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Hierarchical Minimization of Total Completion Time and Number of Tardy Jobs Criteria
E.O. Oyetunji,A.E. Oluleye
Asian Journal of Information Technology , 2012,
Abstract: In this study, the single machine bicriteria scheduling problem of hierarchically minimizing the total completion time of jobs (Ctot) and number of tardy jobs (NT) with release time was explored. Two types of hierarchical minimization models (the case of the total completion time criterion being more important than the number of tardy jobs criterion and the case of the number of tardy jobs criterion being more important than the total completion time criterion) were discussed. Three heuristics (HR4, HR5 and HR6) selected from the literature were used to test the models.
E. O. Oyetunji,A. E. Oluleye
South African Journal of Industrial Engineering , 2012,
Abstract: ENGLISH ABSTRACT: This paper considers the problem of minimizing the number of tardy jobs with release time on a single machine. Given that the problem has been classified as strongly NP-Hard, three heuristics (EOO, HR2, and HR3) are proposed for this problem. They are compared with a heuristic by Dauzere-Perez (selected from the literature). Randomly-generated problems ranging from 3 to 500 jobs are solved. Experimental results show that one of the proposed heuristics (EOO) outperforms other heuristics, both in terms of quality of solution (effectiveness) and speed of execution (efficiency). AFRIKAANSE OPSOMMING: Die navorsing behandel die ministering van voltooiingstyd van die aantal draaltake by ‘n enkele werktuig. As aanvaar word dat die problem geklassifiseer word as hoofsaaklike NP-hard, word voorgestel dat die vraagstuk bestudeer word deur gebruik te maak van drie heuristiese metodes (EOO, HR2, HR3). Die metodes word vergelyk ten opsigte van vertoning met die Dauzere-Perez-metode. Toevalsgegenereerde probleme wat strek vanaf 3 tot 500 draaltake word behandel. Die eksperimentele werk lewer bewys dat die EOO-metode ander metodes die loef afsteek ten opsigte van oplossingsgoedheid en –snelheid.
E. O. Oyetunji,A. E. Oluleye
South African Journal of Industrial Engineering , 2012,
Abstract: ENGLISH ABSTRACT: This paper considers the bi-criteria scheduling problem of simultaneously minimising the total completion time and the number of tardy jobs with release dates on a single machine. Since the problem had been classified as NP-Hard, two heuristics (HR9 and HR10) were proposed for solving this problem. Performance evaluations of the proposed heuristics and selected solution methods (HR7 and BB) from the literature were carried out on 1,100 randomly generated problems ranging from 3 to 500 jobs. Experiment results show that HR7 outperformed HR10 when the number of jobs (n) is less than 30, while HR10 outperformed HR7 for n≥ 30. AFRIKAANSE OPSOMMING: In hierdie artikel word die bi-kriteria-skeduleringsprobleem bestudeer waar die totale voltooiingstyd en die aantal take wat laat is op ‘n enkele masjien geminimiseer moet word. Verskeie heuristieke word voorgestel en getoets om sodoende die beste benadering te identifiseer.
Minimizing the Number of Tardy Jobs with a Subset T of the Jobs to Be Sure on Time  [PDF]
PENG Hong-jie,SU Yong-ying,Tang Guop-chun
Journal of Chongqing Normal University , 2009,
Abstract: The single machine scheduling problem to minimize the number of tardy jobs is one of the most basic scheduling problems in scheduling theory. In 1973, Sidney studied the scheduling problem 1|T|∑Uj to minimize the number of tardy jobs with a subset T of the jobs which must be on time and give a polynomial time algorithm to solve this problem, the optimal could be gotten in time O(n log n ). This algorithm is called Sidney Algorithm by scholars in the following years. In this paper, we have revised Sidney Algorithm as following. Step1, suppose E0=T,j-E0={j1,j2,…,jm},j1 Keywords scheduling --- tardy jobs --- algorithm --- optimality
A mathematical model for weighted tardy jobs scheduling problem with a batched delivery system
Mohammad Mahdavi Mazdeh,Amir Hamidinia,Ayatollah Karamouzian
International Journal of Industrial Engineering Computations , 2011,
Abstract: This study investigates minimizing the number of weighted tardy jobs on a single machine when jobs are delivered to either customers or next station in various size batches. In real world, this issue may happen within a supply chain in which delivering goods to customers entails costs. Under such circumstances, keeping completed jobs to deliver in batches may result in reducing delivery costs; nevertheless, it may add to the tardy jobs, which in turn leads to higher costs. In literature review, minimizing the number of weighted tardy jobs is known as NP-Hard problem, so the present issue aiming at minimizing the costs of delivering, in addition to the aforementioned objective function, remains an NP-Hard problem. In this study, the issue is assessed where the customers are numerous, and a mathematical model is presented. We also present a meta-heuristic method based on simulated annealing (SA) and the performance of the SA is examined versus exact solutions.
