15,796 research outputs found
Stochastic scheduling on unrelated machines
Two important characteristics encountered in many real-world scheduling problems are heterogeneous machines/processors and a certain degree of uncertainty about the actual sizes of jobs. The first characteristic entails machine dependent processing times of jobs and is captured by the classical unrelated machine scheduling model.The second characteristic is adequately addressed by stochastic processing times of jobs as they are studied in classical stochastic scheduling models. While there is an extensive but separate literature for the two scheduling models, we study for the first time a combined model that takes both characteristics into account simultaneously. Here, the processing time of job on machine is governed by random variable , and its actual realization becomes known only upon job completion. With being the given weight of job , we study the classical objective to minimize the expected total weighted completion time , where is the completion time of job . By means of a novel time-indexed linear programming relaxation, we compute in polynomial time a scheduling policy with performance guarantee . Here, is arbitrarily small, and is an upper bound on the squared coefficient of variation of the processing times. We show that the dependence of the performance guarantee on is tight, as we obtain a lower bound for the type of policies that we use. When jobs also have individual release dates , our bound is . Via , currently best known bounds for deterministic scheduling are contained as a special case
Project scheduling under undertainty – survey and research potentials.
The vast majority of the research efforts in project scheduling assume complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. However, in the real world, project activities are subject to considerable uncertainty, that is gradually resolved during project execution. In this survey we review the fundamental approaches for scheduling under uncertainty: reactive scheduling, stochastic project scheduling, stochastic GERT network scheduling, fuzzy project scheduling, robust (proactive) scheduling and sensitivity analysis. We discuss the potentials of these approaches for scheduling projects under uncertainty.Management; Project management; Robustness; Scheduling; Stability;
Learning Scheduling Algorithms for Data Processing Clusters
Efficiently scheduling data processing jobs on distributed compute clusters
requires complex algorithms. Current systems, however, use simple generalized
heuristics and ignore workload characteristics, since developing and tuning a
scheduling policy for each workload is infeasible. In this paper, we show that
modern machine learning techniques can generate highly-efficient policies
automatically. Decima uses reinforcement learning (RL) and neural networks to
learn workload-specific scheduling algorithms without any human instruction
beyond a high-level objective such as minimizing average job completion time.
Off-the-shelf RL techniques, however, cannot handle the complexity and scale of
the scheduling problem. To build Decima, we had to develop new representations
for jobs' dependency graphs, design scalable RL models, and invent RL training
methods for dealing with continuous stochastic job arrivals. Our prototype
integration with Spark on a 25-node cluster shows that Decima improves the
average job completion time over hand-tuned scheduling heuristics by at least
21%, achieving up to 2x improvement during periods of high cluster load
Scheduling under Linear Constraints
We introduce a parallel machine scheduling problem in which the processing
times of jobs are not given in advance but are determined by a system of linear
constraints. The objective is to minimize the makespan, i.e., the maximum job
completion time among all feasible choices. This novel problem is motivated by
various real-world application scenarios. We discuss the computational
complexity and algorithms for various settings of this problem. In particular,
we show that if there is only one machine with an arbitrary number of linear
constraints, or there is an arbitrary number of machines with no more than two
linear constraints, or both the number of machines and the number of linear
constraints are fixed constants, then the problem is polynomial-time solvable
via solving a series of linear programming problems. If both the number of
machines and the number of constraints are inputs of the problem instance, then
the problem is NP-Hard. We further propose several approximation algorithms for
the latter case.Comment: 21 page
Stochastic optimization of product-machine qualification in a semiconductor back-end facility
abstract: In order to process a product in a semiconductor back-end facility, a machine needs to be qualified, first by having product-specific software installed and then running test wafers through it to verify that the machine is capable of performing the process correctly. In general, not all machines are qualified to process all products due to the high machine qualification cost and tool set availability. The machine qualification decision affects future capacity allocation in the facility and subsequently affects daily production schedules. To balance the tradeoff between current machine qualification costs and future potential backorder costs due to not enough machines qualified with uncertain demand, a stochastic product–machine qualification optimization model is proposed in this article. The L-shaped method and acceleration techniques are proposed to solve the stochastic model. Computational results are provided to show the necessity of the stochastic model and the performance of different solution methods.This is an Author's Accepted Manuscript of an article published as Fu, Mengying, Askin, Ronald, Fowler, John, & Zhang, Muhong (2015). Stochastic optimization of product-machine qualification in a semiconductor back-end facility. IIE TRANSACTIONS, 47(7), 739-750. DOI: 10.1080/0740817X.2014.964887. Copyright Taylor & Francis, available online at: http://www.tandfonline.com/doi/abs/10.1080/0740817X.2014.96488
Modelling activity times by hybrid synthetic method
Uncertain (manual) activity times impact a number of manufacturing system modules: plant and layout design, capacity analysis, operator assignment, process planning, scheduling and simulation. Direct observation cannot be used for non-existent production lines. A hybrid direct observation/synthetic method derived from Method Time Measurement available in industry is proposed. To determine accurate activity times required by heuristics and metaheuristics optimisation, manufacturing system modules are modelled by MILP and operator efficiency parameters are used for time standardisation. Among human factors considered are skill and ergonomics. Application to the sterilisation of reusable medical devices is extensively described. Experimental data taken from observation on the field and a worst-case date have shown the model direct applicability for professionals also to non-manufacturing cases
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