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uncertain random programming models in the framework of U-S chance theory and their applications

TOP 2025年第1期33卷 161-194页

作者： Hu, Feng Qu, Ziyi Yang, Deguo Qufu Normal Univ Sch Stat & Data Sci Qufu 273165 Peoples R China Fourth Mil Med Univ Dept Hlth Stat Xian 710032 Peoples R China

In order to handle some problems in which human uncertainties coexist with stochasticities characterized by non-additive probabilities, we develop uncertain random programming models based on four different types of expectations in the framework of U-S chance theory. In this paper, firstly, the operational law for uncertain random variables is proved in this framework. Then, based on sub-linear expectations and Choquet integrals, four types of expectations of uncertain random variables are defined. Finally, four uncertain random programming models are proposed and applied to optimal investment in incomplete financial market and system reliability design.

关键词： uncertain random programming Optimal investment System reliability U-S chance theory

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uncertain random programming with applications

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FUZZY OPTIMIZATION AND DECISION MAKING 2013年第2期12卷 153-169页

作者： Liu, Yuhan Tsinghua Univ Dept Ind Engn Beijing 100084 Peoples R China

uncertain random variable is a tool to deal with a mixture of uncertainty and randomness. This paper presents an operational law of uncertain random variables, and shows an expected value formula by using probability and uncertainty distributions. This paper also provides a framework of uncertain random programming that is a type of mathematical programming involving uncertain random variables. Finally, some applications of uncertain random programming are discussed.

关键词： uncertainty theory Stochastic programming uncertain random programming System reliability

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uncertain random goal programming

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FUZZY OPTIMIZATION AND DECISION MAKING 2018年第4期17卷 375-386页

作者： Qin, Zhongfeng Beihang Univ Sch Econ & Management Beijing 100191 Peoples R China Beihang Univ Minist Educ Key Lab Complex Syst Anal Management & Decis Beijing 100191 Peoples R China

Goal programming provides an efficient technique to deal with decision making problems with multiple conflicting objectives. This paper joins the streams of research on goal programming by providing a so-called uncertain random goal programming to model the multi-objective optimization problem involving uncertain random variables. Several equivalent deterministic forms are derived on the condition that the set of parameters consists of uncertain variables and random variables. Finally, an example is given to illustrate the application of the approach.

关键词： Goal programming uncertainty theory uncertain random variable uncertain random programming uncertain random goal programming

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uncertain random multilevel programming with application to production control problem

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SOFT COMPUTING 2015年第6期19卷 1739-1746页

作者： Ke, Hua Su, Taoyong Ni, Yaodong Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China Univ Int Business & Econ Sch Informat Technol & Management Beijing 100029 Peoples R China

For modeling decentralized decision-making problems with uncertain random parameters, an uncertain random multilevel programming is proposed. For some special case, an equivalent crisp mathematical programming to the established uncertain random programming is presented. A searching method by integrating uncertain random simulations, neural network, and genetic algorithm is produced to search the quasi-optimal solution under some decision-making criterion. Finally, the proposed uncertain random multilevel programming is applied to a production control problem.

关键词： Multilevel programming uncertain random programming uncertain programming uncertainty theory

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Hybrid multilevel programming with uncertain random parameters

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JOURNAL OF INTELLIGENT MANUFACTURING 2017年第3期28卷 589-596页

作者： Ke, Hua Ma, Junjie Tian, Guangdong Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China Tongji Univ Sch Law Shanghai 200092 Peoples R China Northeast Forestry Univ Transportat Coll Harbin 150040 Peoples R China

Multilevel programming is developed for modeling decentralized decision-making processes. For different management requirements and risk tolerances of different-level decision-makers, the decision-making criteria applied in different levels cannot be always the same. In this paper, a hybrid multilevel programming model with uncertain random parameters based on expected value model (EVM) and dependent-chance programming (DCP), named as EVM-DCP hybrid multilevel programming, is proposed. The corresponding concepts of Nash equilibrium and Stackelberg-Nash equilibrium are given. For some special case, an equivalent crisp mathematical programming is proposed. An approach integrating uncertain random simulations, Nash equilibrium searching approach and genetic algorithm is designed. Finally, a numerical experiment of uncertain random supply chain pricing decision problem is given.

