We consider a production planning problem known as the discrete lot-sizing and scheduling problem (DLSP) and study a variant of the DLSP involving several identical parallel resources. We show how to solve the resulting discrete optimisation problem as a mixed-integer linear program using a commercial MIP solver. To achieve this, we exhibit a family of strong valid inequalities for which the associated separation problem is efficiently solvable. Our computational results show that the proposed solution algorithm is capable of providing optimal solutions for medium-sized instances.