Single-Machine Group Scheduling Problems with Variable Job Processing Times

Ping Ji,Lin Li

doi:10.1155/2015/758919

Abstract

This paper considers two resource constrained single-machine group scheduling problems. These problems involve variable job processing times (general position-dependent learning effects and deteriorating jobs); that is, the processing time of a job is defined by the function that involves its starting time and position in the group, and groups’ setup time is a positive strictly decreasing continuous function of the amount of consumed resource. Polynomial time algorithms are proposed to optimally solve the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.

Highlights

IntroductionThe jobs’ processing time is always assumed to be fixed and constant value
In classical scheduling theory, the jobs’ processing time is always assumed to be fixed and constant value
The group setup time was assumed to follow a simple linear timedependent deteriorating model. They examined two models of learning for the job processing time, provided polynomial time solutions for the makespan minimization problems, and showed that the total completion time minimization problems remained polynomially solvable under agreeable conditions

Summary

Introduction

The jobs’ processing time is always assumed to be fixed and constant value. Zhang and Yan [13] introduced a deteriorated and learning effect into a single-machine problem where the learning effect depends on job position, and depends on the group position; the deteriorated effect depends on its starting time of the job They showed that the makespan, the total completion time, and maximum lateness problems remained polynomially optimally solvable under the proposed model. The group setup time was assumed to follow a simple linear timedependent deteriorating model They examined two models of learning for the job processing time, provided polynomial time solutions for the makespan minimization problems, and showed that the total completion time minimization problems remained polynomially solvable under agreeable conditions.

Problem Formulation

Conclusions