Multitasking scheduling problems with a common due-window

Chen Xu,Feifeng Zheng,Yinfeng Xu,Ming Liu

doi:10.1051/ro/2021079

Chen Xu, Feifeng Zheng + Show 2 more

Open Access

https://doi.org/10.1051/ro/2021079

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Abstract

We study multitasking scheduling and due-window assignment problems in a single machine, which can be found in various application domains. In multitasking environment, unfinished job always interrupts in-processing job. In common due window assignment, the aim is to find optimal due window to minimise the value of the earliness and tardiness penalty. In this paper, we study two problems, where the objective of the first problem is minimise the earliness, tardiness, due-window starting time, and due-window size costs, the objective of the second problem is minmax common due-date with completion time penalty, then we obtain some analytical properties and provide polynomial time solutions. Finally, the experimental results show that the proposed methods are effective.

Highlights

Multitasking scheduling has attracted much attention in recently years
Research on multitasking scheduling was in initiated by Hall et al [3], who considered interruption and switching factors, in which a job was interrupted by other unfinished jobs, they developed some new solution algorithms to solve the classical scheduling model
The first objective is minimise, every early job has cost, every late job has cost, in order to minimise cost, we hope to minimise the highest cost among all jobs, so another is to minimized max1≤j≤n {max{αEj + γd1 + δD, βTj + γd1 + δD}}, which α is the unit penalty for earliness, β is the unit penalty for tardiness, γ is the unit penalty for the due-window starting time, δ is the unit penalty for the window size

Summary

Introduction

Multitasking scheduling has attracted much attention in recently years. The multitasking phenomenon can be frequently observed in our daily lives. Managers usually need to arrange a common due-window. In such a case, a batch of work piece are ordered by the same customer, because of the different completion time of each work piece, the cost of batch shipment is relatively high. In order to save transportation costs, it is usually uniform shipment after all the work pieces are processed, so managers should make a common due date which is a predetermined time point. Owing to the practical significance of common due window scheduling in the multitasking environment, there is a need to study the problem under consideration in this research.

Literature interview

Problem statement

Multitasking scheduling problem

Common due-window problem

Minmax common due-window problem

Conclusion