We consider the extended trust region subproblem (eTRS) as the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of the S-Lemma, we derive the necessary and sufficient optimality conditions for eTRS. Then, an OCP/SDP formulation is introduced for the problem. Finally, several illustrative examp...

in this paper, a multi-product single machine scheduling problem with the possibility of producing defected jobs, is considered. we concern rework in the scheduling environment and propose a mixed-integer programming (mip) model for the problem.  based on the philosophy of just-in-time production, minimization of the sum of earliness and tardiness costs is taken into account as the objective fu...