-value-at-risk (CVaR) as the risk measure. We construct two decomposition algorithms based on the generic Benders-decomposition approach to solve such problems. Both single-cut and multicut versions of the proposed decomposition algorithms are presented. We adapt the concepts of the value of perfect information (VPI) and the value of the stochastic solution (VSS) for the proposed risk-averse two-stage stochastic programming framework and define two stochastic measures on the VPI and VSS. We apply the proposed model to disaster management, which is one of the research fields that can significantly benefit from risk-averse two-stage stochastic programming models. In particular, we consider the problem of determining the response facility locations and the inventory levels of the relief supplies at each facility in the presence of uncertainty in demand and the damage level of the disaster network. We present numerical results to discuss how incorporating a risk measure affects the optimal solutions and demonstrate the computational effectiveness of the proposed methods.     

A continuous coupled hydrological and water resources management model

Human exploitation of water resources is widespread and its impact on hydrological fluxes is expected to increase in the future. Water use interacts in a complex manner with the hydrological system causing severe alterations of the hydrological fluxes with multifaceted feedbacks. Implementing this coupling within hydrological models is essential when dealing with the impact of human activities on water resources at all relevant scales. We contribute to the effort in developing models coupling natural and human systems with a distributed continuous model, named GEOTRANSF. The model allows to quantify, within the same framework, alterations in the natural regime and constraints and limitations to water resources availability. After presenting GEOTRANSF, an example of application to a medium-size Alpine catchment with streamflow modified by hydropower and distributed uses is discussed, followed by the analysis of the effect of suitable water uses scenarios in the same catchment.     

Cross-border logistics with fleet management: A goal programming approach

In this paper, we introduce the cross-border logistics problem with fleet management. A major phenomenon of implementation of open-door policy in China is the move of Hong Kong-based manufacturers’ production lines to China, crossing the border to take advantages of lower production costs, lower wages and lower rental costs. The finished products are then transshipped to Hong Kong, an efficient logistics hub well-equipped with reliable transportation facility, for exporting. We present a preemptive goal programming model for multi-objective cross-border logistics problem, in which three objectives are optimized hierarchically. We also describe a framework for incorporating decision-makers’ opinions for determination of goal priorities and target values. A set of Hong Kong data have been used to test the effectiveness and efficiency of the proposed model. Results demonstrate the decision-makers can find the flexibility and robustness of the proposed model by adjusting the goal priorities with respect to the importance of each objective.     

Neuro-dynamic programming for designing water reservoir network management policies

Stochastic dynamic programming (SDP) can improve the management of a multipurpose water reservoir by generating management policies which are efficient with respect to the management objectives (flood protection, water supply for irrigation, hydropower generation, etc.). The improvement in efficiency is even more remarkable for networks of reservoirs. Unfortunately, SDP is affected by the well-known ‘curse of dimensionality’, i.e. computational time and computer memory occupation increase exponentially with the dimension of the problem (number of reservoirs), and the problem rapidly becomes intractable. Neuro-dynamic programming (NDP) can sensibly mitigate this limitation by approximating Bellman functions with artificial neural networks (ANNs). In this paper the application of NDP to the problem of the management of reservoir networks is introduced. Results obtained in a real-world case study are finally presented.