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I am working on a workforce scheduling problem where we want to come up with an intelligent way to identify a set of shift candidates that is just enough to cover all labor demand but also flexible enough to avoid over coverages and adheres to worker preferences. So we have decided to use historical shifts data to predict such set. But it's not just a prediction problem; in addition to predicting the well suited candidates we need to get a smallest such set that covers the labor demand while adhering to other constraints. So was thinking of using the JANOS framework discussed in this paper https://arxiv.org/abs/1911.09461. While formulating it as per this paper, I could only use the prediction output as the decision vars but not the features. My formulation looks like this:

Minimize Sum(y_i)

s.t.

y_i = f(X) (X is the features vector)

Sum(c_ij*y_i) = D_j (c_ij indicates if y_i qualifies for demand D_j)

y_i: binary variable (prediction output from a ML model)

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  • $\begingroup$ It's not clear what the question here is. $\endgroup$
    – prubin
    Dec 28, 2023 at 16:31
  • $\begingroup$ If I use the ML model prediction output only as decision variables for the MIP, it changes the formulation from the one discussed in JANOS paper. So I won't be able to use Gurobi-ML that is based on JANOS and expects both feature vector and prediction output as input to the MIP. $\endgroup$
    – SDC
    Dec 28, 2023 at 17:43

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