Mixed logical–linear programming

Mixed logical–linear programming (MLLP) is an extension of mixed integer–linear programming (MILP). It can represent the discrete elements of a problem with logical propositions and provides a more natural modeling framework than MILP. It can also have computational advantages, partly because it eliminates integer variables when they serve no purpose, provides alternatives to the traditional continuous relaxation, and applies logic processing algorithms. This paper surveys previous work and attempts to organize ideas associated with MLLP, some old and some new, into a coherent framework. It articulates potential advantages of MLLP's wider choice of modeling and solution options and illustrates some of them with computational experiments.