Two-Agent Pareto-Scheduling of Minimizing Total Weighted Completion Time and Total Weighted Late Work

Yuan Zhang,Jinjiang Yuan,Zhichao Geng

doi:10.3390/math8112070

Abstract

We investigate the Pareto-scheduling problem with two competing agents on a single machine to minimize the total weighted completion time of agent A’s jobs and the total weighted late work of agent B’s jobs, the B-jobs having a common due date. Since this problem is known to be NP-hard, we present two pseudo-polynomial-time exact algorithms to generate the Pareto frontier and an approximation algorithm to generate a (1+ϵ)-approximate Pareto frontier. In addition, some numerical tests are undertaken to evaluate the effectiveness of our algorithms.

Highlights

Problem description and motivation: Multi-agent scheduling has attracted an ever-increasing research interest due to its extensive applications
Falling into the category of Pareto-scheduling, the problem studied in this paper aims at generating all Pareto-optimal points (PoPs) and the corresponding Pareto-optimal schedules (PoSs)
In the prophase work (Zhang and Yuan [20]), we proved that the constrained scheduling problem of minimizing the total late work of agent A’s jobs with equal due dates subject to the makespan of agent

Summary

Introduction

Problem description and motivation: Multi-agent scheduling has attracted an ever-increasing research interest due to its extensive applications (see the book of Agnetis et al [1]). Among the common four problem-versions (including lexical-, positive-combination-, constrained-, and Pareto-scheduling, as shown in Li and Yuan [2]) for a given group of criteria for multiple agents, Pareto-scheduling has the most important practical value, since it reflects the effective tradeoff between the actual and (usually) conflicting requirements of different agents. Assume that two agents (A and B) compete to process their own sets of independent and non-preemptive jobs on a single machine. All jobs are available at time zero, and are scheduled consecutively without idle time due to the regularity of the objective functions as shown later. Each job JjX has a processing time p X j and a

Objectives

Results

Conclusion