Business Case Studies & Business Publications

Using Binary Variables to Represent Logi...

Ovchinnikov, Anton...

Technical Note

Using Binary Variables to Represent Logical Conditions in Optimization Models

Ovchinnikov, Anton S.

QA-0786 | Published April 11, 2012 | 5 pages Technical Note

Collection: Darden School of Business

Product Details

Logical conditions that link different elements of a business decision are very common in managerial practice. For example, a firm can ship only to and from warehouses that are open; patients needing MRIs can only get service in clinics that have MRI equipment; regarding an old power plant, one can decide to close it or retrofit it, but one obviously cannot retrofit a closed plant. The list goes on. In quantitative modeling of such situations, a natural step is to use IF statements such as IF(a warehouse in city N is open, then we can ship to/from it; otherwise no shipments can be made in/out of a warehouse in N). In optimization models, however, IF statements lead to non-linearity with all the associated challenges. Fortunately, nearly all logical conditions can be modeled linearly using binary variables. This note describes some helpful modeling techniques for doing that.