Mixed-integer Linear Programming Models in Supply-Chain and Reliability Management

供应链和可靠性管理中的混合整数线性规划模型

• 批准号: 1949403
• 金额: --
• 依托单位: University of Southampton
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1949403
• 关键词: Mixed; integer; Linear; Programming; Models

This project focusses on bilevel optimisation. Bilevel optimisation problems consist of two problems, defined as the leaders and the follower's problems and we can think of these two problems being solved sequentially. The leader shall go first, defining their variables such that they will maximise their objective. The follower, will then optimise their problem, with the leader's variables acting as parameters. One can think of this as the follower reacting to the leader. The follower's variables are contained within the leaders problem and will affect their objective. Hence, when the leader is optimising, they must ensure that the followers variables in their problem, will match the reaction of the follower, otherwise their solution is not a feasible one. Due to this reaction structure, bilevel optimisation has applications within, among others, the energy and transportation sectors. One of the state of the art techniques used to solve bilevel problems is to exchange the follower's problem for constraints which are necessary for optimality. One such method is known as the Value Function Approach, ensuring that the follower's variables in the leader's problem are indeed optimal for the follower.However, the value function is a complex function, difficult to evaluate, which cannot always be explicitly included in the leader's problem. The aim of this project is to utilise the Value Function Approach for a specific bilevel problem in which the leader's variables affect the follower's objective, but not their variables.The goal of this research is to conceive an efficient algorithm based on the Value Function Approach for this problem type, which shall be quicker than generic bilevel solvers applied to such problems.

这个项目的重点是双层优化。双层优化问题由两个问题组成，定义为领导者和追随者的问题，我们可以认为这两个问题是顺序解决的。领导者应该先开始，定义他们的变量，这样他们就能最大限度地实现他们的目标。跟随者将优化他们的问题，领导者的变量作为参数。人们可以把这看作是追随者对领导者的反应。追随者的变量包含在领导者的问题中，并将影响他们的目标。因此，当领导者进行优化时，他们必须确保他们问题中的追随者变量与追随者的反应相匹配，否则他们的解决方案不是可行的。由于这种反应结构，双层优化在能源和运输部门等领域有应用。用于解决双层问题的最新技术之一是将跟随者的问题交换为最优性所必需的约束。其中一种方法被称为价值函数法（Value Function Approach），它确保领导者问题中的追随者变量确实是追随者的最优变量。然而，价值函数是一个复杂的函数，很难评估，不能总是显式地包含在领导者问题中。本研究的目的是利用价值函数法求解一类特殊的两层问题，其中领导者的变量影响跟随者的目标，但不影响他们的变量，本研究的目的是构思一种基于价值函数法的高效算法，这种算法比一般的两层求解器应用于此类问题要快。