scholarly journals A polynomial time approximation scheme for a single machine scheduling problem using a hybrid evolutionary algorithm

2012 ◽  
Author(s):  
Boris Mitavskiy ◽  
Jun He
Keyword(s):  
Evolutionary Algorithm ◽  
Polynomial Time ◽  
Single Machine ◽  
Approximation Scheme ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Hybrid Evolutionary Algorithm

A PTAS for single-machine scheduling with release dates and job delivery to minimize makespan

2019 ◽  
Vol 53 (4) ◽  
pp. 1261-1266 ◽  
Author(s):  
Lingfa Lu ◽  
Liqi Zhang
Keyword(s):  
Single Machine ◽  
Approximation Scheme ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Polynomial Time Approximation Scheme ◽  
Round Trip ◽  
Time Approximation ◽  
Job Delivery ◽  
Capacitated Vehicle

We consider the single-machine scheduling problem with release dates and job delivery to minimize makespan. Preemption is not allowed in the processing of the jobs. All jobs are first processed on a single machine and then delivered by a capacitated vehicle to a single customer. The vehicle can deliver at most c ≥ 1 jobs in each shipment. The round-trip transportation time between the machine and customer is a constant T > 0. The problem was proved to be strongly NP-hard and a 3/2-approximation algorithm was presented in the literature. In this paper we provide a polynomial-time approximation scheme (PTAS) for the problem.

scholarly journals Scheduling Simple Linear Deteriorating Jobs with Rejection

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Juan Zou ◽  
Yuzhong Zhang
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Release Dates ◽  
Polynomial Time Approximation Scheme ◽  
Machine Model ◽  
Time Approximation ◽  
Total Penalty ◽  
Polynomial Time Approximation

We consider the problems of scheduling deteriorating jobs with release dates on a single machine (parallel machines) and jobs can be rejected by paying penalties. The processing time of a job is a simple linear increasing function of its starting time. For a single machine model, the objective is to minimize the maximum lateness of the accepted jobs plus the total penalty of the rejected jobs. We show that the problem is NP-hard in the strong sense and presents a fully polynomial time approximation scheme to solve it when all jobs have agreeable release dates and due dates. For parallel-machine model, the objective is to minimize the maximum delivery completion time of the accepted jobs plus the total penalty of the rejected jobs. When the jobs have identical release dates, we first propose a fully polynomial time approximation scheme to solve it. Then, we present a heuristic algorithm for the case where all jobs have to be accepted and evaluate its efficiency by computational experiments.

scholarly journals Strongly Fully Polynomial Time Approximation Scheme for the weighted completion time minimization problem on two-parallel capacitated machines

2017 ◽  
Vol 51 (4) ◽  
pp. 1177-1188 ◽  
Author(s):  
Imed Kacem ◽  
Myriam Sahnoune ◽  
Günter Schmidt
Keyword(s):  
Polynomial Time ◽  
Completion Time ◽  
Approximation Scheme ◽  
Dynamic Programming Algorithm ◽  
Scheduling Problem ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Time Minimization ◽  
Weighted Completion Time ◽  
Polynomial Time Approximation

We consider the total weighted completion time minimization for the two-parallel capacitated machines scheduling problem. In this problem, one of the machines can process jobs until a certain time T1 after which it is no longer available. The other machine is continuously available for performing jobs at any time. We prove the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the studied problem, which extends the results for the unweighted version (see [I. Kacem, Y. Lanuel and M. Sahnoune, Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem, Int. J. Plann. Sched. 1 (2011) 32–41]). Our FPTAS is based on the simplification of a dynamic programming algorithm. Moreover, we present a set of numerical experiments and we discuss the results.

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