A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines

TL;DR

This paper introduces exact polynomial algorithms with efficient runtimes for the Common Due-Date scheduling problem on single and parallel machines, including non-identical ones, optimizing job scheduling to minimize penalties.

Contribution

It presents novel polynomial-time algorithms for CDD scheduling on single and parallel machines, extending to non-identical machines and dynamic cases, with proven optimality and practical benchmarks.

Findings

Algorithms run in O(n log n) time for both cases

Optimal solutions are proven for single machine case

Approach applicable to non-identical parallel machines

Abstract

This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of $O(n \log n)$ for both cases, where $n$ is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR-library.