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24 References# Single machine batch scheduling with jointly compressible setup and processing times

**Abstract**

A single machine batch scheduling problem is addressed. A batch is a set of jobs processed contiguously and completed together when the processing of all jobs in the batch is finished. Processing of a batch requires a machine setup time common for all batches. Two external resources can be used to linearly compress setup and job processing times. The setup times are jointly compressible by one resource and the job processing times are jointly compressible by another resource, i.e., the amount of resource consumption for setup time compression is the same for all setups and the amount of resource consumption for job processing time compression is the same for all jobs. Polynomial time algorithms are presented to find an optimal batch sequence and optimal amounts of resource consumption such that either total job completion time is minimized, subject to an upper bound on total weighted resource consumption, or total weighted resource consumption is minimized, subject to an upper bound on total job completion time. The algorithms are based on results from linear programming and from batch scheduling with fixed setup and processing times.

- CitationsCitations24
- ReferencesReferences24

- "In most studies on scheduling with controllable processing times, researchers assume that the job processing time is a bounded linear function form described as follows (e.g. Biscup and Cheng 1999; Janiak and Kovalyov 1996; Ng, Cheng, and Kovalyov 2004): "

[Show abstract] [Hide abstract]**ABSTRACT:**This paper addresses the bicriteria scheduling problems with simultaneous consideration of job rejection, controllable processing times and rate-modifying activity on a single machine. A job is either rejected, in which case a rejection penalty will be incurred, or accepted and processed on the machine. The rate-modifying activity is an activity on the machine that changes the processing times of the jobs scheduled after the activity. The processing time of a job scheduled after the rate-modifying activity decreases with a job-dependent factor. The processing time of each job can also be controlled by allocating extra resource which is either a linear or a convex function of the amount of a common continuously divisible resource allocated to the job. The objective is to determine the rejected job set, the accepted job sequence, the time (location) of the rate-modifying activity and the resource allocation that jointly find the trade-off between two criteria, where the first criterion is measured as the sum of total completion time and resource consumption cost while the second criterion is the total rejection cost. We consider four different models for treating the two criteria. The computational complexity status and solution procedures are provided for the problems under consideration.- "We note that the uncertainties of the processing times in problem F2|p L ij ≤ p ij ≤ p U ij |C max are due to external forces while in a scheduling problem with controllable processing times the objective is both to set the processing times and find an optimal schedule (see, e.g., articles10111213). Our approach was originally proposed in [8] and developed in [14,15] for the C max criterion, and in [16] for the total completion time criterion, C i . "

- "We note that the uncertainties of the processing times in problem F2|p L ij ≤ p ij ≤ p U ij |C max are due to external forces while in a scheduling problem with controllable processing times the objective is both to set the processing times and find an optimal schedule (see, e.g., articles10111213). Our approach was originally proposed in [8] and developed in [14,15] for the C max criterion, and in [16] for the total completion time criterion, C i . "

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