342 research outputs found
Single machine scheduling problems with uncertain parameters and the OWA criterion
In this paper a class of single machine scheduling problems is discussed. It
is assumed that job parameters, such as processing times, due dates, or weights
are uncertain and their values are specified in the form of a discrete scenario
set. The Ordered Weighted Averaging (OWA) aggregation operator is used to
choose an optimal schedule. The OWA operator generalizes traditional criteria
in decision making under uncertainty, such as the maximum, average, median or
Hurwicz criterion. It also allows us to extend the robust approach to
scheduling by taking into account various attitudes of decision makers towards
the risk. In this paper a general framework for solving single machine
scheduling problems with the OWA criterion is proposed and some positive and
negative computational results for two basic single machine scheduling problems
are provided
On the approximability of robust spanning tree problems
In this paper the minimum spanning tree problem with uncertain edge costs is
discussed. In order to model the uncertainty a discrete scenario set is
specified and a robust framework is adopted to choose a solution. The min-max,
min-max regret and 2-stage min-max versions of the problem are discussed. The
complexity and approximability of all these problems are explored. It is proved
that the min-max and min-max regret versions with nonnegative edge costs are
hard to approximate within for any unless
the problems in NP have quasi-polynomial time algorithms. Similarly, the
2-stage min-max problem cannot be approximated within unless the
problems in NP have quasi-polynomial time algorithms. In this paper randomized
LP-based approximation algorithms with performance ratio of for
min-max and 2-stage min-max problems are also proposed
Complexity of the robust weighted independent set problems on interval graphs
This paper deals with the max-min and min-max regret versions of the maximum
weighted independent set problem on interval graphswith uncertain vertex
weights. Both problems have been recently investigated by Nobibon and Leus
(2014), who showed that they are NP-hard for two scenarios and strongly NP-hard
if the number of scenarios is a part of the input. In this paper, new
complexity and approximation results on the problems under consideration are
provided, which extend the ones previously obtained. Namely, for the discrete
scenario uncertainty representation it is proven that if the number of
scenarios is a part of the input, then the max-min version of the problem
is not at all approximable. On the other hand, its min-max regret version is
approximable within and not approximable within for
any unless the problems in NP have quasi polynomial algorithms.
Furthermore, for the interval uncertainty representation it is shown that the
min-max regret version is NP-hard and approximable within 2
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