Optimal Workday Length Considering Worker Fatigue and Employer Profit

Abstract

The relationship between workday duration, daily production rate, and worker fatigue accumulation has lately gained lot of attention in the field of Ergonomics and Safety Engineering. However, it has been overlooked in studies on Operations Research and Production Planning. Besides, analytical models that investigate this relationship are scarce. At first glance, it may seem that long work hours increase the daily work output, but the worker fatigue accumulation increases with long working hours, leading to lower daily production. Thus, there is a trade-off between long and short working hours. The purpose of this paper is two-fold, the first of which is revising the widely adopted 8-hour workday standard and the second one is the determination of the economic daily production quantity when the worker fatigue accumulation and recovery are considered. Although the proposed model seems mathematically intractable, its key properties allowed us to simplify and devise an efficient algorithm for it. This algorithm is derived based on Karush–Kuhn–Tucker theorems and finds the global optimal solution in only one iteration. The numerical results show that the widely adopted 8-hour workday standard is generally not optimal for neither the worker nor the employer.

Keywords: 8-hour workday standard, workday duration, worker fatigue, Productivity, Production