关键词： Multilevel programming uncertain variable uncertain random programming Dependent-chance programming Expected value model

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uncertain random Hybrid Multilevel programming

Uncertain Random Hybrid Multilevel Programming

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The Thirteenth International Conference on Information and Management Sciences

作者： Hua Ke Junjie Ma Guangdong Tian School of Economics and Management Tongji University School of Law Tongji University Transportation College Northeast Forestry University

Multilevel programming is developed for modeling decentralized decision-making *** different management requirements and risk tolerances of different-level decision-makers,the decision-making criteria applied in different levels cannot be always the *** this paper,a hybrid multilevel programming model with uncertain random parameters based on expected value model(EVM)and dependentchance programming(DCP),named as EVM-DCP hybrid multilevel programming,is *** corresponding concepts of Nash equilibrium and Stackelberg-Nash equilibrium are *** some special case,an equivalent crisp mathematical programming is *** approach integrating uncertain random simulations,Nash equilibrium searching approach and genetic algorithm is designed.

关键词： Multilevel programming uncertainty theory uncertain random programming Dependent-chance programming Expected value model

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Multi-objective optimization in uncertain random environments

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FUZZY OPTIMIZATION AND DECISION MAKING 2014年第4期13卷 397-413页

作者： Zhou, Jian Yang, Fan Wang, Ke Shanghai Univ Sch Management Shanghai 200444 Peoples R China

uncertain random variables are used to describe the phenomenon of simultaneous appearance of both uncertainty and randomness in a complex system. For modeling multi-objective decision-making problems with uncertain random parameters, a class of uncertain random optimization is suggested for decision systems in this paper, called the uncertain random multi-objective programming. For solving the uncertain random programming, some notions of the Pareto solutions and the compromise solutions as well as two compromise models are defined. Subsequently, some properties of these models are investigated, and then two equivalent deterministic mathematical programming models under some particular conditions are presented. Some numerical examples are also given for illustration.

关键词： Multi-objective optimization Multi-objective programming uncertain random variable uncertain random programming uncertainty theory

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uncertain random newsboy problem

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2014年第1期26卷 483-490页

作者： Ding, Sibo B. Henan Univ Technol Sch Management Zhengzhou 450001 Peoples R China

The classic newsboy problem assumes the market demand to be a random variable. However, when the decision maker wants to expand the market share, he has to provide a subjective estimate of new market demand distribution due to the lack of historical data. Thus, randomness and uncertainty simultaneously appear in a newsboy problem. The aim of this work is to extend the analysis of the classic newsboy problem to the case when market demand is assumed to be an uncertain random variable. A mathematical model is formulated, and a simple equation is derived for determining the optimal order quantity to maximize the expected profit. Furthermore, uncertain random newsboy problem is compared with stochastic newsboy problem and uncertain newsboy problem. Three kinds of newsboy problems have the same optimal service level. The latter two newsboy problems are two special cases of uncertain random newsboy problem. Finally, a numerical example has been presented to illustrate the model.

关键词： Newsboy problem uncertainty theory chance theory uncertain random programming uncertain random variable

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A new model and algorithm for uncertain random parallel machine scheduling problem

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SOFT COMPUTING 2019年第15期23卷 6555-6566页

作者： Ma, Weimin Liu, Yang Zhang, Xingfang Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China Liaocheng Univ Sch Math Sci Liaocheng 252059 Shandong Peoples R China

The paper presents a new model for uniform parallel machine scheduling problem with uncertainty and randomness simultaneously for processing times of jobs based on chance theory. The objective of the model is to minimize expected completion time. The constraint of the model is that uncertain random completion time of scheduling is less than or equal to expected completion time. The model is transformed to a crisp non-deterministic polynomial hard mathematical programming model based on chance theory. Firstly, simulation techniques of the objective function and the left chance constraint are proposed. Then, two heuristic methods to solve the crisp model are presented. Finally, they are integrated into two hybrid intelligent algorithms for searching the quasi-optimal schedule. Besides, the effectiveness of the model and its hybrid intelligent algorithms are verified by a numerical example generated randomly.

关键词： Parallel machine scheduling uncertainty theory Chance theory uncertain random programming Hybrid intelligent algorithm

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The Minimum Cost Flow Problem of uncertain random Network

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2018年第3期35卷 1850016.1-1850016.1页

作者： Abdi, Soheila Baroughi, Fahimeh Alizadeh, Behrooz Sahand Univ Technol Dept Appl Math Fac Basic Sci Tabriz Iran

The aim of this paper is to present a novel method for solving the minimum cost flow problem on networks with uncertain-random capacities and costs. The objective function of this problem is an uncertain random variable and the constraints of the problem do not make a deterministic feasible set. Under the framework of uncertain random programming, a corresponding alpha-minimum cost flow model with a prespecified confidence level alpha, is formulated and its main properties are analyzed. It is proven that there exists an equivalence relationship between this model and the classical deterministic minimum cost flow model. Then an algorithm is proposed to find the maximum amount of alpha such that for it, the feasible set of alpha-minimum cost flow model is nonempty. Finally, a numerical example is presented to illustrate the efficiency of our proposed method.

关键词： uncertain random programming minimum cost flow problem chance theory uncertainty theory

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