A mathematical model for optimal switching problem of production line based on the OCRA method for ergonomics

Abstract

The rapid development of automation technology in recent years has led to extensive research on how machines can replace human labor. However, many manufacturing companies may find the costs of smart production prohibitively high, while flexible manual production can result in higher profits. According to reports on the burden of disease in different countries, upper limb musculoskeletal disorders (UL-WMSDs) are the most prevalent occupational disease in industrialized countries, and they account for a significant portion of compensation. These disorders are often linked to the working environment, intensity, and duration of work. In this paper, the OCRA (Occupational Repetitive Action) index method is employed to assess the biomechanical risks associated with repetitive movements of the upper limb, and mathematical models were developed to automatically estimate the force, posture, and repetitive elements in this method. This paper proposes the OCRA index model for ergonomics based on the optimal switching problem when the processing time follows either an exponential or a generally distributed pattern. Finally, based on the switching model, numerical experiments were conducted in a medium-high action frequency scenario in order to evaluate the effect of speed changes on the OCRA index before and after switching. The experimental results enable us to find the optimal combination of the processing speed and the reference process k to minimize the total processing time in a safe ergonomic risk range.