Constraints :: SAS/OR(R) 12.3 User's Guide: Mathematical Programming Examples

The following constraints are used in this example:

bounds on variables
for $\text {period} \in \text {PERIODS}$ and $\text {type} \in \text {TYPES}$ ,

$\Variable{Output[period,type]} = \Argument{min\_ level[type]} \cdot \Variable{NumWorking[period,type]} + \Variable{Excess[period,type]}$
for $\text {period} \in \text {PERIODS}$ ,

$\sum _{\text {type} \in \text {TYPES}} \Variable{Output[period,type]} \ge \Argument{demand[period]}$
for $\text {period} \in \text {PERIODS}$ ,

$\sum _{\text {type} \in \text {TYPES}} \Argument{max\_ level[type]} \cdot \Variable{NumWorking[period,type]} \ge (1 + \Argument{reserve}) \cdot \Argument{demand[period]}$
for $\text {period} \in \text {PERIODS}$ and $\text {type} \in \text {TYPES}$ ,

$\Variable{Excess[period,type]} \le (\Argument{max\_ level[type]} - \Argument{min\_ level[type]}) \cdot \Variable{NumWorking[period,type]}$

for $\text {period} \in \text {PERIODS}$ and $\text {type} \in \text {TYPES}$ ,

$\displaystyle \Variable{NumStartup[period,type]}$	$\displaystyle \ge \Variable{NumWorking[period,type]}$
$\displaystyle$	$\displaystyle - (\text {if period} - 1 \in \text {PERIODS, then \Variable{NumWorking[period}$-1,$\Variable{type]}};$
$\displaystyle$	$\displaystyle \quad \text {else \Variable{NumWorking[}$\|\text {PERIODS}\|$,\Variable{type]}})$