Single-Machine Parallel-Batch Scheduling with Nonidentical Job Sizes and Rejection

Miaomiao Jin,Xiaoxia Liu,Wenchang Luo

doi:10.3390/math8020258

Abstract

We investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. In this problem, a set of jobs with different processing times and nonidentical sizes is given to be possibly processed on a parallel-batch processing machine. Each job is either accepted and then processed on the machine or rejected by paying its rejection penalty. Preemption is not allowed. Our task is to choose the accepted jobs and schedule them as batches on the machine to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs. We provide an integer programming formulation to exactly solve our problem. Then, we propose three fast heuristic algorithms to solve the problem and evaluate their performances by using a small numerical example.

Highlights

We investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection
The processing time for a parallel batch is defined as the longest processing time of the jobs in the batch
Our task is to choose the accepted jobs and schedule them as batches on the single machine to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs

Summary

Introduction

We investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. Liu and Yu [4] considered the single-machine batch processing scheduling problem with jobs having release dates and the objective function is to minimize the makespan. Lu et al [9] studied an unbounded parallel-batch processing machine scheduling problem with release dates and rejection with the goal to minimize the makespan plus the total rejection penalty. They showed that the problem is weakly. For the bounded parallel-batch processing machine scheduling problem with release dates and rejection, Lu et al [10] proved that it is strongly NP-hard and presented a two-approximation algorithm and a polynomial time approximation scheme (PTAS); Cao and Yang [11] derived a PTAS He et al [12].

Integer Programming Formulation

Three Heuristics Algorithms

A numerical Example

Concluding Remarks