Optimal solutions for unrelated parallel machines scheduling problems using convex quadratic reformulations

We consider the unrelated parallel machines scheduling problem where jobs have earliness and tardiness penalties and a common due date. We formulate this problem and some of its variants as 0-1 programs with quadratic objective function subject to linear constraints. The main contribution of this paper is to use and develop different convex reformulations to solve exactly the quadratic programs. We show that this new link between quadratic programming and scheduling can be theoretically and practically interesting.