Order scheduling in an environment with dedicated resources in parallel

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 may have a release date r _j and a due date d _j. The different product types for order j can be produced at the same time. We consider the class of objectives Σ f_j(C_j) that includes objectives such as the total weighted completion time Σ w_jC_j and the total weighted tardiness Σ w_jT_j of the n orders. We present structural properties of the various problems and a complexity result. In particular, we show that minimizing Σ C_j when m ≥ 3 is strongly NP-hard. We introduce two new heuristics for the Σ C_j objective. An empirical analysis shows that our heuristics outperform all heuristics that have been proposed for this problem in the literature.