scholarly journals Online Bi-Criteria Scheduling on Batch Machines with Machine Costs

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 960 ◽  
Author(s):  
Wenhua Li ◽  
Weina Zhai ◽  
Xing Chai
Keyword(s):  
Online Algorithms ◽  
Competitive Ratio ◽  
Processing Time ◽  
Positive Root ◽  
Batch Scheduling ◽  
Cost Functions ◽  
Fixed Cost ◽  
Machine Cost ◽  
The Cost ◽  
Over Time

We consider online scheduling with bi-criteria on parallel batch machines, where the batch capacity is unbounded. In this paper, online means that jobs’ arrival is over time. The objective is to minimize the maximum machine cost subject to the makespan being at its minimum. In unbounded parallel batch scheduling, a machine can process several jobs simultaneously as a batch. The processing time of a job and a batch is equal to 1. When job J j is processed on machine M i , it results cost c i j . We only consider two types of cost functions: c i j = a + c j and c i j = a · c j , where a is the fixed cost of machines and c j is the cost of job J j . The number of jobs is n and the number of machines is m. For this problem, we provide two online algorithms, which are showed to be the best possible with a competitive ratio of ( 1 + β m , ⌈ n m ⌉ ) , where β m is the positive root of the equation ( 1 + β m ) m + 1 = β m + 2 .

OPTIMAL SEMI-ONLINE ALGORITHMS FOR m-BATCH-MACHINE FLOW SHOP SCHEDULING

2012 ◽  
Vol 04 (04) ◽  
pp. 1250051 ◽  
Author(s):  
MING LIU ◽  
CHENGBIN CHU
Keyword(s):  
Online Algorithms ◽  
Processing Time ◽  
Flow Shop ◽  
Optimal Algorithm ◽  
Flow Shop Scheduling ◽  
Shop Scheduling ◽  
Batch Machine ◽  
Processing Times ◽  
Batch Processing Machine ◽  
Over Time

This paper deals with semi-online scheduling on m-batch-machine flow shop. The objective is to minimize the makespan. A parallel batch processing machine can handle up to B jobs simultaneously. We study an unbounded model where B = ∞. The jobs that are processed together construct a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. The problem is online in the sense that jobs arrive over time. Let pi, j(i = 1,…,m) denote the processing time of job Jj on machines Mi, respectively. Let Jj+1 be the following job of Jj in a job instance. We study semi-online problem with jobs' nondecreasing processing times. We focus on the case where p1, j = ⋯ = pm, j for i = 1, …, m and pi, j+1 ≥ βpi, j (β ≥ 1). For this problem, we propose an optimal algorithm [Formula: see text] with a competitive ratio [Formula: see text].

Online Algorithms for Scheduling Unit Length Jobs on Unbounded Parallel-Batch Machines with Linearly Lookahead

2019 ◽  
Vol 36 (05) ◽  
pp. 1950024
Author(s):  
Chengwen Jiao ◽  
Jinjiang Yuan ◽  
Qi Feng
Keyword(s):  
Online Algorithms ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Positive Root ◽  
Unit Length ◽  
Online Scheduling ◽  
Time Interval ◽  
Steady Growth ◽  
Scheduling Model

In this paper, we propose a new online scheduling model with linear lookahead intervals, which has the character that at any time [Formula: see text], one can foresee the jobs that will coming in the time interval [Formula: see text] in which [Formula: see text]. In this new lookahead model, the length of the lookahead intervals are variable as the time going on and the number of jobs increasing, and has the tend of steady growth. In this paper, we consider online scheduling of unit length jobs on [Formula: see text] identical parallel-batch machines under this new lookahead model to minimize makespan. The batch capacity is unbounded, that is [Formula: see text]. We present an optimal online algorithm for [Formula: see text], and provide a best possible online algorithm of competitive ratio [Formula: see text] for [Formula: see text], where [Formula: see text] is the positive root of [Formula: see text].

scholarly journals Cost efficiency of institutional incentives for promoting cooperation in finite populations

2021 ◽  
Vol 477 (2254) ◽  
Author(s):  
Manh Hong Duong ◽  
The Anh Han
Keyword(s):  
Phase Transition ◽  
Optimization Problem ◽  
Cost Functions ◽  
Critical Threshold ◽  
Minimum Level ◽  
Weak Selection ◽  
Optimal Cost ◽  
Institutional Incentives ◽  
The Cost ◽  
Over Time

