A New Whole Programming Formulation for the Container Scaling Problem

The work proposes a new Integer Programming formulation for container scaling in Kubernetes clusters, modeled as a Problem of Packing in Multiple Backpacks with Relocation Penalty Over Time. The formulation seeks to minimize the total cost of operating the cluster, considering fixed and variable costs associated with the activation and use of nodes, as well as penalties for failures and unnecessary migrations of pods between periods. The proposal promotes greater stability in allocations and efficiency in the use of resources, surpassing the kube-scheduler in reducing operating costs, although with greater computational time.