Single-Machine Scheduling with Learning Effects and Maintenance: A Methodological Note on Some Polynomial-Time Solvable Cases

Kuo-Ching Ying,Chung-Cheng Lu,Shih-Wei Lin,Jie-Ning Chen

doi:10.1155/2017/7532174

Abstract

This work addresses four single-machine scheduling problems (SMSPs) with learning effects and variable maintenance activity. The processing times of the jobs are simultaneously determined by a decreasing function of their corresponding scheduled positions and the sum of the processing times of the already processed jobs. Maintenance activity must start before a deadline and its duration increases with the starting time of the maintenance activity. This work proposes a polynomial-time algorithm for optimally solving two SMSPs to minimize the total completion time and the total tardiness with a common due date.

Highlights

The single-machine scheduling problem (SMSP) is one of the most extensively studied classical scheduling problems owing to its wide range of applications in many realistic systems [1]
Most SMSPs assume that job processing times are fixed and known throughout the process, and SMSPs with learning effects constitute a relatively new subfield in the area of scheduling
An algorithm for solving the two SMSPs was developed, and the SMSPs were proved to be solvable in polynomial time with the explicit consideration of learning and the variable maintenance

Summary

Introduction

The single-machine scheduling problem (SMSP) is one of the most extensively studied classical scheduling problems owing to its wide range of applications in many realistic systems [1]. With respect to sum-of-processing-time-based learning effects, Kuo and Yang [25, 26] were among the pioneers that considered the processing times of jobs that had already been preprocessed and proposed two learning models, pj,[k] = pj(1 + ∑ki=−11 p[i])a and pj,[k] = pj(∑ki=−11 p[i])a, for SMSPs with time-dependent learning. In some situations, position-based learning and sum-ofprocessing-times-based learning exist simultaneously, such as those that involve a robot with a neural network system, as is used in many assembly lines and has been discussed by Lee and Wu [30] This fact has motivated recent studies [30,31,32,33,34,35] that consider both learning effects at once.

Problem Definition

Polynomial-Time Algorithm

Conclusions and Recommendations for Future Studies