The Algorithmic Landscape of Fair and Efficient Distribution of Delivery Orders in the Gig Economy

Distributing services, goods, and tasks in the gig economy heavily relies upon on-demand workers (aka agents), leading to new challenges varying from logistics optimization to the ethical treatment of gig workers. We focus on fair and efficient distribution of delivery tasks -- placed on the vertices of a graph -- among a fixed set of agents. We consider the fairness notion of minimax share (MMS), which aims to minimize the maximum (submodular) cost among agents and is particularly appealing in applications without monetary transfers. We propose a novel efficiency notion -- namely non-wastefulness -- that is desirable in a wide range of scenarios and, more importantly, does not suffer from computational barriers. Specifically, given a distribution of tasks, we can, in polynomial time, i) verify whether the distribution is non-wasteful and ii) turn it into an equivalent non-wasteful distribution. Moreover, we investigate several fixed-parameter tractable and polynomial-time algorithms and paint a complete picture of the (parameterized) complexity of finding fair and efficient distributions of tasks with respect to both the structure of the topology and natural restrictions of the input. Finally, we highlight how our findings shed light on computational aspects of other well-studied fairness notions, such as envy-freeness and its relaxations.