Single-Machine Scheduling with Upper Bounded Maintenance Time under the Deteriorating Effect

Pengfei Xue,Yulin Zhang

doi:10.1155/2013/756251

Abstract

We consider a single-machine scheduling problem with upper bounded actual processing time and upper bounded maintenance time under deteriorating effect. The actual processing time of a job is a position-dependent power function. If the actual processing time of a job exceeds the upper bound, tardiness penalty of the job should be paid. And if the maintenance time exceeds the corresponding upper bound, tardiness penalty of the maintenance should also be paid. The maintenance duration studied in the paper is a position-dependent exponential function. The objective is to find jointly the optimal maintenance frequency and the optimal job sequence to minimize the total cost, which is a linear function of the makespan and the total tardiness. We show that the studied scheduling problem can be transformed as a classic assignment problem to solve. There is also shown that a special case of the scheduling problem can be optimally solved by a lower order algorithm.

Highlights

In recent years, scheduling problems with the deteriorating effect have attracted increasing attention
This paper investigates a scheduling problem with upper bounded actual processing time of a job and upper bounded maintenance time under deteriorating effect
The objective is to minimize the total cost that is a linear function of the makespan and the tardiness penalties

Summary

Introduction

In recent years, scheduling problems with the deteriorating effect have attracted increasing attention. Rustogi and Strusevich [10] presented polynomial-time algorithms for single-machine problems with generalized positional deterioration effects under machine maintenance They assumed that the decisions should be taken regarding possible sequences of jobs and on the number of maintenance activities to be included into a schedule to minimize the overall makespan. A single-machine scheduling problem with a cyclic process of deteriorating effect and maintenance activities was addressed by Kuo and Yang [20]. For the problem, they provided polynomial algorithms to minimize the makespan. L. Yang [12] considered a single-machine scheduling problem with positiondependent deteriorating effect under variable maintenance activities to minimize the makespan of all jobs.

Notations and Problem Formulation

Total Cost Minimization

Conclusions