In contrast to classic Vehicle Routing Problems (VRPs), where the objective is to minimize the routing cost while serving all customers, Vehicle Routing Problems with Profits (VRPPs) maximize overall profit collected at customers, under limited fleet size and route duration, which prevent from serving all customers.

In both settings, optimal cost-/profit-based solutions lead to unbalanced routes between drivers, hence the need to integrate equity concerns. For classic VRPs, equity is typically defined in terms of workload distribution (drivers aim to reduce their workload, e.g., minimizing their route cost, or number of customers served) and has gained significant attention the recent literature [3]. For VRPPs, however, defining equity in terms of driver's profit is more appropriate (drivers aim to earn more), yet the topic has received little attention despite its relevance.

Consider, for example, a delivery company with a limited number of drivers using electric bikes constrained by battery capacity. Then, not all customers can be served. If drivers are paid proportionally to the profit generated by the demands they serve, the objective of the company is to maximize the overall profit, while ensuring a fair profit distribution between drivers.

The aim of this work is to propose appropriate strategies for profit equity in VRPPs and to assess trade-offs between overall profit and profit equity.