Single machine batch scheduling with jointly compressible setup and processing times

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.