Simulation-based optimization for strategic design problems

我们探索一种新颖的方法来解决各种现实生活中的战略设计问题，包括物流规划、呼叫中心人员配备、库存管理、供应链设计、电信网络设计和航空公司调度。这是典型的，对于这些和其他现实的问题，该过程的随机性质不能被捕获使用一个已知的概率分布函数，或者如果这是可能的，所得到的性能指标没有一个封闭的形式表示。这些问题的特点是一个随机组件，必须考虑到在战略设计阶段，通常采用随机规划和排队论。我们探索另一个场地，对随机分量的分布和设置类型施加较少的限制，该方法的第一步是以一种将数学规划部分隔离在一个子程序中的方式来分解问题，子问题和仿真组件在另一个。这两个子问题使用主问题进行协调。由于子问题通常很难解决（特别是仿真问题），因此有必要使用快速收敛到理想解的方法来解决主问题。为此，将使用分析中心切割平面法（ACCPM）。该应用程序是解决实践中出现的困难数学规划问题的主要研究计划的一部分。该研究计划结合了数学规划和模拟，以捕捉这些问题的复杂性，而不需要限制性的假设。它将使研究生能够在建模和解决复杂的现实生活中的问题，这将对一些行业产生直接影响的培训。

We explore a novel approach to solve a variety of real-life strategic design problems that include logistics planning, call center staffing, inventory management, supply chain design, telecommunication network design, and airline scheduling. It is typical for these, and other realistic problems, that the stochastic nature of the process can not be captured using a known probability distribution function, or if this is possible the resulting performance measures do not have a closed form expression. These problems are characterized by a stochastic component that has to be taken into account at the strategic design stage, and are typically approached using stochastic programming and queuing theory. We explore another venue that imposes less restrictions on the type of distribution and setting of the stochastic component, leading to mathematical programs where some of the terms in the objective function or the constraints do not have a closed form expression and have to be evaluated using a simulation subroutine.The first step in the approach is to decompose the problem in a way that isolates the mathematical programming component in one subproblem and the simulation component in another. The two subproblems are coordinated using a master problem. As the subproblems are typically hard to solve (especially the simulation one), it is necessary to tackle the master problem using a method that converges quickly to a desirable solution. For that, the Analytic Center Cutting Plane Method (ACCPM) will be used.The application is part of a major research program to solve hard mathematical programming problems that arise in practice. The research program  combines mathematical programming and simulation to capture the complexities of such problems, without the need for  restrictive assumptions. It will  enable the training of graduate students in the modelling and solution of complex real-life problems that will hav a  direct impact on a number of industries.