Time-optimal control in a single machine problem with resource constraints
Automatica (Journal of IFAC)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Fuzzy Optimization and Decision Making
A survey of scheduling with controllable processing times
Discrete Applied Mathematics
A new approach to the learning effect: Beyond the learning curve restrictions
Computers and Operations Research
Single-machine group scheduling with resource allocation and learning effect
Computers and Industrial Engineering
Single machine batch scheduling problem with fuzzy batch size
Computers and Industrial Engineering
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We consider the problem of scheduling n jobs on a single machine where each job has a deadline and a processing time that is a linear decreasing function of the amount of a common discrete resource allocated to the job. Jobs may be combined to form batches containing contiguously scheduled jobs. For each batch, a constant set-up time is needed before the first job of the batch is processed. The completion time of each job in a batch coincides with the completion time of the last job in the batch. A schedule specifies the sequence of jobs and the size of each batch, i.e. the number of jobs it contains. The objective is to find simultaneously a resource allocation and a schedule which is feasible with respect to the deadlines so as to minimize the total weighted resource consumption. The problem is shown to be NP-hard even for the special case of common parameters. Two dynamic programming algorithms are presented for the general problem, as well as a fully polynomial approximation scheme.