Simulation-based optimization for strategic design problems

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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.