482 research outputs found
Order Acceptance and Scheduling: A Taxonomy and Review
Over the past 20 years, the topic of order acceptance has attracted considerable attention from those who study scheduling and those who practice it. In a firm that strives to align its functions so that profit is maximized, the coordination of capacity with demand may require that business sometimes be turned away. In particular, there is a trade-off between the revenue brought in by a particular order, and all of its associated costs of processing. The present study focuses on the body of research that approaches this trade-off by considering two decisions: which orders to accept for processing, and how to schedule them. This paper presents a taxonomy and a review of this literature, catalogs its contributions and suggests opportunities for future research in this area
Any-Order Online Interval Selection
We consider the problem of online interval scheduling on a single machine,
where intervals arrive online in an order chosen by an adversary, and the
algorithm must output a set of non-conflicting intervals. Traditionally in
scheduling theory, it is assumed that intervals arrive in order of increasing
start times. We drop that assumption and allow for intervals to arrive in any
possible order. We call this variant any-order interval selection (AOIS). We
assume that some online acceptances can be revoked, but a feasible solution
must always be maintained. For unweighted intervals and deterministic
algorithms, this problem is unbounded. Under the assumption that there are at
most different interval lengths, we give a simple algorithm that achieves a
competitive ratio of and show that it is optimal amongst deterministic
algorithms, and a restricted class of randomized algorithms we call memoryless,
contributing to an open question by Adler and Azar 2003; namely whether a
randomized algorithm without access to history can achieve a constant
competitive ratio. We connect our model to the problem of call control on the
line, and show how the algorithms of Garay et al. 1997 can be applied to our
setting, resulting in an optimal algorithm for the case of proportional
weights. We also discuss the case of intervals with arbitrary weights, and show
how to convert the single-length algorithm of Fung et al. 2014 into a classify
and randomly select algorithm that achieves a competitive ratio of 2k. Finally,
we consider the case of intervals arriving in a random order, and show that for
single-lengthed instances, a one-directional algorithm (i.e. replacing
intervals in one direction), is the only deterministic memoryless algorithm
that can possibly benefit from random arrivals. Finally, we briefly discuss the
case of intervals with arbitrary weights.Comment: 19 pages, 11 figure
New Results on Online Resource Minimization
We consider the online resource minimization problem in which jobs with hard
deadlines arrive online over time at their release dates. The task is to
determine a feasible schedule on a minimum number of machines. We rigorously
study this problem and derive various algorithms with small constant
competitive ratios for interesting restricted problem variants. As the most
important special case, we consider scheduling jobs with agreeable deadlines.
We provide the first constant ratio competitive algorithm for the
non-preemptive setting, which is of particular interest with regard to the
known strong lower bound of n for the general problem. For the preemptive
setting, we show that the natural algorithm LLF achieves a constant ratio for
agreeable jobs, while for general jobs it has a lower bound of Omega(n^(1/3)).
We also give an O(log n)-competitive algorithm for the general preemptive
problem, which improves upon the known O(p_max/p_min)-competitive algorithm.
Our algorithm maintains a dynamic partition of the job set into loose and tight
jobs and schedules each (temporal) subset individually on separate sets of
machines. The key is a characterization of how the decrease in the relative
laxity of jobs influences the optimum number of machines. To achieve this we
derive a compact expression of the optimum value, which might be of independent
interest. We complement the general algorithmic result by showing lower bounds
that rule out that other known algorithms may yield a similar performance
guarantee
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