# A PTAS for the Multiple Parallel Identical Multi-stage Flow-shops to Minimize the Makespan

## Location

Room 2904 A

## Session Format

Paper Presentation

## Research Area Topic:

Computer Science - Computational Sciences

## Abstract

Scheduling is the process of arranging, controlling and optimizing work and workloads in a production process or manufacturing process. It has wide applications in manufacturing and engineering, as it can have a major impact on the productivity of a process. We will focus on one specific scheduling problem --- parallel k-stage flow-shops problem and propose an efficient algorithm. This theoretical result has been submitted to an international conference and is under the peer review. The abstract of this paper is as follows.

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 non-trivial and interesting, to enumerate over schedules for big jobs, solve a linear programming for small jobs, and add the fractional small jobs at the end.

## Presentation Type and Release Option

Presentation (Open Access)

## Start Date

4-16-2016 1:30 PM

## End Date

4-16-2016 2:30 PM

## Recommended Citation

Tong, Weitian, "A PTAS for the Multiple Parallel Identical Multi-stage Flow-shops to Minimize the Makespan" (2016). *GS4 Georgia Southern Student Scholars Symposium*. 162.

https://digitalcommons.georgiasouthern.edu/research_symposium/2016/2016/162

A PTAS for the Multiple Parallel Identical Multi-stage Flow-shops to Minimize the Makespan

Room 2904 A

Scheduling is the process of arranging, controlling and optimizing work and workloads in a production process or manufacturing process. It has wide applications in manufacturing and engineering, as it can have a major impact on the productivity of a process. We will focus on one specific scheduling problem --- parallel k-stage flow-shops problem and propose an efficient algorithm. This theoretical result has been submitted to an international conference and is under the peer review. The abstract of this paper is as follows.

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 non-trivial and interesting, to enumerate over schedules for big jobs, solve a linear programming for small jobs, and add the fractional small jobs at the end.