Optimization for Due-Window Assignment Scheduling with Position-Dependent Weights

Li-Yan Wang,Wei-Wei Liu,Ji-Bo Wang,Bo Zhang,Dan-Yang Lv

doi:10.1155/2020/9746538

Abstract

This paper considers a single-machine due-window assignment scheduling problem with position-dependent weights, where the weights only depend on their position in a sequence. The objective is to minimise the total weighted penalty of earliness, tardiness, due-window starting time, and due-window size of all jobs. Optimal properties of the problem are given, and then, a polynomial-time algorithm is provided to solve the problem. An extension to the problem is offered by assuming general position-dependent processing time.

Highlights

In scheduling theory, due-windows are jobdependent either if they are dictated by the customer or they are decision variables
Most studies considered the Common due-window (CON-DW) assignment method, e.g., Mosheiov and Sarig [6] addressed a minmax CON-DW assignment problem, the objective of which is to minimise the largest cost among earliness, tardiness, due-window starting time, and due-window size. ey proved that the single-machine and two-machine flow-shop problems can be solved in polynomial time. ey proved that the cases of parallel identical machines and uniform machines are NP-hard
Wang et al [18] considered CON-DW and Slack due-window (SLK-DW) assignment methods with position-dependent weights, i.e., the weight does not correspond with the job but with the position in which some job is scheduled. ey proved that both these due-window assignment methods with position-dependent weights can be solved in polynomial time, respectively. “ e scheduling with due-window assignment has many real-world applications

Summary

Introduction

In scheduling theory, due-windows are jobdependent either if they are dictated by the customer (i.e., given constants) or they are decision variables (i.e., duewindow assignment). Most studies considered the CON-DW assignment method, e.g., Mosheiov and Sarig [6] addressed a minmax CON-DW assignment problem, the objective of which is to minimise the largest cost among earliness, tardiness, due-window starting time, and due-window size. For the weighted sum of earliness, tardiness, and due-window location penalty minimization, they proposed a polynomial-time algorithm to solve the problem. Ey proved that both these due-window assignment methods with position-dependent weights can be solved in polynomial time, respectively. E contributions of this paper are given as follows: (1) the structural properties of scheduling problems are derived; (2) the total weighted penalty of earliness, tardiness, due-window starting time, and duewindow size of all jobs’ minimization can be solved in polynomial time; and (3) it is further extended the model to the case with general position-dependent processing time.

Problem Description

Main Results

An Extension

Conclusion and Future