Minimizing total tardiness on one machine is NP-hard
Mathematics of Operations Research
Intelligent scheduling
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Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Order scheduling in dedicated and flexible machine environments
Order scheduling in dedicated and flexible machine environments
A note on the complexity of the concurrent open shop problem
Journal of Scheduling
Scheduling orders for multiple product types to minimize total weighted completion time
Discrete Applied Mathematics
Distributed order scheduling and its application to multi-core dram controllers
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Solving two-machine assembly scheduling problems with inventory constraints
Computers and Industrial Engineering
Minimizing the sum of weighted completion times in a concurrent open shop
Operations Research Letters
Minimizing the total weighted completion time of fully parallel jobs with integer parallel units
Theoretical Computer Science
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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 rj and a due date dj. The different product types for order j can be produced at the same time. We consider the class of objectives 驴 fj(Cj) that includes objectives such as the total weighted completion time 驴 wj Cj and the total weighted tardiness 驴 wj Tj of the n orders. We present structural properties of the various problems and a complexity result. In particular, we show that minimizing 驴 Cj when m 驴 3 is strongly NP-hard. We introduce two new heuristics for the 驴 Cj objective. An empirical analysis shows that our heuristics outperform all heuristics that have been proposed for this problem in the literature.