Bin Packing with Linear Usage Costs

TL;DR

This paper introduces a variant of bin packing that incorporates linear usage costs to model energy consumption in data centres, providing new bounds and constraints for efficient virtual machine placement.

Contribution

It extends classical bin packing to include linear costs, develops LP-based lower bounds, and enhances the global constraint with cost information for better energy-efficient management.

Findings

LP-based lower bounds improve solution quality

Extended global constraint effectively models energy costs

Method enhances virtual machine placement efficiency

Abstract

Bin packing is a well studied problem involved in many applications. The classical bin packing problem is about minimising the number of bins and ignores how the bins are utilised. We focus in this paper, on a variant of bin packing that is at the heart of efficient management of data centres. In this context, servers can be viewed as bins and virtual machines as items. The efficient management of a data-centre involves minimising energy costs while ensuring service quality. The assignment of virtual machines on servers and how these servers are utilised has a huge impact on the energy consumption. We focus on a bin packing problem where linear costs are associated to the use of bins to model the energy consumption. We study lower bounds based on Linear Programming and extend the bin packing global constraint with cost information.