Simulation Optimization is Evolving

Abstract

Michael Fu’s paper comparing the theory and practice of simulation optimization implies that there is disconnect between academic research and commercial software. This author agrees wholeheartedly with this premise. The disconnect exists for several good reasons which, for the most part, do not include ignorance of past work. One reason, as Michael Fu points out, is that the problems academics solve are usually modeled with a small number of continuous variables without any constraints. Although these types of problems permit rich mathematical analyses, they seldom represent anything of interest for a practitioner. Most of the problems to which commercial optimizers are subjected contain many variables, usually discrete, with multiple constraints that may be linear or nonlinear in nature. Just as few results from nonlinear programming have been of use to researchers solving integer programs, it should be of no large surprise that few optimization principles can be translated from the academic simulation optimization literature to commercial products. Another reason for the disconnect is that the practical constraints imposed by general-purpose commercial software are often not taken into consideration by academic research. In particular, the general simulation community knows extremely little about the core algorithms and techniques used in optimization. For this reason, actual implementations must be extremely easy to use and, even more importantly, easy to interpret. Complex analyses with multiple choices will only confuse the typical user. Furthermore, actual programming restrictions often limit the flexibility of a commercial system in ways that restrict the types of analyses possible. Variance reduction techniques based on common random numbers may look promising on paper but are often quite difficult to implement using commercial simulation packages. Lastly, and perhaps most significantly in the commercial world, a reason for the disconnect between practitioners and academics is in the very definition of optimization. For better or worse, “optimization” in the commercial market usually means solution improvement. It is not defined in terms of an optimal answer but rather in moving toward a high-quality solution. The perceived need for a provably optimal answer is almost nonexistent. For the remainder of this commentary, I will focus on what commercial optimization does do rather than what it has not adopted from the simulation literature. Finally, I will make some comments concerning how simulation optimization is evolving and present an example of a real-world simulation optimization problem in the field of customer relationship management. These uses of simulation have produced widespread benefits in industry, reducing costs and increasing profits through improved decisions. In spite of its acknowledged benefits, simulation has suffered a limitation that has prevented it from uncovering the best decisions in critical practical settings. This limitation arises out of an inability to evaluate more than a fraction of the immense range of options available. Practical problems in areas such as manufacturing, marketing, logistics, and finance typically pose vast numbers of interconnected alternatives to consider. As a consequence, the decision-making goal of identifying and evaluating the best (or near best) options has been impossible to achieve in many applications. In all but the most trivial problems, traditional techniques such as design of experiments have been inadequate.