scholarly journals Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

2021 ◽  
Vol 11 (8) ◽  
pp. 3677
Author(s):  
Yassine Ouazene ◽  
Nhan-Quy Nguyen ◽  
Farouk Yalaoui
Keyword(s):  
Computational Analysis ◽  
Parallel Machines ◽  
Production Systems ◽  
Identical Parallel Machines ◽  
Workload Balancing ◽  
Processing Times ◽  
Use Of Resources ◽  
Maximum Completion Time ◽  
Completion Times ◽  
Identical Jobs

This paper considers the problem of assigning nonpreemptive jobs on identical parallel machines to optimize workload balancing criteria. Since workload balancing is an important practical issue for services and production systems to ensure an efficient use of resources, different measures of performance have been considered in the scheduling literature to characterize this problem: maximum completion time, difference between maximum and minimum completion times and the Normalized Sum of Square for Workload Deviations. In this study, we propose a theoretical and computational analysis of these criteria. First, we prove that these criteria are equivalent in the case of identical jobs and in some particular cases. Then, we study the general version of the problem using jobs requiring different processing times and establish the theoretical relationship between the aforementioned criteria. Based on these theoretical developments, we propose new mathematical formulations to provide optimal solutions to some unsolved instances in order to enhance the latest benchmark presented in the literature.

Online Parallel-Machine Scheduling in KRT Environment to Minimize Total Weighted Completion Time

2018 ◽  
Vol 35 (04) ◽  
pp. 1850024
Author(s):  
Wenjie Li ◽  
Hailing Liu ◽  
Shisheng Li
Keyword(s):  
Online Algorithm ◽  
Parallel Machines ◽  
Parallel Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Identical Parallel Machines ◽  
Feasible Schedule ◽  
Processing Times ◽  
Online Setting ◽  
Completion Times ◽  
Equal Processing Times

This paper studies online scheduling on [Formula: see text] identical parallel machines under the KRT environment, where jobs arrive over time and “KRT” means that in the online setting no jobs can be released when all of the machines are busy. The goal is to determine a feasible schedule to minimize the total of weighted completion times. When [Formula: see text], we prove that WSPT is an optimal online algorithm. When [Formula: see text], we first present a lower bound [Formula: see text], and then show that WSPT is a 2-competitive online algorithm for the case [Formula: see text]. For the case in which [Formula: see text] and all jobs have equal processing times, we provide a best possible online algorithm with a competitive ratio of [Formula: see text].

Penjadwalan Mesin dengan Metode Integer Linear Programming pada PT. XYZ

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Fransiskus Lauson Matondang ◽  
Rosnani Ginting
Keyword(s):  
Integer Programming ◽  
Time Delays ◽  
Parallel Machines ◽  
Research Concept ◽  
Total Settlement ◽  
Approach Method ◽  
Additional Costs ◽  
Maximum Completion Time ◽  
Completion Times ◽  
Better Than

PT XYZ sering mengalami keterlambatan waktu karena dalam setiap keterlambatan yang dilakukan selalu ada penalty yang diberikan kepada perusahaan dan hal ini mengakibatkan tambahan biaya , oleh karena itu hal ini harus dihindari dengan membuat penjadwalan yang efisien, dalam hal ini dilakukanlah perbaikan dengan meminimisasi waktu penyelesaian maksimum Cmax pada mesin paralel yang berpola aliran flowshop (dan tidak boleh dilakukan interupsi yang dilakukan pada pekerjaan yang sedang diproses, untuk melakukan pekerjaan lainnya, satu lintasan hanya memproduksi satu produk dan hanya satu produk juga yang dikerjakan secara langsung. Waktu penyelesaian yang berbeda dari setiap mesin dengan pengerjaannya juga adalah masalah yang dihadapi untuk menjadikan mesin mesin ini sesuai menjadi satu penjadwalan yang terintegrasi dengan metode integer programming yang membuat penjadwalan dengan konsep riset operasi dengan metode pendekatan 0-1 utuk menjadi lebih efisien lagi , dihasilkan minimisasi keterlambatan total penyelesaian order dengan 42,28 menit lebih baik dari sebelumnya.   PT XYZ often experiences time delays because in every delay made there is always a penalty given to the company and this results in additional costs, therefore this must be avoided by making efficient scheduling, in this case repairs are carried out by minimizing the maximum completion time of Cmax on parallel machines that are patterned with flowshop flow (and no interruptions should be carried out on the work being processed, to do other work, one track only produces one product and only one product is directly worked. Different completion times of each machine with the workmanship is also the problem faced to make this machine suitable to be one scheduling integrated with integer programming methods that makes scheduling with the operational research concept with the 0-1 approach method to be more efficient, resulting in minimization of the delay in the total settlement of orders with 42.28 minutes was better than before.

