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Staffing problems – which require difficult decisions about the recruitment, training, layoffs, and scheduling of workers – are common across a broad range of manufacturing and service industries. In this example, you’ll learn how to model and solve a complex staffing problem by creating an optimal multi-period operation plan that minimizes the total number of layoffs and costs.

More information on this type of model can be found in example #5 of the fifth edition of Model Building in Mathematical Programming by H. Paul Williams on pages 256 – 257 and 303 – 304.

This modeling example is at the advanced level, where we assume that you know Python and the Gurobi Python API and that you have advanced knowledge of building mathematical optimization models. Typically, the objective function and/or constraints of these examples are complex or require advanced features of the Gurobi Python API.

Access the Jupyter Notebook Modeling Example

Click on the button below to access the example in Google Colab, which is a free, online Jupyter Notebook environment that allows you to write and execute Python code through your browser. 

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How to Run the Jupyter Notebook Modeling Example

  • To run the example the first time, choose “Runtime” and then click “Run all”.
  • All the cells in the Jupyter Notebook will be executed.
  • The example will install the gurobipy package, which includes a limited Gurobi license that allows you to solve small models.
  • You can also modify and re-run individual cells.
  • For subsequent runs, choose “Runtime” and click “on “Restart and run all”.
  • The Gurobi Optimizer will find the optimal solution of the modeling example.

Check out the Colab Getting Started Guide for full details on how to use Colab Notebooks as well as create your own.

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