Institutions can provide incentives to enhance cooperation in a population where this behaviour is infrequent. This process is costly, and it is thus important to optimize the overall spending. This problem can be mathematically formulated as a multi-objective optimization problem where one wishes to minimize the cost of providing incentives while ensuring a minimum level of cooperation, sustained over time. Prior works that consider this question usually omit the stochastic effects that drive population dynamics. In this paper, we provide a rigorous analysis of this optimization problem, in a finite population and stochastic setting, studying both pairwise and multi-player cooperation dilemmas. We prove the regularity of the cost functions for providing incentives over time, characterize their asymptotic limits (infinite population size, weak selection and large selection) and show exactly when reward or punishment is more cost efficient. We show that these cost functions exhibit a phase transition phenomenon when the intensity of selection varies. By determining the critical threshold of this phase transition, we provide exact calculations for the optimal cost of the incentive, for any given intensity of selection. Numerical simulations are also provided to demonstrate analytical observations. Overall, our analysis provides for the first time a selection-dependent calculation of the optimal cost of institutional incentives (for both reward and punishment) that guarantees a minimum level of cooperation over time. It is of crucial importance for real-world applications of institutional incentives since the intensity of selection is often found to be non-extreme and specific for a given population.

scholarly journals Online Scheduling on a Single Machine with Grouped Processing Times

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Qijia Liu ◽  
Long Wan ◽  
Lijun Wei
Keyword(s):  
Single Machine ◽  
Competitive Ratio ◽  
Processing Time ◽  
Online Algorithm ◽  
Arrival Time ◽  
Online Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Over Time

We consider the online scheduling problem on a single machine with the assumption that all jobs have their processing times in[p,(1+α)p], wherep>0andα=(5-1)/2. All jobs arrive over time, and each job and its processing time become known at its arrival time. The jobs should be first processed on a single machine and then delivered by a vehicle to some customer. When the capacity of the vehicle is infinite, we provide an online algorithm with the best competitive ratio of(5+1)/2. When the capacity of the vehicle is finite, that is, the vehicle can deliver at mostcjobs at a time, we provide another best possible online algorithm with the competitive ratio of(5+1)/2.

A Best Possible Online Algorithm for the Parallel-Machine Scheduling to Minimize the Maximum Weighted Completion Time

2015 ◽  
Vol 32 (04) ◽  
pp. 1550030 ◽  
Author(s):  
Wenjie Li
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Completion Time ◽  
Processing Time ◽  
Online Algorithm ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Identical Machines ◽  
Weighted Completion Time ◽  
Over Time

In this paper, we consider the online scheduling on m identical machines in which jobs arrive over time. The goal is to determine a nonpreemptive schedule that minimizes the weighted makespan, i.e., the maximum weighted completion time of jobs. When m = 1, we first present a lower bound 2, and then provide an online algorithm with a competitive ratio of 3. For the case in which m ≥ 1, and all jobs have a common processing time p > 0, we obtain a best possible online algorithm with a competitive ratio of [Formula: see text].

The cost of homelessness: Assessing change over time

2003 ◽  
Author(s):  
M. Spano ◽  
P. Toro ◽  
M. Goldstein
Keyword(s):  
Change Over Time ◽  
The Cost ◽  
Over Time

The Internet Trap

2018 ◽  
Author(s):  
Matthew Hindman
Keyword(s):  
The Internet ◽  
Net Neutrality ◽  
The Public ◽  
Attention Economy ◽  
Digital News ◽  
The Cost ◽  
Over Time

The Internet was supposed to fragment audiences and make media monopolies impossible. Instead, behemoths like Google and Facebook now dominate the time we spend online—and grab all the profits from the attention economy. This book explains how this happened. It sheds light on the stunning rise of the digital giants and the online struggles of nearly everyone else—and reveals what small players can do to survive in a game that is rigged against them. The book shows how seemingly tiny advantages in attracting users can snowball over time. The Internet has not reduced the cost of reaching audiences—it has merely shifted who pays and how. Challenging some of the most enduring myths of digital life, the book explains why the Internet is not the postindustrial technology that has been sold to the public, how it has become mathematically impossible for grad students in a garage to beat Google, and why net neutrality alone is no guarantee of an open Internet. It also explains why the challenges for local digital news outlets and other small players are worse than they appear and demonstrates what it really takes to grow a digital audience and stay alive in today's online economy. The book shows why, even on the Internet, there is still no such thing as a free audience.

