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

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

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