Mixed integer formulations using natural variables for single machine scheduling around a common due date

While almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we in this work mixed integer formulations. We consider a single machine problem that aims at minimizing the weighted sum of earliness–tardiness penalties around common due date. Using natural variables, provide one compact formulation for unrestrictive case and, general case, non-compact based on non-overlapping inequalities. show separation related to latter is solved polynomially. In formulation, solutions are only encoded by extreme points. establish theoretical framework validity such using inequalities, could be used other problems. A Branch-and-Cut algorithm together with an experimental analysis proposed assess practical relevance programming methods.