Mining: Which Pits to Work and When to Close Them Down

Constraints

The following constraints are used in this example:

  • bounds on variables

  • for $\text {year} \in \text {YEARS}$,

    \[ \Variable{ExtractedPerYear[year]} = \sum _{\text {mine} \in \text {MINES}} \Variable{Extract[mine,year]} \]

  • for $\text {mine} \in \text {MINES}$ and $\text {year} \in \text {YEARS}$,

    \[ \Variable{Extract[mine,year]} \le \Argument{Extract[mine,year].ub} \cdot \Variable{IsWorked[mine,year]} \]

  • for $\text {year} \in \text {YEARS}$,

    \[ \sum _{\text {mine} \in \text {MINES}} \Variable{IsWorked[mine,year]} \le \Argument{max\_ num\_ worked\_ per\_ year} \]

  • for $\text {mine} \in \text {MINES}$ and $\text {year} \in \text {YEARS}$,

    \[ \Variable{IsWorked[mine,year]} \le \Variable{IsOpen[mine,year]} \]

  • for $\text {mine} \in \text {MINES}$ and $\text {year} \in \text {YEARS} \setminus \{ 1\} $,

    \[ \Variable{IsOpen[mine,year]} \le \Variable{IsOpen[mine,year}-1\Variable{]} \]

  • for $\text {year} \in \text {YEARS}$,

    \[ \frac{\sum \limits _{\text {mine} \in \text {MINES}} \Argument{quality[mine]} \cdot \Variable{Extract[mine,year]}}{\Variable{ExtractedPerYear[year]}} = \Argument{quality\_ required[year]} \]