The job responsibility is exactly the same in the department.

The department has a total number of working hours required. The total retention is about 50% a year, and the hiring cost is about $2000 per person.

Salary is about $12 per hour. Full time works 40 hours, while part time works 20 hours per week.

Is this an optimization or simulation problem? I guess the output is a range of workers required. How to model this?

  • $\begingroup$ As Oguz says, more details are required. In particular, you need to specify what decisions you (as manager of the department) need to make, and what criterion (cost?) you are using to evaluate decisions. Then you need get into assumptions (e.g., known labor demand) and parameters (e.g., hiring costs, wages, ...). $\endgroup$
    – prubin
    Sep 30, 2019 at 20:11
  • $\begingroup$ As others have said: It's not really clear whether you are asking "is this optimization or simulation?" or "how do I model this problem?" or "what is the optimal headcount for this specific instance?" $\endgroup$ Sep 30, 2019 at 23:09

1 Answer 1


If you want to find the number of workers that you need for the job to be done while the hiring cost and available hours differ from full-time work to part-time work and on the other hand you want to minimize the cost, that is exactly an optimization problem with the following specifications:

  1. Objective function: will be the summation of all hiring costs. We want to minimize this value.
  2. Constraint on available time:
    • each part-time worker can not exceed the 20 hours available working time.
    • Full-time workers can not work more than 40 hours

I think there should be also some constraints in the model related to the number of hours that is necessary for the job to be done, some budget limitations and etc.

If you put more details in your question, I believe it will be easier for answerers to help you in the modeling step.

  • 1
    $\begingroup$ Agreed. Btw, one thing to consider in these planning scenarios is uncertainty: you don't want to hire just enough people, because if somebody gets sick, pregnant or the retention rate is lower than expected, you are in trouble. If you don't have any data, you could eyeball this, however any sort of data (especially if it is "big") can really help you make more informed decisions by quantifying the uncertainty. $\endgroup$
    – Richard
    Oct 1, 2019 at 8:07

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