Improving Mathematical Exposition of an Industrial-Scale Linear Program

Industrial-scale models require considerable setup time; hence, once built, they are used in myriad ways to consider closely related cases. In practice, the code for these models frequently evolves without appropriate notational choices, largely as a result of the lengthy development time of, and the number of individuals contributing to, their formulation. This leads to inefficiencies and obfuscates model structures that might be leveraged to expedite solutions. In this paper, we advocate for an emerging literature on model formulation "best practices" and present the reformulation of a widely used industrial-scale linear program. The efficient mathematical expression of this linear program, used to plan capacity expansion in the energy sector, allows for greater transparency of model structures and enhanced ability to identify computational performance improvements, as well as a lucid interpretation of its solutions. This type of formulation is employed in several mathematical programming courses at our university as an example of the advantages of best practices; the model more broadly is used widely to inform policy in the U.S. energy sector.