Improved algorithms for two single machine scheduling problems

AbstractIn this paper, we investigate two single machine scheduling problems. The first problem addresses a class of the two-stage scheduling problems in which the first stage is job production and the second stage is job delivery. For the case that jobs are processed on a single machine and delivered by a single vehicle to one customer area, with the objective of minimizing the time when all jobs are completed and delivered to the customer area and the vehicle returns to the machine, an approximation algorithm with a worst-case ratio of 53 is known and no approximation can have a worst-case of 32 unless P=NP. We present an improved approximation algorithm with a worst-case ratio of 5335, which only leaves a gap of 170. The second problem is a single machine scheduling problem subject to a period of maintenance. The objective is to minimize the total completion time. The best known approximation algorithm has a worst-case ratio of 2017. We present a polynomial time approximation scheme

Single Objective Evolutionary Algorithm for Job Shop Scheduling Problem

Abstract-Job shop scheduling belongs to the class of NPhard problems. There are a number of algorithms in literature for finding near optimal solution for the job shop scheduling problem. Many of these algorithms exploit the problem specific information and hence are less general. However, single objective evolutionary algorithms for job shop scheduling are general and produce better results. In this paper, we discuss approaches to developing single objective evolutionary algorithm for solving the job shop scheduling problem. Initial population is generated randomly. Two-row chromosome structure is adopted based on working procedure and machine distribution. The relevant crossover and mutation operation is also designed. It jumped from the local optimal solution, and the search area of solution is improved. Finally, the algorithm is tested on instances of 8 working procedure and 5 machines. The result shows that the evolutionary algorithm has been successfully applied to the job shop scheduling problems efficiency. Index Terms-job shop scheduling, evolutionary algorith

Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

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

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.Comment: Book Chapter 22 page

Common Due-Date Problem: Exact Polynomial Algorithms for a Given Job Sequence

This paper considers the problem of scheduling jobs on single and parallel machines where all the jobs possess different processing times but a common due date. There is a penalty involved with each job if it is processed earlier or later than the due date. The objective of the problem is to find the assignment of jobs to machines, the processing sequence of jobs and the time at which they are processed, which minimizes the total penalty incurred due to tardiness or earliness of the jobs. This work presents exact polynomial algorithms for optimizing a given job sequence or single and parallel machines with the run-time complexities of $O(n \log n)$ and $O(mn^2 \log n)$ respectively, where $n$ is the number of jobs and $m$ the number of machines. The algorithms take a sequence consisting of all the jobs $(J_i, i=1,2,\dots,n)$ as input and distribute the jobs to machines (for $m>1$) along with their best completion times so as to get the least possible total penalty for this sequence. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we present the results for the benchmark instances and compare with previous work for single and parallel machine cases, up to $200$ jobs.Comment: 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computin