Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Minimizing the makespan on a batch machine with non-identical job sizes: an exact procedure
Computers and Operations Research
Batch processing with interval graph compatibilities between tasks
Discrete Applied Mathematics
Flowshop scheduling problem with a batching machine and task compatibilities
Computers and Operations Research
Scheduling hybrid flowshop with parallel batching machines and compatibilities
Computers and Operations Research
Single machine parallel-batch scheduling with deteriorating jobs
Theoretical Computer Science
On scheduling an unbounded batch machine
Operations Research Letters
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The problem of scheduling n jobs on an unbounded batching machine to minimize a regular objective function is studied. In this problem intervals for job processing times are given. The machine can process any number of jobs in a batch, provided that the processing time intervals of these jobs have a non-empty intersection. The jobs in the same batch start and complete together, and the batch processing time is equal to the left endpoint of the intersection of the processing time intervals in this batch. Properties of an optimal schedule are established and an enumerative algorithm based on these properties is developed. For the total completion time minimization, a dynamic programming algorithm is developed. Minimizing the makespan is shown to be solvable in O(nlogn) time and minimizing the maximum lateness is proved to be NP-hard.