Optimization for Due-Date Assignment Single-Machine Scheduling under Group Technology

Li-Yan Wang,Mengqi Liu,Yuan-Yuan Lu,Ji-Bo Wang,Wei-Wei Liu,Lei Xie

doi:10.1155/2021/6656261

Abstract

In this paper, the single-machine scheduling problem is studied by simultaneously considering due-date assignment and group technology (GT). The objective is to determine the optimal sequence of groups and jobs within groups and optimal due-date assignment to minimize the weighted sum of the absolute value in lateness and due-date assignment cost, where the weights are position dependent. For the common (CON) due-date assignment, slack (SLK) due-date assignment, and different (DIF) due-date assignment, an O n log n time algorithm is proposed, respectively, to solve the problem, where n is the number of jobs.

Highlights

It is well known that firms can increase production efficiency by adopting the group technology (GT). e group technology is an approach to manufacturing that seeks to improve efficiency in highvolume production by exploiting the similarities of different products and activities in their production (Neufeld et al [1] and Yang et al [2]). rough decades of application, people have found many advantages of the group technology
Li et al [17] considered three due-date assignment methods under group technology. e objective function is to minimize the weighted sum of earliness, tardiness, due-date assignment, and completion time
For each of the three due-date assignment methods, there exists an optimal schedule with zero machine idle times

Summary

Introduction

It is well known that firms can increase production efficiency by adopting the group technology (GT). e group technology is an approach to manufacturing that seeks to improve efficiency in highvolume production by exploiting the similarities of different products and activities in their production (Neufeld et al [1] and Yang et al [2]). rough decades of application, people have found many advantages of the group technology. Brucker [21] considered the CON due-date scheduling problem of minimizing the total cost comprising the total weighted absolute lateness value and common due-date (CON) cost, where the weight is position dependent He proved that the problem can be solved in a time O(n log n). Under the linear and convex resource consumption functions, they proved that the CON and SLK due-date assignment problems can be solved in polynomial time, respectively. We proceed to the study Brucker [21], Liu et al [18], and Wang et al [19], which is an extension of their work from considering the CON, SLK, and DIF due-date assignment scheduling problems with group technology and position-dependent weights.

Problem Formulation

Main Results

Conclusions