A Distributed Online Heuristic for a Large-scale Workforce Task Assignment and Multi-vehicle Routing Problem

This paper presents a novel formulation for a workforce routing, task assignment, and scheduling problem with privacy by design , drawing inspiration from multi-vehicle routing problems. We examine a real case study involving a large number of technicians tasked with refurbishing and repairing a large number of photo booth machines spread across a wide geographic area, spanning a country. We then introduce a novel heuristic distributed online optimization algorithm, based on gossiping, to: i) assign daily refurbishing and repair tasks to technicians; ii) plan optimal routes for each technician to execute the assigned tasks; iii) dynamically update task assignments and routes in real-time to accommodate delays and unforeseen impediments encountered by technicians (such as traffic jams). The objective is to maximize enterprise profit by effectively managing the workforce. The proposed method inherently safeguards the privacy of real-time geolocation data for the entire workforce, ensuring it remains undisclosed and inaccessible to the company's ICT infrastructure. We provide a numerical simulation utilizing real data, supplied by DEDEM S.p.A., demonstrating the performance of the proposed heuristic in terms of expected net profit for the company.