  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.