A Bi-Criteria Algorithm for the Simultaneous Minimization of Makespan and Number of Tardy Jobs on a Single Machine with Sequence Dependent Set-up Time
V.O. Oladokun,O.E. Charles-Owaba,F.O. Olaosebikan
Research Journal of Applied Sciences, Engineering and Technology , 2011,
Abstract: Scheduling models based on efficient resources utilization without sufficient consideration for customer satisfaction or vice-visa is inadequate in many real-life multi-criteria scheduling problems. This work was aimed at the development of a bi-criteria algorithm for the simultaneous optimization of Makespan (Cmax) and Number of tardy jobs (NT) in a single machine problem with Sequence dependent set-up time. An existing single criterion algorithm, the Set Sequencing Algorithm, was adapted to solve the bi-criteria problem. Graphical User Interface (GUI) based software of the new algorithm was developed and its performance was evaluated with a real life problem and 150 randomly generated problems, with problem sizes ranging from between 20 and 150. The values of Cmax and NT of the solution sequences were analysed. The output sequences gave an average reduction of 32.10% in both measures of performance compared with the input sequences. The software was also shown to be user friendly. It is concluded that Set sequencing Algorithm is suitable for bi criteria scheduling optimization.
Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint  [PDF]
Ehsan Molaee,Ghasem Moslehi
Journal of Industrial Engineering , 2014, DOI: 10.1155/2014/568317
Abstract: Most scheduling problems are based on the assumption that machines work continuously during the planning horizon. This assumption is not true in many production environments because the machine may not be available during one or more periods such as during breakdowns or maintenance operations. In this paper, the problem of the single machine scheduling with one unavailability period and nonresumable jobs with the aim of minimizing the number of tardy jobs is studied. A number of theorems are proved and a heuristic procedure is developed to solve the problem. A branch-and-bound approach is also presented which includes upper and lower bounds and efficient dominance rules. Computational results for 2680 problem instances show that the branch-and-bound approach is capable of solving 98.7% of the instances optimally, bearing witness to the efficiency of the proposed procedure. Our results also indicate that the proposed approaches are more efficient when compared to other methods. 1. Introduction Most scheduling problems take the fact that the machine works continuously during the planning horizon for granted. This assumption may be unrealistic in many production environments as the machine becomes unavailable during breakdowns or maintenance operations. The number of tardy jobs is one of the important objective functions in scheduling problems. This target has wide applications in many production and service environments and reflects factors of external cost based on due dates such as customer satisfaction. The number of tardy jobs can represent orders of customers that are not satisfied. In this paper, the single machine scheduling problem with a known unavailability period and nonresumable jobs with the objective of minimizing the number of tardy jobs is considered. According to Pinedo [1] separation, this problem is denoted by . So far, a few researchers have studied single machine problems with availability constraints. In these problems, there are three general states for jobs including resumable, nonresumable, and semiresumable states. According to the resumable scenario, job preemption is allowed. This means that if a job cannot be finished before a nonavailability period of the machine, its processing can be resumed when the machine is available again. According to the nonresumable scenario, preemption is undesirable and the whole processing of the job should be repeated if it cannot be finished before the unavailability period. In the semiresumable state, part of the processing should be repeated if it cannot be finished before the nonavailability
A Study of Scheduling Problems to Minimize the Number of Tardy Jobs  [PDF]
TANG Guo-chun
Journal of Chongqing Normal University , 2009,
Abstract: The single machine scheduling problem to minimize the number of tardy jobs is one of the most basic and importang scheduling problems in classical scheduling theory. An algorithm of Moore, which is sometimes known as the Moore-Hodgson algorithm, solves the problem in O(n log n) time. This algorithm repeatedly adds jobs in EDD order to the end of a partial schedule of on=time jobs. If the addition of job j results in this job completed after time dj, then a job in the partial schedule with the largest processing time is removed and declared late. Discarding a job with the largest processing time increases the opportunity for subsequent jobs to be completed by their due dates. In the past 40 years, lots of researchers studied it with ever-increasing interests and their profound results appeared continually. For example, Sidney generalizes this algorihm to handle the case that a specified subset of jobs must be on time. He observes that jobs of the specified subset are not considered when discarding jobs, and that it may be necessary to discard more than one job to ensure that the last job in the current partial schedule is on time. Adaptations of Moore-Hodgson's algorithm to both problem I|(ri≤rj)→(di≦dj)|∑Ujand problem I |(pi≤pj)→(wi≧wj) |∑wjuj for the cases of both agreeability of release dates with due dates, and reverse agreeability of processing times with weights are proposed by both Kise, Ibaraki and Mine, and Lawler, respectively. In this paper we review results and their significances on the problems obtained by master students in Chongqing Normal University,including classical ones and their generalizations.
