Multitasking Scheduling with Shared Processing

TL;DR

This paper extends a shared processing multitasking scheduling model to parallel machines with variable sharing ratios, analyzing complexity and approximation algorithms for minimizing makespan and total completion time.

Contribution

It generalizes the shared processing model to multiple machines with variable sharing ratios and provides approximation schemes under certain conditions.

Findings

No polynomial approximation if sharing ratios are arbitrary.

Classical algorithms perform well when sharing ratios have a lower bound.

Polynomial time approximation schemes are developed for fixed number of machines.

Abstract

Recently, the problem of multitasking scheduling has attracted a lot of attention in the service industries where workers frequently perform multiple tasks by switching from one task to another. Hall, Leung and Li (Discrete Applied Mathematics 2016) proposed a shared processing multitasking scheduling model which allows a team to continue to work on the primary tasks while processing the routinely scheduled activities as they occur. The processing sharing is achieved by allocating a fraction of the processing capacity to routine jobs and the remaining fraction, which we denote as sharing ratio, to the primary jobs. In this paper, we generalize this model to parallel machines and allow the fraction of the processing capacity assigned to routine jobs to vary from one to another. The objectives are minimizing makespan and minimizing the total completion time. We show that for both objectives, there is no polynomial time approximation algorithm unless P=NP if the sharing ratios are arbitrary for all machines. Then we consider the problems where the sharing ratios on some machines have a constant lower bound. For each objective, we analyze the performance of the classical scheduling algorithms and their variations and then develop a polynomial time approximation scheme when the number of machines is a constant.