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

bounds on variables

for $i \in \text {INDUSTRIES}$ ,

$\Variable{StaticProduction[i]} = \Argument{demand[i]} + \sum _{j \in \text {INDUSTRIES}} \Argument{production\_ coeff[i,j]} \cdot \Variable{StaticProduction[j]}$

for $i \in \text {INDUSTRIES}$ and $\text {year} \in \{ 1, \dots , \Argument{num\_ years}+1\}$ ,

$\Variable{ProductiveCapacity[i,year]} = \Argument{init\_ productive\_ capacity[i]} + \sum _{y=2}^\text {year} \Variable{ExtraCapacity[i,y]}$

for $i \in \text {INDUSTRIES}$ and $\text {year} \in \text {YEARS0}$ ,

$\displaystyle$	$\displaystyle \quad \Variable{Stock[i,year]} + \Variable{Production[i,year]}$
$\displaystyle$	$\displaystyle = (\text {if year}\ \in \text {YEARS then}\ \Argument{demand[i]}\ \text {else}\ 0)$
$\displaystyle$	$\displaystyle + \sum _{j \in \text {INDUSTRIES}} \Argument{production\_ coeff[i,j]} \cdot \Variable{Production[j,year}+1\Variable{]}$
$\displaystyle$	$\displaystyle + \sum _{j \in \text {INDUSTRIES}} \Argument{productive\_ capacity\_ coeff[i,j]} \cdot \Variable{ExtraCapacity[j,year}+2\Variable{]}$
$\displaystyle$	$\displaystyle + \Variable{Stock[i,year}+1\Variable{]}$

for $\text {year} \in \{ 1, \dots , \Argument{num\_ years}+1\}$ ,

$\displaystyle$	$\displaystyle \quad \sum _{j \in \text {INDUSTRIES}} \Argument{production\_ coeff[`manpower,j]} \cdot \Variable{Production[j,year]}$
$\displaystyle$	$\displaystyle + \sum _{j \in \text {INDUSTRIES}} \Argument{productive\_ capacity\_ coeff[`manpower,j]} \cdot \Variable{ExtraCapacity[j,year}+1\Variable{]}$
$\displaystyle$	$\displaystyle \le \Argument{manpower\_ capacity}$

for $i \in \text {INDUSTRIES}$ and $\text {year} \in \{ 1, \dots , \Argument{num\_ years}+1\}$ ,

$\Variable{Production[i,year]} \le \Variable{ProductiveCapacity[i,year]}$