Perancangan dan Pembuatan Alat Bantu Meja Putar untuk Mesin Cnc 4 Axis

2016 ◽  
Vol 10 (2) ◽  
pp. 162-171
Author(s):  
Hafid Hafid ◽  
Tatang Sutisna
Keyword(s):  
Processing Time ◽  
Rotary Table ◽  
Engineering Process ◽  
Cnc Machine ◽  
Economical Analysis ◽  
Machining Center ◽  
Design And Manufacturing ◽  
The Cost ◽  
Productivity And Competitiveness

The design and manufacturing of the rotary table with the specification Ø 170 mm (6 inches) for CNC machine 4 axis has been done. The objective of manufacturing a rotary table is to increase the efficiency of CNC machine Hardford 4 axis to be above 80% in line machining center CV. IM’s workshop. The engineering methods was taken, consist of: working preparation, manufacturing of working drawing, engineering process, the manufacturing and testing. The prototype has been tested and operated, the resulting of increasing productivity of which were as follows: the process of assembling was increased to be 3 time ( before 1 time) and processing time for a specific case reduced from 5 hours to 3 hours, number of operators for the case of assembling the rotary reduced to 1 person (before 4 persons), safety and security become to be better. The results show increased efficiency of CNC machine Hardford, from under 50% to be above 80%. Based on the economical analysis obtained by the cost of good sold (C.G.S) of the rotary table is IDR 34.060.000. The results presented in this paper is expected to be case study for developing a business of the metal and engineering SMEs domestic to the effort of improving efficiency, quality, productivity and competitiveness in global market.ABSTRAKPerancangan dan pembuatan alat bantu meja putar (rotary table) dengan spesifikasi teknis Ø 170 mm (6 inci) untuk mesin CNC 4 axis telah dilakukan. Tujuan pembuatan rotary table adalah untuk meningkatkan efisiensi mesin CNC Hardford 4 axis di atas 80% pada line machining center Bengkel CV. IM. Metode rancang bangun yang dilakukan, meliputi: persiapan kerja, pembuatan gambar kerja, proses engineering, pembuatan dan uji coba. Prototip tersebut telah diuji coba dan dioperasikan dengan hasil peningkatan produktivitas sebagai berikut: proses pengerjaan bongkar pasang meningkat menjadi 3 kali (sebelumnya 1 kali) dan waktu pengerjaan untuk kasus tertentu berkurang dari 5 jam menjadi 3 jam, jumlah operator untuk kasus bongkar pasang rotary berkurang menjadi 1 orang (sebelumnya 4 orang), keselamatan kerja dan keamanan menjadi lebih baik. Hasil peningkatan berupa efisiensi mesin CNC Hardford 4 axis dari sebelumnya di bawah 50% menjadi di atas 80%. Berdasarkan hasil perhitungan analisis ekonomi diperoleh harga pokok produksi (HPP) alat bantu meja putar adalah sebesar Rp. 34.060.000. Bahasan ini diharapkan menjadi contoh kasus bagi pengembangan usaha IKM logam dan mesin dalam negeri untuk meningkatkan efisiensi, mutu, produktivitas dan keunggulan daya saing di pasar global.Kata kunci: alat bantu meja putar, mesin CNC, harga pokok produksi

scholarly journals Application of the theory of decision making under risk and uncertainty at modelling of costs

2010 ◽  
Vol 56 (No. 5) ◽  
pp. 201-208 ◽  
Author(s):  
M. Beranová ◽  
D. Martinovičová
Keyword(s):  
Decision Making ◽  
Financial Accounting ◽  
Cost Functions ◽  
Risk And Uncertainty ◽  
Managerial Decision ◽  
Managerial Decision Making ◽  
Bayesian Theorem ◽  
Long Run ◽  
Short Run ◽  
The Cost

The costs functions are mentioned mostly in the relation to the Break-even Analysis where they are presented in the linear form. But there exist several different types and forms of cost functions. Fist of all, it is necessary to distinguish between the short-run and long-run cost function that are both very important tools of the managerial decision making even if each one is used on a different level of management. Also several methods of estimation of the cost function's parameters are elaborated in the literature. But all these methods are based on the past data taken from the financial accounting while the financial accounting is not able to separate the fixed and variable costs and it is also strongly adjusted to taxation in the many companies. As a tool of the managerial decision making support, the cost functions should provide a vision to the future where many factors of risk and uncertainty influence economic results. Consequently, these random factors should be considered in the construction of cost functions, especially in the long-run. In order to quantify the influences of these risks and uncertainties, the authors submit the application of the Bayesian Theorem.

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