A Particle Swarm Optimization Algorithm for Scheduling Against Restrictive Common Due Dates

Andreas C Nearchou,Sotiris L Omirou

doi:10.1080/18756891.2013.802874

Abstract

Focusing on the just-in-time (JIT) operations management, earliness as well as, tardiness of jobs’ production and delivery should be discouraged. In accordance to this philosophy, scheduling problems involving earliness and tardiness penalties are very critical for the operations manager. In this paper, a new population heuristic based on the particle swarm optimization (PSO) technique is presented to solve the single machine early/tardy scheduling problem against a restrictive common due date. This type of scheduling sets costs depending on whether a job finished before (earliness), or after (tardiness) the specified due date. The objective is to minimize a summation of earliness and tardiness penalty costs, thus pushing the completion time of each job as close as possible to the due date. The problem is known to be NP-hard, and therefore large size instances cannot be addressed by traditional mathematical programming techniques. The performance of the proposed PSO heuristic is measured over benchmarks problems with up to 1000 jobs taken from the open literature, and found quite high and promising in respect to the quality of the solutions obtained. Particularly, PSO was found able to improve the 82% of the existing best known solutions of the examined benchmarks test problems.

Highlights

Sequencing and scheduling problems involving due dates, play a crucial role in real-world production and operations management
In today production management, scheduling against common due dates with respect to earliness and tardiness penalties is of great importance mainly due to its compliance with the principles of just-in-time ‘philosophy’
This is a typical discrete combinatorial optimization problem (COP) known to be intractable, meaning that, the search for optimal schedules using traditional mathematical programming techniques is only possible for very small size instances of the problem

Summary

Introduction

Sequencing and scheduling problems involving due dates, play a crucial role in real-world production and operations management This type of scheduling sets penalty costs depending on whether a job finished before (earliness), or after (tardiness) the specified due date. This paper deals with the single-machine early/tardy scheduling problem (SMETSP) of a set of jobs with a common due date (CDD) and objective the minimization of the jobs’ total earliness and tardiness. Souza and Wolsey[13] proposed branch and bound algorithms for solving a class of four different scheduling problems (including SMETSP) with 20 and 30 jobs. The performance of the proposed PSO algorithm is examined over the most restricted instances against CDDs of the Biskup and Feldmann (2001)’s benchmarks[25]; including 140 instances in total ranging from 10 to 1000 jobs.

Problem formulation

Properties for the unrestricted CDD SMETSP

Solution space and encoding mechanisms

PSO implementation for the SMETSP

Findings

Conclusion