Simulation-based optimization for strategic design problems

我们探索了一种新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、呼叫中心人员配置、库存管理、供应链设计、电信网络设计和航空公司调度。对于这些和其他现实问题来说，典型的情况是不能使用已知的概率分布函数来捕捉过程的随机性质，或者如果这是可能的，则所产生的性能测量没有封闭形式的表达式。这些问题的特点是在战略设计阶段必须考虑的随机成分，通常使用随机规划和排队理论来处理。我们探索了另一种对随机分量的分布和设置施加较少限制的场所，从而产生了数学规划，其中目标函数或约束中的一些项没有闭合形式的表达式，必须使用模拟子例程进行评估。该方法的第一步是将问题分解，将数学规划分量分离到一个子问题中，而将模拟分量分离到另一个子问题中。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(特别是模拟问题)，因此有必要使用一种快速收敛到所需解决方案的方法来解决主问题。为此，将使用解析中心割平面法(ACCPM)。这一应用是解决实际中出现的困难数学规划问题的重大研究计划的一部分。该研究计划还将数学编程和模拟相结合，以捕捉此类问题的复杂性，而不需要进行限制性假设。它还将使研究生能够在建模和解决复杂的现实生活问题方面进行培训，这些问题将对一些行业产生直接影响。

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.