A polynomial-time approximation scheme for parallel two-stage flowshops under makespan constraint

TL;DR

This paper introduces a polynomial-time approximation scheme for scheduling parallel two-stage flowshops under makespan constraints, combining techniques from flowshop and knapsack problems, with applications in cloud computing.

Contribution

It provides the first PTAS for the problem when the number of flowshops is fixed, answering an open question about its approximability.

Findings

Developed a PTAS for fixed number of flowshops

Utilized guessing strategies and LP rounding techniques

Achieved near-optimal scheduling under makespan constraints

Abstract

As a hybrid of the Parallel Two-stage Flowshop problem and the Multiple Knapsack problem, we investigate the scheduling of parallel two-stage flowshops under makespan constraint, which was motivated by applications in cloud computing and introduced by Chen et al. [3] recently. A set of two-stage jobs are selected and scheduled on parallel two-stage flowshops to achieve the maximum total profit while maintaining the given makespan constraint. We give a positive answer to an open question about its approximability proposed by Chen et al. [3]. More specifically, based on guessing strategies and rounding techniques for linear programs, we present a polynomial-time approximation scheme (PTAS) for the case when the number of flowshops is a fixed constant.