On makespan improvement in flow shops with multiple processors

Abstract

Application of a makespan improvement heuristic in the¯ow shop with multiple processors (FSMP) scheduling environment is presented. The Exchange Heuristic (EH) is a multiple-pass procedure that has successfully been utilized in the job shop and project scheduling environments. Promising FSMP application is evidenced via empirical study of two problem sets. One set consists of 653 small-to mediumsized problems with known optimal makespans and the other set consists of larger problems with 100 activities (twenty jobs and ® ve stages). Findings indicate that the EH is able to produce FSMP makespan improvements without substantial increases in computational time. Furthermore, optimal solutions to two 20-job, 5 machine FSMP problems are identi® ed and can be used as benchmarks in future studies.

The hybrid flow shop scheduling problem

“…A number of such heuristics, for instance, are proposed in [44] and [167] for the m-stage problem with any number of machines per stage. Later, [165] proposed an improvement heuristic for the m-stage HFS with the makespan criterion. [167] proposes a simple heuristic for the minimization of makespan in a similar shop but with limited buffers.…”

Minimizing The Number of Tardy Jobs in Hybrid Flow Shops with Non-Identical Multiple Processors

“…The assumptions used in this work are consistent with general studies in scheduling (French 1982) and particular investigations in other FSMP studies (Santos, Hunsucker, and Deal (2001), Brah and Loo (1999), Hunsucker and Shah (1994), among others) and are as follows:…”

Two hybrid flow shop scheduling lines with assembly stage and compatibility constraints

“…For the FHm; ðRM ðkÞ Þ m k¼1 jj C max problem, [9] propose branch-and-bound algorithms. Also, [10,11] determine lower bounds, while heuristics and metaheuristics are proposed in [12][13][14][15]. Moreover, neural networks are presented in [16], and ant-colony algorithms in [17].…”

“…Constraints (10)) follow the idea proposed by [36] for sub-tours elimination purposes and establish the completion time of the jobs by considering the setup and the processing times; B is a big number that can be easily bounded. Constraints (12) indicate the simultaneous arrival of a product's components at the assembly stage. Finally, the last two constraints establish the nature of the variables.…”