Solving the fair electric load shedding problem in developing countries

Often because of limitations in generation capacity of power stations, many developing countries frequently resort to disconnecting large parts of the power grid from supply, a process termed load shedding. This leaves households in disconnected parts without electricity, causing them inconvenience and discomfort. Without fairness being taken into due consideration during load shedding, some households may suffer more than others. In this paper, we solve the fair load shedding problem (FLSP) by creating solutions which connect households to supply based on some fairness criteria (i.e., to fairly connect homes to supply in terms of duration, their electricity needs, and their demand), which we model as their utilities. First, we briefly describe some state-of-art household-level load shedding heuristics which meet the first criteria. Second, we model the FLSP as a resource allocation problem, which we formulate into two Mixed Integer Programming (MIP) problems based on the Multiple Knapsack Problem. In so doing, we use the utilitarian, egalitarian and envy-freeness social welfare metrics to develop objectives and constraints that ensure our FLSP solutions results in fair allocations that consider the utilities of agents. Then, we solve the FLSP and show that our MIP models maximize the groupwise and individual utilities of agents, and minimize the differences between their pairwise utilities under a number of experiments. When taken together, our endeavour establishes a set of benchmarks for fair load shedding schemes, and provide insights for designing fair allocation solutions for other scarce resources.