Batching to minimize flow times on one machine
Management Science
One-pass batching algorithms for the one-machine problem
Discrete Applied Mathematics
Batch sizing and job sequencing on a single machine
Annals of Operations Research
Batching to minimize weighted mean flow time on a single machine with batch size restrictions
Computers and Industrial Engineering
A polynomial algorithm for a one machine batching problem
Operations Research Letters
Scheduling with batching: minimizing the weighted number of tardy jobs
Operations Research Letters
Single machine batch scheduling with deadlines and resource dependent processing times
Operations Research Letters
Minimizing flow-time on a single machine with integer batch sizes
Operations Research Letters
Batching in single operation manufacturing systems
Operations Research Letters
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In a batch scheduling problem, jobs are grouped (group is called batch) and scheduled in batches, and a setup time is incurred when starting a new batch. Processing times are assumed to be identical for all jobs. Setup times are assumed to be identical for all batches. Though all batch sizes cannot exceed a common upper bound, the upper bound is flexible and satisfaction degree with respect to the upper limit to be maximized is given. Also the other two objectives, i.e., the maximum completion time and the flow-time are to be minimized. Usually there exists no solution optimizing three objectives at a time. Therefore we define non-dominated solutions consisting of batch size, batch number and allocation of jobs to batches. First we propose an efficient algorithm for a sub-problem with fixed upper limit of batch size, fixed batch number based on a Lagrange relaxation procedure. Based on the properties of non-dominated solutions clarified in this paper, we propose an efficient algorithm to find some non-dominated solutions. Finally we summarize the results in this paper and discuss further research problems.