The Due Date Assignment Scheduling Problem with Delivery Times and Truncated Sum-of-Processing-Times-Based Learning Effect

Jin Qian,Yu Zhan

doi:10.3390/math9233085

Abstract

This paper considers a single-machine scheduling problem with past-sequence-dependent delivery times and the truncated sum-of-processing-times-based learning effect. The goal is to minimize the total costs that comprise the number of early jobs, the number of tardy jobs and due date. The due date is a decision variable. There will be corresponding penalties for jobs that are not completed on time. Under the common due date, slack due date and different due date, we prove that these problems are polynomial time solvable. Three polynomial time algorithms are proposed to obtain the optimal sequence.

Highlights

Scheduling problems are widely used in manufacturing, logistics, and other practical applications
1: First step: All jobs were sorted by increasing processing time, i.e., p1 ≤ · · · ≤ pn. 2: Second step: When h was from 0 to n, the objective function values were calculated, respectively. 3: Last step: The optimal position of h was determined by the smallest value of the objective function, and the optimal sequence was arrangedn an ascending order of normal processing time
Under the common due date, slack due date and different due date, a single-machine scheduling problem with delivery times and the truncated sum-of-processing-times-based learning effect was studied in this paper

Summary

Introduction

Scheduling problems are widely used in manufacturing, logistics, and other practical applications. For a real-word example of our scheduling problems, consider a processing enterprise that has no inventory capacity. The processing time of the product becomes shorter. If the product is produced before the pick-up time or after the pick-up time, an additional delivery fee will be incurred. The delivery price of each early (tardy) job is a fixed charge. The methods to solve the scheduling problem mainly include two types: the exact algorithm and approximate algorithm. For large-scale non-polynomial time-solvable scheduling problems, intelligent algorithms and machine learning algorithms can be used to solve them. A single-machine scheduling problem is considered that contains due dates, the delivery time and learning effect. The actual processing time of a job is a learning function of the previous processing time. Under the common due date, slack due date and different due date, three polynomial time algorithms are proposed to obtain the optimal sequence

Literature Review

Notation and Problem Statement

1: First step

Findings

Extension

Conclusions