Stochastic Extensible Bin Packing
Guillaume Sagnol, Daniel Schmidt genannt Waldschmidt

TL;DR
This paper studies the stochastic extensible bin packing problem, analyzing policy ratios and proposing bounds, with applications to scheduling and stochastic environments, including improved bounds for specific distributions.
Contribution
It introduces tight bounds on the price of non-splittability and fixed assignments, and analyzes a fixed assignment variant of the LEPT rule with near-optimal approximation ratios.
Findings
Price of non-splittability has a tight upper bound of 2.
LEPT variant achieves a tight approximation ratio of approximately 1.368.
Bounds are improved for distributions with bounded Pietra index or stochastic dominance.
Abstract
We consider the stochastic extensible bin packing problem (SEBP) in which items of stochastic size are packed into 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 . Moreover, we develop an analysis of a fixed assignment variant of the LEPT rule…
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Taxonomy
TopicsScheduling and Optimization Algorithms · Advanced Manufacturing and Logistics Optimization · Optimization and Packing Problems
