Scheduling orders for multiple product types with due date related objectives

We consider m machines in parallel with each machine capable of producing one specific product type. There are n orders with each one requesting specific quantities of the various different product types. Order j has a release date rj and a due date dj. The different product types for order j can be produced at the same time. We consider various due date related objectives such as the minimization of the maximum lateness Lmax and the total number of late orders ∑Uj∑Uj. We present polynomial time algorithms for the easy cases and heuristics for NP-hard cases. For minimizing ∑Uj∑Uj, we also propose an exact algorithm based on Constraint Propagation and bounding strategy. The effectiveness of the algorithms is demonstrated through an empirical study.