Due‐Window Assignment and Scheduling with Multiple Rate‐Modifying Activities under the Effects of Deterioration and Learning

Zhanguo Zhu,Linyan Sun,Feng Chu,Ming Liu

doi:10.1155/2011/151563

Abstract

This paper discusses due‐window assignment and scheduling with multiple rate‐modifying activities. Multiple types of rate‐modifying activities are allowed to perform on a single machine. The learning effect and job deterioration are also integrated concurrently into the problem which makes the problem more realistic. The objective is to find jointly the optimal location to perform multiple rate‐modifying activities, the optimal job sequence, and the optimal location and size of the due window to minimize the total earliness, tardiness, and due‐window‐related costs. We propose polynomial time algorithms for all the cases of the problem under study.

Highlights

With the complexity of the manufacturing activities more researchers focus on variants of classical scheduling problems that reflect the reality, such as learning effect, rate-modifying activity, deteriorating effects, and due-window assignment
The phenomenon of the actual job processing times decreasing due to repetition of tasks by workers is known as the learning effect
We present that some properties of an optimal solution for the common due-window assignment problem proved by Mosheiov and Sarig 30 still hold for the problem discussed in this paper

Summary

Introduction

With the complexity of the manufacturing activities more researchers focus on variants of classical scheduling problems that reflect the reality, such as learning effect, rate-modifying activity, deteriorating effects, and due-window assignment. Yang et al considered due-window assignment and scheduling with job-dependent aging effects and deteriorating maintenance In their study, they proposed a model with a deteriorating maintenance and provided polynomial time solutions. Zhao and Tang investigated due-window assignment and scheduling with a rate-modifying activity under the assumption of deteriorating jobs that the processing time of a job is a linear function of its starting time They proposed an O n4 algorithm to solve the problem optimally, where n is the number of jobs. We discuss single-machine scheduling problem with due-window assignment and multiple rate-modifying activities which is an extension of the work by Mosheiov and Sarig 30 , Ji and Cheng 11 , and Yang et al 31.

Problem Formulation

Preliminary Works

An Optimal Solution Policy

14 The problem can be formulated as follows

Conclusions