Mathematical Modeling in Logistics: In for a Penny, in for a Pound

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Several articles in this issue of the Journal of Business Logistics identify opportunities, which promise to bring significant advances in theory and practice by encouraging methodologies that enable us to address complex questions with greater efficacy. This enables us to address areas of practice and theory where complexity had impeded academic advancement. Analytical modeling in logistics often requires unnecessarily limiting assumptions to make the models tractable. Sometimes these assumptions are regarding the probability distribution of demand or demand during lead time, as is the case with the loss integral, which decorates so many of our textbooks and chalkboards. However, in the real world, it is common for hybrid replenishment processes to be used, demand is often non-stationary, demand during lead time is discrete, and, as a result, the density function and expected values may not exist. With discrete event simulation, these restrictions are unnecessary. Phil Evers and Xiang Wan discuss discrete event simulation within the context of systems modeling. Evers and Wan point out that the power and ease of simulation has increased, eliminating the need for programing and even providing tools to make results more dynamically presentable. Assuming the researcher has a thorough functional understanding of simulation modeling and of the question being asked, the current tools available for simulation put this methodology firmly in the hands of all researchers. Metahueristics offer an underutilized solution to problems of too high complexity to be addressed in a timely fashion by optimization, as presented by Stanley Griffis, John Bell, and David Closs. Metaheuristics may not obtain globally optimal solutions; however, they obtain near optimal solutions in an efficient manner not obtainable by traditional optimization solutions. In this way, they are more apt to address the complexity of real-life systems. Simultaneous sourcing and routing decisions are excellent candidates for metaheuristics solutions, because of their complexity. Griffis, Bell, and Closs present ant colony optimization, genetic algorithm, simulated annealing, and tabu search metaheuristics as solutions to this type of high-complexity problem. Michael Bartolacci, Larry LeBlanc, Yasanur Kayikci, and Thomas Grossman discuss practical issues of optimization in logistics. Optimization tools that are now available to businesses include spreadsheets as well as the less-common algebraic optimization models. Increased access to data and more widely available computational power have allowed for more widespread use of optimization in practical business operations. Although these applications have practical limitations, especially as multi-echelon optimization tools have not been well developed, they also offer greater power to day-to-day business logistics management than ever before. Dale Rogers, Benjamin Melamed, and Ronald Lembke provide a case in point—reverse logistics. Although the reverse logistics stream is a rough parallel of the forward logistics stream, there are some areas in which it is not only different but is also more complex. Rogers, Melamed, and Lembke argue that the types of tools that are used on forward logistics are also applicable to reverse logistics; however the tools will need to be developed specifically for reverse logistics. Reverse logistics streams can be modeled, just as forward logistics can, however the increased complexity of reverse logistics makes the modeling process more challenging. Reverse logistics is an area, which has been less thoroughly studied than other disciplines, but offers opportunities for improving business logistics, perhaps using the tools mentioned by Evers and Wan or Griffis, Bell, and Closs. Recently, we have embarked on a focused endeavor to identify and encourage addressing old questions with new methods or addressing new and more challenging questions altogether. As we stated then, the low-hanging fruit has been picked, it is time to reach for the higher branches (Waller and Fawcett 2011). This thought leader series, as part of that effort, is intended to bring to light methodologies that are newly available, or areas which have been under-addressed in our discipline. Simulation and metaheuristics represent relevant methodologies with numerous real opportunities in business logistics. Applied logistics optimization and reverse logistics represent areas that have not been fully addressed, partly because of their complexity, which no longer need be a hindrance, given the methods available to us. Simple, unrealistic models sometimes offer insights to larger, more complex models. However, at Journal of Business Logistics, as simulation methods and technology are advanced, metaheuristics exist to find near optimal solutions, and powerful optimization is now in the hands of nearly any manager, let us not just model these simple systems, let us model the realistic, complex systems—in for a penny, in for a pound. We are grateful to the following researchers for their contribution to this Thought Leader series: Phil Evers, Xiang Wan, Stanley Griffis, John Bell, David Closs, Dale Rogers, Benjamin Melamed, Ronald Lembke, Michael Bartolacci, Larry LeBlanc, Yasanur Kayikci, and Thomas Grossman. We thank Christopher Vincent for his helpful comments, edits and input. His additions resulted in a significant improvement to this manuscript.