SEMI-ONLINE MACHINE COVERING

2007 ◽  
Vol 24 (03) ◽  
pp. 373-382 ◽  
Author(s):  
SHENG-YI CAI
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Parallel Machines ◽  
Identical Parallel Machines ◽  
Processing Times ◽  
First Case ◽  
Machine Covering

This paper investigates two different semi-online versions of the machine covering, which is the problem of assigning a set of jobs to a system of m(m ≥ 3) identical parallel machines so as to maximize the earliest machine completion time. In the first case, we assume that the largest processing times is known in advance. In the second case, we assume that the total processing times of all jobs is known in advance. For each version we propose a semi-online algorithm and investigate its competitive ratio. The competitive ratio of each algorithm is [Formula: see text], which is shown to be the best possible competitive ratio for each semi-online problem.

Scheduling identical jobs on uniform parallel machines with random processing times

1998 ◽  
Vol 35 (1-2) ◽  
pp. 109-112 ◽  
Author(s):  
Mohamed I. Dessouky ◽  
Richard L. Marcellus ◽  
Li Zhang
Keyword(s):  
Parallel Machines ◽  
Processing Times ◽  
Identical Jobs

Hybrid Multi-Objective Methods to Solve Reentrant Shops

2012 ◽  
Vol 3 (4) ◽  
pp. 15-32
Author(s):  
Frédéric Dugardin ◽  
Farouk Yalaoui ◽  
Lionel Amodeo
Keyword(s):  
Local Search ◽  
Design Of Experiment ◽  
Completion Time ◽  
Parallel Machines ◽  
Flow Shop ◽  
Hybrid Flow Shop ◽  
Identical Parallel Machines ◽  
Multi Objective ◽  
Local Searches ◽  
Maximum Completion Time

This article examines the multi-objective scheduling of a reentrant hybrid flow shop. This type of shop is composed of several stages made of several identical parallel machines. When a task has to be processed on a stage, it is assigned to the machine with the smallest workload. This problem shows a reentrant structure: each task must be processed several times at each stage. In this paper, this problem is solved by minimizing two objectives: the makespan (maximum completion time of the jobs) and the total tardiness of the tasks. A new method is improved with different local searches: Adjacent and Non Adjacent Pairwise Interchange, Extract and Backward-Shifted Reinsertion, and Extract and Forward-Shifted Reinsertion. Every local search is tuned with statistical method (design of experiment) and the best one is worked out. This method is compared with the best one in several instances. The results involve three different measures.

Scheduling with Discretely Compressible Processing Times to Minimize Makespan

2014 ◽  
Vol 575 ◽  
pp. 926-930
Author(s):  
Shu Xia Zhang ◽  
Yu Zhong Zhang
Keyword(s):  
Dynamic Programming ◽  
Polynomial Time ◽  
Processing Time ◽  
Parallel Machines ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Identical Parallel Machines ◽  
Processing Times ◽  
Release Times ◽  
Scheduling Model

In this paper, we address the scheduling model with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost on identical parallel machines. Jobs may have simultaneous release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

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