Approximation Algorithms for Scheduling with Rejection on Two Unrelated Parallel Machines

Feng Lin,Zengxia Cai,Xianzhao Zhang

doi:10.14569/ijacsa.2015.061134

Feng Lin, Zengxia Cai + Show 1 more

Open Access

https://doi.org/10.14569/ijacsa.2015.061134

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Abstract

In this paper, we study the scheduling problem with rejection on two unrelated parallel machines. We may choose to reject some jobs, thus incurring the corresponding penalty. The goal is to minimize the makespan plus the sum of the penalties of the rejected jobs. We first formulate this scheduling problem into an integer program, then relax it into a linear program. From the optimal solution to the linear program, we obtain the two algorithms using the technique of linear programming rounding. In conclusion, we present a deterministic 3-approximation algorithm and a randomized 3-approximation algorithm for this problem.

Highlights

The unrelated parallel machine scheduling problem to minimize makespan, R Cmax following the notation of Graham et al [1], is one of the classic NP- hard problems in combinatorial optimization
The scheduling problem with rejection arises in make-toorder production systems with limited production capacity and tight delivery requirements, where simultaneous job rejection and scheduling decisions have to be made for maximizing the total revenue
Skutella and Woeginger [6] consider the preemptive scheduling with rejection, and the goal is to optimize the preemptive makespan on the m parallel machines plus the sum of the penalties of the rejected jobs

Summary

INTRODUCTION

The unrelated parallel machine scheduling problem to minimize makespan, R Cmax following the notation of Graham et al [1], is one of the classic NP- hard problems in combinatorial optimization. Skutella and Woeginger [6] consider the preemptive scheduling with rejection, and the goal is to optimize the preemptive makespan on the m parallel machines plus the sum of the penalties of the rejected jobs They provide a complete classification of these scheduling problems on complexity and approximability. The objective is to minimize the scheduling cost of the accepted jobs plus The total penalty of the rejected jobs They propose two fully polynomial time approximation schemes for the problems under consideration.

A 3-APPROXIMATION ALGORITHM FOR

1: Whenever z

A RANDOMIZED 3-APPROXIMATION ALGORITHM FOR

CONCLUSION