Fair Division Algorithms for Electricity Distribution
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In many developing countries, the total electricity demand is larger than the limited generation capacity of power stations. Many countries adopt the common practice of routine load shedding - disconnecting entire regions from the power supply - to maintain a balance between demand and supply. Load shedding results in inflicting hardship and discomfort on households, which is even worse and hence unfair to those whose need for electricity is higher than that of others during load shedding hours. Recently, Oluwasuji et al. [2020] presented this problem and suggested several heuristic solutions. In this work, we study the electricity distribution problem as a problem of fair division, model it using the related literature on cake-cutting problems, and discuss some insights on which parts of the time intervals are allocated to each household. We consider four cases: identical demand, uniform utilities; identical demand, additive utilities; different demand, uniform utilities; different demand, additive utilities. We provide the solution for the first two cases and discuss the novel concept of q-times bin packing in relation to the remaining cases. We also show how the fourth case is related to the consensus k-division problem. One can study objectives and constraints using utilitarian and egalitarian social welfare metrics, as well as trying to keep the number of cuts as small as possible. A secondary objective can be to minimize the maximum utility-difference between agents.
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