Closest assignment constraints and location models: Properties and structure

Formulations of location–allocation models must address the assignment of demand to facilities. Many models allow demand to be assigned to a non-closest facility. However, many applications exist where closest assignment (CA) is preferred. Several types of constraints have been introduced over the last 25 years to force CA. The objectives of this paper are to identify applications for closest assignment constraints, to review previous work, to propose necessary improvements to one of the major CA constraints, and to offer a comparison of the different integer–linear approaches to CA. In addition, new constraints are presented that are designed to ensure equal allocations in the event of equidistant closest facilities. We also note, as have previous researchers, that ‘closest assignment’ generalizes to ‘most preferred’ assignment with no alterations to constraint structures.