Bounds for nonpreemptive scheduling of jobs with similar processing times on multiprocessor systems using the LPT-Algorithm

Computing ◽  
1991 ◽  
Vol 46 (3) ◽  
pp. 183-191 ◽  
Author(s):  
H. Kellerer
Keyword(s):  
Multiprocessor Systems ◽  
Processing Times ◽  
Lpt Algorithm ◽  
Nonpreemptive Scheduling ◽  
Similar Processing

Optimal Scheduling on Parallel Processors with Precedence Constraints and General Costs

1997 ◽  
Vol 11 (1) ◽  
pp. 79-93 ◽  
Author(s):  
Zhen Liu ◽  
Rhonda Righter
Keyword(s):  
Forest Structure ◽  
Parallel Processors ◽  
Ratio Distribution ◽  
Processing Times ◽  
Weighted Number ◽  
Number Of Late Jobs ◽  
The Cost ◽  
Nonpreemptive Scheduling ◽  
Late Jobs ◽  
Weighted Flowtime

We consider preemptive and nonpreemptive scheduling of partially ordered tasks on parallel processors, where the precedence relations have an intervalorder, an in-forest, or a uniform out-forest structure. Processing times of tasks are random variables with an increasing in likelihood ratio distribution in the nonpreemptive case and an exponential distribution in the preemptive case. We consider a general cost that is a function of time and of the uncompleted tasks and show that the most successors (MS) policy stochastically minimizes the cost function when it satisfies certain agreeability conditions. A consequence is that the MS policy stochastically minimizes makespan, weighted flowtime, and the weighted number of late jobs.

Fuzzy Flexible-Flow Shops at Two Machine Centers

1998 ◽  
Vol 2 (4) ◽  
pp. 142-149 ◽  
Author(s):  
Tzung-Pei Hong ◽  
◽  
Wei-Chou Chen ◽  
Keyword(s):  
Job Scheduling ◽  
Flow Shop ◽  
Flow Shops ◽  
Processing Times ◽  
Task Sequencing ◽  
Lpt Algorithm ◽  
Machine Centers ◽  
One Machine Scheduling ◽  
Operation Center ◽  
One Machine

In simple-flow shop problems, each machine operation center has one machine. If a machine center has more than one machine, scheduling becomes a flexible shop flow problem. Flexible shop flows are thus generalizations of simple shop flow. Processing time for each job was previously assumed to be known exactly, but in many real-world applications, processing times vary dynamically due to human or operating factors. We apply fuzzy concepts to represent uncertainty in processing times for flexible-flow shops with two machine centers, then propose a fuzzy heuristic algorithm for job scheduling. We first use a fuzzy LPT algorithm to allocate jobs, then use a fuzzy Johnson algorithm to deal with task sequencing. The proposed method lets jobs be scheduled more flexibly than conventionally.

scholarly journals Approximate and robust bounded job start scheduling for Royal Mail delivery offices

2021 ◽  
Author(s):  
Dimitrios Letsios ◽  
Jeremy T. Bradley ◽  
Suraj G ◽  
Ruth Misener ◽  
Natasha Page
Keyword(s):  
Processing Time ◽  
Approximation Ratio ◽  
Optimization Approach ◽  
Scheduling Problems ◽  
Processing Times ◽  
Lexicographic Optimization ◽  
Lpt Algorithm ◽  
Scheduling Under Uncertainty ◽  
Recovery Approach ◽  
Delivery Scheduling

AbstractMotivated by mail delivery scheduling problems arising in Royal Mail, we study a generalization of the fundamental makespan scheduling $$P||C_{\max }$$ P | | C max problem which we call the bounded job start scheduling problem. Given a set of jobs, each specified by an integer processing time $$p_j$$ p j , that have to be executed non-preemptively by a set of m parallel identical machines, the objective is to compute a minimum makespan schedule subject to an upper bound $$g\le m$$ g ≤ m on the number of jobs that may simultaneously begin per unit of time. With perfect input knowledge, we show that Longest Processing Time First (LPT) algorithm is tightly 2-approximate. After proving that the problem is strongly $${\mathcal {N}}{\mathcal {P}}$$ N P -hard even when $$g=1$$ g = 1 , we elaborate on improving the 2-approximation ratio for this case. We distinguish the classes of long and short instances satisfying $$p_j\ge m$$ p j ≥ m and $$p_j<m$$ p j < m , respectively, for each job j. We show that LPT is 5/3-approximate for the former and optimal for the latter. Then, we explore the idea of scheduling long jobs in parallel with short jobs to obtain tightly satisfied packing and bounded job start constraints. For a broad family of instances excluding degenerate instances with many very long jobs, we derive a 1.985-approximation ratio. For general instances, we require machine augmentation to obtain better than 2-approximate schedules. In the presence of uncertain job processing times, we exploit machine augmentation and lexicographic optimization, which is useful for $$P||C_{\max }$$ P | | C max under uncertainty, to propose a two-stage robust optimization approach for bounded job start scheduling under uncertainty aiming in a low number of used machines. Given a collection of schedules of makespan $$\le D$$ ≤ D , this approach allows distinguishing which are the more robust. We substantiate both the heuristics and our recovery approach numerically using Royal Mail data. We show that for the Royal Mail application, machine augmentation, i.e., short-term van rental, is especially relevant.

A new tool for rapid development of electron microscopy negatives and micrographs: Initial impressions of the MOHR/PRO-8 processor

1992 ◽  
Vol 50 (2) ◽  
pp. 972-973
Author(s):  
James C. Long
Keyword(s):  
Electron Microscopy ◽  
Processing Time ◽  
Rapid Development ◽  
Processing Times ◽  
Initial Impressions ◽  
Transport Method

Over the years, many techniques and products have been developed to reduce the amount of time spent in a darkroom processing electron microscopy negatives and micrographs. One of the latest tools, effective in this effort, is the Mohr/Pro-8 film and rc paper processor.At the time of writing, a unit has been recently installed in the photographic facilities of the Electron Microscopy Center at Texas A&M University. It is being evaluated for use with TEM sheet film, SEM sheet film, 35mm roll film (B&W), and rc paper.Originally designed for use in the phototypesetting industry, this processor has only recently been introduced to the field of electron microscopy.The unit is a tabletop model, approximately 1.5 × 1.5 × 2.0 ft, and uses a roller transport method of processing. It has an adjustable processing time of 2 to 6.5 minutes, dry-to-dry. The installed unit has an extended processing switch, enabling processing times of 8 to 14 minutes to be selected.

Robust Scheduling for Flexible Job-Shop Problems with Uncertain Processing Times

2015 ◽  
Vol 135 (6) ◽  
pp. 713-720
Author(s):  
Wan-Ling Li ◽  
Tomohiro Murata ◽  
Muhammad Hafidz Fazli bin Md Fauadi
Keyword(s):  
Job Shop ◽  
Flexible Job Shop ◽  
Robust Scheduling ◽  
Processing Times
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