Data centres and similar server clusters consume a large amount of energy. However, not all consumed energy produces useful work. Servers consume a disproportional amount of energy when they are idle, underutilised, or overloaded. The effect of these conditions can be minimised by attempting to balance the demand for and the supply of resources through a careful prediction of future workloads and their efficient consolidation. In this paper we extend the cutting stock problem for consolidating workloads having stochastic characteristics. Hence, we employ the aggregate probability density function of co-located and simultaneously executing services to establish valid patterns. A valid pattern is one yielding an overall resource utilisation below a set threshold. We tested the scope and usefulness of our approach on a 16-core server with 29 different benchmarks. The workloads of these benchmarks have been generated based on the CPU utilisation traces of 100 real-world virtual machines which we obtained from a Google data centre hosting more than 32000 virtual machines. Altogether, we considered 600 different consolidation scenarios during our experiment. We compared the performance of our approach-system overload probability, job completion time, and energy consumption-with four existing/proposed scheduling strategies. In each category, our approach incurred a modest penalty with respect to the best performing approach in that category, but overall resulted in a remarkable performance clearly demonstrating its capacity to achieve the best trade-off between resource consumption and performance.

The primary objective in cutting and packing problems is trim loss or material input minimization (in stock cutting) or value maximization (in knapsack-type problems). However, in real-life production we usually have many other objectives (costs) and constraints. Probably the most complex auxiliary criteria in one-dimensional stock cutting are the number of different cutting patterns (setups) and the maximum number of open stacks during the cutting process. There are applications where the number of stacks is restricted to two. We design a sequential heuristic to minimize material input and show its high effectiveness for this purpose. Then we extend it to restrict the number of open stacks to any given limit. Then, the heuristic is simplified and integrated into a setup-minimization approach in order to combine setup and open-stacks minimization. To get a smaller number of open stacks, we may split up the problem into several parts of smaller sizes. Different solutions are evaluated in relation to the multiple objectives using the Pareto criterion.