# Investigation of Workforce Dynamical Behaviour from a Phase Plane Perspective

### Timo Lahteenmaa-Swerdlyk, François-Alex Bourque

#### 2024

#### Abstract

The purpose of this work was to investigate the population dynamics of on-the-job training. The ratio of mentees to mentors was considered, and its effect on overwhelming (saturating) the training system was analysed when undergoing a growth phase between two healthy states. This analysis was completed by analytically solving a simplified continuous model of the problem with constant input parameters. The model was investigated through a phase-plane interpretation, or the mentee versus mentor population as the system evolves. The key input parameter of the analysis was the saturation limit: the ratio of mentees to mentors above which the system becomes saturated. This value can be modified by adjusting various factors such as the quality, quantity, and/or the delivery method of the training. Of special interest was the time for the system to evolve as the saturation limit was varied. It was discovered that the system behaviour can fall into three categories based on its value. If the saturation limit is very low, the system will remain saturated and never reach a steady state. If the threshold is very high, the system will remain unsaturated (healthy) and reach steady state at inputted target populations, albeit in a relatively slow timeframe. Finally, for a particular middle range of values, the system will reach steady state at inputted target populations in an optimal time by crossing into and out of saturation. Therefore, finding the optimal values for the input parameters will depend on a compromise between reaching the target state quickly and not exceeding the target population levels, which will depend on the priorities of the organization. Given that any occupation with on-the-job training could experience such effects during a transition, understanding the dynamics of saturation is thus essential to design an efficient training system.

Download#### Paper Citation

#### in Harvard Style

Lahteenmaa-Swerdlyk T. and Bourque F. (2024). **Investigation of Workforce Dynamical Behaviour from a Phase Plane Perspective**. In *Proceedings of the 13th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES*; ISBN 978-989-758-681-1, SciTePress, pages 35-46. DOI: 10.5220/0012270900003639

#### in Bibtex Style

@conference{icores24,

author={Timo Lahteenmaa-Swerdlyk and François-Alex Bourque},

title={Investigation of Workforce Dynamical Behaviour from a Phase Plane Perspective},

booktitle={Proceedings of the 13th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES},

year={2024},

pages={35-46},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012270900003639},

isbn={978-989-758-681-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES

TI - Investigation of Workforce Dynamical Behaviour from a Phase Plane Perspective

SN - 978-989-758-681-1

AU - Lahteenmaa-Swerdlyk T.

AU - Bourque F.

PY - 2024

SP - 35

EP - 46

DO - 10.5220/0012270900003639

PB - SciTePress