6841
eng
reportzib
0
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2018-04-23
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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, bins 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 $1+1/e \approx 1.368$ under a reasonable assumption on the distributions of job durations.
Furthermore, we prove that the price of fixed assignments, 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.
1438-0064
urn:nbn:de:0297-zib-68415
Guillaume Sagnol
Guillaume Sagnol
Daniel Schmidt genannt Waldschmidt
Alexander Tesch
ZIB-Report
18-19
eng
uncontrolled
Approximation Algorithms
eng
uncontrolled
Stochastic Scheduling
eng
uncontrolled
Extensible Bin Packing
Scheduling theory, stochastic [See also 68M20]
Mathematical Optimization
Sagnol, Guillaume
Tesch, Alexander
BMBF-IBOSS
Mathematics of Health Care
https://opus4.kobv.de/opus4-zib/files/6841/stoch_EBP_zib.pdf