A PTAS for the Multiple Parallel Identical Multi-stage Flow-Shops to Minimize the Makespan
Document Type
Presentation
Presentation Date
7-1-2016
Abstract or Description
In the parallel k-stage flow-shops problem, we are given m identical k-stage flow-shops and a set of jobs. Each job can be processed by any one of the flow-shops but switching between flow-shops is not allowed. The objective is to minimize the makespan, which is the finishing time of the last job. This problem generalizes the classical parallel identical machine scheduling (where k=1) and the classical flow-shop scheduling (where m=1) problems, and thus it is NP-hard. We present a polynomial-time approximation scheme for the problem, when m and k are fixed constants. The key technique is to enumerate over schedules for big jobs, solve a linear programming for small jobs, and add the fractional small jobs at the end. Such a technique has been used in the design of similar approximation schemes.
Sponsorship/Conference/Institution
International Workshop on Frontiers in Algorithmics (FAW)
Location
Qingdao, China
Recommended Citation
Tong, Weitian, Eiji Miyano, Randy Goebel, Guohui Lin.
2016.
"A PTAS for the Multiple Parallel Identical Multi-stage Flow-Shops to Minimize the Makespan."
Department of Computer Science Faculty Presentations.
Presentation 3.
https://digitalcommons.georgiasouthern.edu/compsci-facpres/3
