Continuos or discrete variables?

[Nub_User]

What is the most suitable approach for VENSIM and for the essence of SD? Should we model discrete variables (such as the number of employees in a company) as continuous or discrete variables?

When considering the amount of personnel in a company, we never have fractions of people as employees; we always have a whole number of staff. Therefore, in VENSIM it is possible to model it like discrete variable adjusting the equations (such as input and output flow) to operate discretely. This result can be achieved by incorporating functions such as Integer or Step. But, also implies that a "quantum leap" occurs between the values obtained at each time interval (t0, t1, ..., tn).

Could this cause problems of numerical continuity or loss of information in VENSIM calculations, especially if the model is complex and combines this approach with continuous variables, such as leadership level?

Could it be that VENSIM, based on the essence of SD, would prefer it to be modeled as a continuous variable and that only if we need to present the information in some managerial dashboard, we process the continuous outputs of the model to transform them into discrete ones? Is that correct?

Thank you very much.

[tomfid]

https://metasd.com/2017/01/forrester-on ... ous-flows/

[tomfid]

Like Forrester, I think that discrete quantities are rarely a good place to start. Things that are theoretically only available in integer quantities either don't matter, or have qualifications. For example, people are certainly available in integer quantities. But what about the work-equivalent of people? Suppose, for example, a person works 8 hours overtime per week, so they look like 1.2 full time equivalent people? Usually it's not worth worrying about the integer constraint in such cases.

[tomfid]

On the other hand, if you're interested in stochastic extinction of a disease in a small population, integer values may matter.

It's impossible to answer these questions in general; some specifics of the question to be answered must be known.

[Nub_User]

Thank you very much for the detailed response. I understand your argument and Forrester's regarding the loss of certain complexity when discretizing, and I am reflecting on its implications.

I'm thinking about an example model that represents a production line of tables using level variables (considering the table as a product that doesn't have intermediate states, i.e., it's either manufactured or not within the time interval considered in the model, thus being discrete variables). Additionally, the rates of change of these level variables are determined by the quantity of factory personnel (also level and discrete variables) whose productivity depends on management leadership, employee motivation, experience, and fatigue (all continuous auxiliary variables). Assuming that in the event of a considerable increase in leadership, there would be productivity ramp-ups impacting the quantities produced, and that this would increase employee fatigue, decreasing productivity and leading to a new equilibrium.

Indeed, this model could be further complexified by modeling multiple production lines representing the manufacturing of different table models. Each production line with its own set of variables representing the production process, personnel, and factors influencing productivity. The mix of products that arises spontaneously due to the dynamic productivity would determine the consumption of material resources (wood) for each line and for the factory as a whole (also discrete variables).