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2 Foundations of Computing and Decision Sciences

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Batch scheduling in a two-stage flexible flow shop problem

Gerstl E., Mosheiov G., Sarig A.

Foundations of Computing and Decision Sciences

2014

Vol. 39, No. 1

3--16

We study a special two-stage flexible flowshop, which consists of several parallel identical machines in the first stage and a single machine in the second stage. We assume identical jobs, and the option of batching, with a required setup time prior to the processing of a new batch. We also consider the option to use only a subset of the available machines. The objective is minimum makespan. A unique optimal solution is introduced, containing the optimal number of machines to be used, the sequence of batch sizes, and the batch schedule. The running time of our proposed solution algorithm is independent of the number of jobs, and linear in the number of machines.

Scheduling and due-date assignment problems with job rejection

Mosheiov G., Sarig A.

Foundations of Computing and Decision Sciences

2009

Vol. 34, No. 3

193-208

Scheduling with rejection reflects a very common scenario, where the scheduler may decide not to process a job if it is not profitable. We study the option of rejection in several popular and well-known scheduling and due-date assignment problems. A number of settings are considered: due-date and due-window assignment problems with job-independent costs, a due-date assignment problem with job-dependent weights and unit jobs, minimum total weighted earliness and tardiness cost with job-dependent and symmetric weights (known as TWET), and several classical scheduling problems (minimum makespan, flow-time, earliness-tardiness) with position-dependent processing times. All problems (excluding TWET) are shown to have a polynomial time solution. For the (NP-hard) TWET, a pseudo-polynomial time dynamic programming algorithm is introduced and tested numerically.