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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.

A two-stage flow shop scheduling with a critical machine and batch availability

Gerstl E., Mosheiov G.

Foundations of Computing and Decision Sciences

2012

Vol. 37, No. 1

39-56

We study a two-stage flowshop, where each job is processed on the first (critical) machine, and then continues to one of two second-stage (dedicated) machines. We assume identical (but machine-dependent) job processing times. Jobs are processed on the critical machine in batches, and a setup time is required when starting a new batch. The setting assumes batch-availability, i.e., jobs become available for the second stage only when their entire batch is completed on the critical machine. We consider three objective functions: minimum makespan, minimum total load, and minimum weighted flow-time. Polynomial time dynamic programming algorithms are introduced, which are numerically shown to be able to solve problems of medium size in reasonable time. A heuristic for makespan minimization is presented and shown numerically to be both accurate and efficient.

Job-Dependent Due-Window Assignment Based On A Common Flow Allowance

Mosheiov G., Oron D.

Foundations of Computing and Decision Sciences

2010

Vol. 35, No. 3

185-195

A due-window assignment model is an extension of the classical due-date assignment, where a time interval (rather than a time point) is determined, such that jobs completed within this time interval are not penalized. Jobs completed outside the due-window are penalized according to their earliness/tardiness values. In this paper we solve a job-dependent due-window assignment problem, assuming a common flow allowance. We introduce an efficient 0(n log n) solution algorithm (where n is the number of jobs). We then consider the case of position-dependent processing times, showing that the problem remains solvable in polynomial time.

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.