Factory Planning 2: When Should Machines Be Down for Maintenance

Constraints

The following additional constraints are used in this example:

  • for $\mr{machine\_ type} \in \mr{MACHINE\_ TYPES~ and~ period} \in \mr{PERIODS}$,

    \begin{align*} & \quad \sum _{\text {product} \in \text {PRODUCTS}} \Argument{production\_ time[product,machine\_ type]} \cdot \Variable{Make[product,period]} \\ & \le \Argument{num\_ hours\_ per\_ period} \cdot \left(\Argument{num\_ machines[machine\_ type]} - \Variable{NumMachinesDown[machine\_ type,period]}\right) \end{align*}

  • for $\mr{machine\_ type} \in \mr{MACHINE\_ TYPES}$,

    \[ \sum _{\text {period} \in \text {PERIODS}} \Variable{NumMachinesDown[machine\_ type,period]} = \Argument{num\_ machines\_ needing\_ maintenance[machine\_ type]} \]