Consistent notation for presenting complex optimization models in technical writing

Abstract

With an increase in computational power, and with recent advances in software, practitioners are formulating ever more complicated optimization models, many of which are drawn from interdisciplinary applications and are designed to reflect the details of real-world systems. While such models have proven useful in providing implementable solutions with a verified impact, they are also more cumbersome to document in a clear and concise manner. In this paper, we recommend: (i) conventions for defining sets, parameters, and variables, (ii) ways of presenting the objective and constraints, and (iii) means by which to organize formulations. While other conventions may be perfectly acceptable, we suggest one set of guidelines for graduate students, academics, and practitioners in need of clearly and easily presenting a large, complex optimization model. Self-study and/or the introduction of these principles into an applied, advanced graduate class can remove ambiguity from model formulations and improve the communication between modelers and their intended audience.