Operations research practitioners frequently need to enforce logical conditions, such as if-then implications, within a mixed-integer linear program (MILP). Unfortunately, it is not always clear how to represent such conditions as linear constraints. This chapter review techniques that use binary variables to write linear constraints that enforce various types of logical conditions. Sometimes, these binary variables represent yes/no decisions that already have meaning within the model, while other times auxiliary binary variables are added to the formulation with the sole purpose of enforcing the desired logic.

Forrester, Richard J., and Lucas A. Waddell. Modeling Using Logical Constraints. In Encyclopedia of Optimization, 3rd ed., edited by Panos M. Pardalos and Oleg A. Prokopyev, 5 pp. Cham: Springer, 2023. https://link.springer.com/referenceworkentry/10.1007/978-3-030-54621-2_834-1

Richard Forrester is a professor of Mathematics and Data Analytics at Dickinson College.

For more information on the published version, visit Springer's Website. https://link.springer.com/referencework/10.1007/978-3-030-54621-2

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