Markov Decision Process for Mixed-Model Assembly Line design under process time uncertainty

Abstract

The industry is increasingly confronted with the challenge of process duration uncertainty in production systems. These variations are particularly problematic for manufacturers that utilize Multi-Manned Mixed-Model Assembly Lines, as they can cause significant disruptions that may stop the production line. Our study explores the benefit of walking workers to dynamically adjust the workforce in response to unexpected variations in process durations at different stations, a common scenario in the automotive industry. We model the dynamic workforce assignment decision as a Markov Decision Process (MDP), and this MDP accounts for uncertainties in process times, and it incorporates dynamic task assignment and workers’ movements. This MDP is subsequently translated into a linear program that we integrate into a higher-level Mixed-Integer Linear Programming model responsible for dimensioning the workforce and selecting equipment in the station. This approach results in the creation of assembly lines designed to be resilient in the face of unexpected variations in task process durations. To deal with scalability issues, we employ the Benders decomposition algorithm. The paper also presents a validation with data from a car manufacturer that reinforces the practical applicability of our methodology. Additionally, we provide managerial insights on effectively managing process time uncertainty in automotive production systems, empowering decision-makers with optimization strategies, cost-reduction approaches, and resilience-building techniques to enhance the performance and reliability of Mixed-Model Assembly Lines.