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Peak demand minimization via sliced strip packing

Deppert, MA and Jansen, K and Khan, A and Rau, M and Tutas, M (2021) Peak demand minimization via sliced strip packing. In: 24th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, 16-18 Aug 2021, Seattle.

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Official URL: https://doi.org/10.4230/LIPIcs-APPROX/RANDOM.2021....


We study the Nonpreemptive Peak Demand Minimization (NPDM) problem, where we are given a set of jobs, specified by their processing times and energy requirements. The goal is to schedule all jobs within a fixed time period such that the peak load (the maximum total energy requirement at any time) is minimized. This problem has recently received significant attention due to its relevance in smart-grids. Theoretically, the problem is related to the classical strip packing problem (SP). In SP, a given set of axis-aligned rectangles must be packed into a fixed-width strip, such that the height of the strip is minimized. NPDM can be modeled as strip packing with slicing and stacking constraint: each rectangle may be cut vertically into multiple slices and the slices may be packed into the strip as individual pieces. The stacking constraint forbids solutions where two slices of the same rectangle are intersected by the same vertical line. Nonpreemption enforces the slices to be placed in contiguous horizontal locations (but may be placed at different vertical locations). We obtain a (5/3 + ε)-approximation algorithm for the problem. We also provide an asymptotic efficient polynomial-time approximation scheme (AEPTAS) which generates a schedule for almost all jobs with energy consumption (1 + ε)OPT. The remaining jobs fit into a thin container of height 1. The previous best result for NPDM was a 2.7 approximation based on FFDH 41. One of our key ideas is providing several new lower bounds on the optimal solution of a geometric packing, which could be useful in other related problems. These lower bounds help us to obtain approximative solutions based on Steinberg's algorithm in many cases. In addition, we show how to split schedules generated by the AEPTAS into few segments and to rearrange the corresponding jobs to insert the thin container mentioned above. © Max A. Deppert, Klaus Jansen, Arindam Khan, Malin Rau, and Malte Tutas; licensed under Creative Commons License CC-BY 4.0

Item Type: Conference Paper
Publication: Leibniz International Proceedings in Informatics, LIPIcs
Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information: The copyright for this article belongs to Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Keywords: Approximation algorithms; Containers; Energy utilization; Polynomial approximation, Approximation; Asymptotics; Minimisation; Non-preemptive; Peak demand; Peak demand minimization; Polynomial time approximation schemes; Stackings; Strip packing; Strip packing problem, Geometry
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 29 Nov 2021 09:37
Last Modified: 29 Nov 2021 09:37
URI: http://eprints.iisc.ac.in/id/eprint/70289

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