7122
2018
eng
327
347
11312
conferenceobject
0
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The Price of Fixed Assignments in Stochastic Extensible Bin Packing
We consider the stochastic extensible bin packing problem (SEBP) in which n items of stochastic size are packed into m bins of unit capacity. In contrast to the classical bin packing problem, the number of bins is fixed and they can be extended at extra cost. This problem plays an important role in stochastic environments such as in surgery scheduling: Patients must be assigned to operating rooms beforehand, such that the regular capacity is fully utilized while the amount of overtime is as small as possible.
This paper focuses on essential ratios between different classes of policies: First, we consider the price of non-splittability, in which we compare the optimal non-anticipatory policy against the optimal fractional assignment policy. We show that this ratio has a tight upper bound of 2. Moreover, we develop an analysis of a fixed assignment variant of the LEPT rule yielding a tight approximation ratio of (1+eā1)ā1.368 under a reasonable assumption on the distributions of job durations.
Furthermore, we prove that the price of fixed assignments, related to the benefit of adaptivity, which describes the loss when restricting to fixed assignment policies, is within the same factor. This shows that in some sense, LEPT is the best fixed assignment policy we can hope for.
WAOA 2018: Approximation and Online Algorithms
10.1007/978-3-030-04693-4_20
Lecture Notes in Computer Science
yes
urn:nbn:de:0297-zib-68415
accepted for publication
2018-07-23
Guillaume Sagnol
Guillaume Sagnol
Daniel Schmidt genannt Waldschmidt
Alexander Tesch
Mathematical Optimization
Sagnol, Guillaume
Tesch, Alexander
BMBF-IBOSS
Mathematics of Health Care