基于乐观值和悲观值的不确定机会约束规划模型及应用  

Model and application of uncertain chance-constrained programming based on optimistic and pessimistic value

作　　者：亓尧 王瑛[1] 孟祥飞[1] 吕茂隆 孙贇 QI Yao;WANG Ying;MENG Xiangfei;Lü Maolong;SUN Yun(Equipment Management and Safety Engineering College, Air Force Engineering University, Xi’an 710051, China)

机构地区：[1]空军工程大学装备管理与安全工程学院,陕西西安710051

出　　处：《系统工程与电子技术》2019年第2期336-341,共6页Systems Engineering and Electronics

基　　金：国家自然科学基金(71601183)资助课题

摘　　要：为了克服随机规划、模糊规划以及不确定规划期望值模型在实际应用中的局限性,基于乐观值和悲观值,提出了新的不确定机会约束规划模型。首先,根据目标函数的分类,分别定义了收益函数和成本函数的乐观值与悲观值,并在此基础上建立了不确定机会约束规划Maximax、Maximin、Minimin和Minimax模型;其次,给出了不确定机会约束规划模型的等价转化方法,将无法直接求解的不确定模型转化为可直接求解的等价确定模型,并分析了乐观值和悲观值随信度水平变化的规律;最后,以西安市某快递营业网点出行时间计划问题为例,对本文提出的模型、方法以及信度水平的影响进行了分析,指出信度水平实际上反映了决策者的风险偏好程度,实例结果表明本文提出的模型及方法具有可行性、有效性和实用性。To overcome the application limitations of stochastic programming, fuzzy programming and uncertain programming expected value model, a uncertain chance-constrained programming model is proposed based on optimistic and pessimistic values. Firstly, the optimistic and pessimistic values of the revenue function and cost function are defined based on the classification of objective functions. On this basis, the Maximax, Maximin, Minimin, and Minimax models of uncertain chance-constrained programming are established. Secondly , the equivalent transformation methods are proposed, making it possible to solve the uncertain chance-constrained programming models directly. The influences of belief degree on the models are also studied. Finally, the proposed models, methods and the influences of belief degree are analyzed by an example of the travel time planning problem of an express delivery network in Xi’an. And it is also pointed out that the belief degree can reflect the risk preference of the decision makers in this case. The results prove the feasibility, validity and practicability of the proposed models and methods.

关 键 词：不确定规划 机会约束 乐观值 悲观值 信度水平 

分 类 号：O221.6[理学—运筹学与控制论]