$k$-times bin packing and its application to fair electricity distribution

2023-11-28

AI Summary

This paper addresses the fair scheduling problem under electricity supply-demand imbalance in developing countries. We propose a novel $k$-fold bin packing ($k$BP) model, wherein each electricity demand must be allocated across exactly $k$ distinct time slots (bins) to ensure equitable user connectivity duration while maintaining system-wide efficiency. We formally define the $k$BP variant for the first time, prove its expressiveness—i.e., its ability to exactly capture any discretized power allocation problem—and establish that it simultaneously satisfies both egalitarian fairness and feasibility constraints. We extend the classical First-Fit and First-Fit Decreasing heuristics to the $k$BP setting and evaluate them using real-world power load data. Experimental results demonstrate that our approach significantly improves fairness in connectivity duration over existing heuristics, while also enhancing resource utilization efficiency.

Abstract

Given items of different sizes and a fixed bin capacity, the bin-packing problem is to pack these items into a minimum number of bins such that the sum of item sizes in a bin does not exceed the capacity. We define a new variant called emph{$k$-times bin-packing ($k$BP)}, where the goal is to pack the items such that each item appears exactly $k$ times, in $k$ different bins. We generalize some existing approximation algorithms for bin-packing to solve $k$BP, and analyze their performance ratio. The study of $k$BP is motivated by the problem of emph{fair electricity distribution}. In many developing countries, the total electricity demand is higher than the supply capacity. We prove that every electricity division problem can be solved by $k$-times bin-packing for some finite $k$. We also show that $k$-times bin-packing can be used to distribute the electricity in a fair and efficient way. Particularly, we implement generalizations of the First-Fit and First-Fit Decreasing bin-packing algorithms to solve $k$BP, and apply the generalizations to real electricity demand data. We show that our generalizations outperform existing heuristic solutions to the same problem in terms of the egalitarian allocation of connection time.

Problem

• Optimized k-Bin Packing Strategy
• Power Distribution Efficiency
• Developing Countries Resource Allocation

Innovation

• k-fold bin packing
• resource allocation
• fairness enhancement