Factory Planning 1: What to Make, On What Machines, and When

Constraints

The following constraints are used in this example:

  • bounds on decision variables

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

    \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 \Argument{num\_ machines\_ per\_ period[machine\_ type,period]} \end{align*}

  • for $\text {product} \in \text {PRODUCTS and period} \in \text {PERIODS}$,

    \begin{align*} & \quad \text {(if period} - 1 \in \text {PERIODS, then }\Variable{Store[product,period}-1\Variable{]};\text {else } 0)\\ & + \Variable{Make[product,period]} \\ & =\Variable{Sell[product,period]} + \Variable{Store[product,period]} \end{align*}