Group Scheduling Problems with Time-Dependent and Position-Dependent DeJong’s Learning Effect

Li Sun,Jia-Zhen Huo,Lei Ning

doi:10.1155/2020/5161872

Abstract

In this paper, we introduce a group scheduling model with time-dependent and position-dependent DeJong’s learning effect. The objectives of scheduling problems are to minimize makespan, the total completion time, and the total weighted completion time, respectively. We show that the problems remain solvable in polynomial time under the proposed model.

Highlights

IntroductionThe scheduling models routinely assume that job processing times are known and fixed throughout the period of production process
In classical scheduling problems, the scheduling models routinely assume that job processing times are known and fixed throughout the period of production process
For the 1|GT, si, pA[i][r] p[i][r](M + (1 − M) at[i][r] rb)|Cmax problem, the optimal schedule is obtained: (i) the job sequence in each group is in the smallest normal processing time order (SPT) and (ii) the groups can be sequenced in any order

Summary

Introduction

The scheduling models routinely assume that job processing times are known and fixed throughout the period of production process. This assumption may be unrealistic in many situations that the processing time of jobs may be shortened due to learning effect over time. The existing learning effect scheduling model suffers the drawback that when a job’s position or the starting processing time is sufficiently large in a schedule, its actual processing time is close to zero (infinity). Is paper is to introduce a new scheduling model with position-dependent and timedependent processing time, which overcomes the above shortcomings and is more general and realistic than the models existing in the literature.

Review of Existing Models

Problem Formulation

Result of Optimization

Conclusions