On the variable common due date, minimal tardy jobs bicriteria two-machine flow shop problem with ordered machines  [PDF]
Aleksandar Ilic
Computer Science , 2013,
Abstract: We consider a special case of the ordinary NP-hard two-machine flow shop problem with the objective of determining simultaneously a minimal common due date and the minimal number of tardy jobs. In [S. S. Panwalkar, C. Koulamas, An O(n^2) algorithm for the variable common due date, minimal tardy jobs bicriteria two-machine flow shop problem with ordered machines, European Journal of Operational Research 221 (2012), 7-13.], the authors presented quadratic algorithm for the problem when each job has its smaller processing time on the first machine. In this note, we improve the running time of the algorithm to O(n log n) by efficient implementation using recently introduced modified binary tree data structure.
Alex Saleh,Emsosfi Zaini
Jurnal Teknik Industri , 2009,
Abstract: This research discusses jobs scheduling model on flowshop-4-stage for fabrication and assembly processes. Each job consists of a unique component and a common component. Both the unique and common components are processed on the first three machines and assembled on the fourth machine. The unique components are processed individually, while common components are processed in batches for which respective constant setups are needed. The criteria used for the models are to minimize maximum lateness and number of tardy jobs. The development is executed to accommodate the possibility of tardy jobs. A proposed algorithm is initiated with jobs scheduling using the earliest due date (EDD) rule for the single machine, and batching process using the dynamic programming principle. Number of tardy jobs improved based on Hodgson Algorithm. The proposed algorithm is not an optimal algorithm as we can not guarantee optimal in scheduling process, nevertheless the batching method can bring out an optimal solution. This research also discusses numerical cases to show model behavior. Abstract in Bahasa Indonesia: Penelitian ini membahas model penjadwalan job pada flowshop-4-stage untuk proses fabrikasi dan perakitan. Setiap job terdiri dari 1 unique component dan 1 common component, yang keduanya diproses pada tiga mesin pertama secara serial dan dirakit pada mesin keempat. Unique component diproses satu per satu sedangkan common component diproses dalam batch dengan waktu setup yang konstan untuk setiap batch. Kriteria yang digunakan adalah minimisasi lateness maksimum dan jumlah tardy jobs. Pengembangan model dilakukan untuk mengakomodasi adanya job yang terlambat. Algoritma dimulai dengan proses penjadwalan job dengan menggunakan aturan earliest due date (EDD) untuk mesin tunggal, dan proses batching dengan menggunakan pemrograman dinamis. Jumlah tardy jobs diperbaiki dengan Algoritma Hodgson. Algoritma yang diusulkan bukan merupakan algoritma optimal karena proses penjadwalan yang tidak dijamin optimal, meskipun proses batching dapat menghasilkan solusi optimal. Penelitian ini dilengkapi dengan contoh numerik untuk menunjukkan perilaku model. Kata kunci: flowshop-4-stage, unique component, common component, penjadwalan batch, lateness maksimum , jumlah tardy jobs.
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