Multiple choice programming: A state-of-the-art review

Abstract

Multiple choice programming, originated from Healy Jr, belongs to the non-convex mathematical programming with special ordered sets of variables type 1 as identified by Beale and Tomlin. The high applicability of multiple choice programming in many decision-making problems has made it a focus of many OR researchers and practitioners in the fields of integer programming, and combinatorics. We report a survey on the structures of multiple choice programming problems and their solution approaches. Applications of multiple choice programming and some prospective future researches are also discussed.