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

The following constraints are used in this example:

bounds on variables
for $d \in \text {DAYS}$ ,

$\sum _{i \in \text {NODES}} \Argument{requirement[i]} \cdot \Variable{UseNode[i,d]} \le \Argument{capacity}$
for $i \in \text {NODES}$ ,

$\sum _{d \in \text {DAYS}} \Variable{UseNode[i,d]} = \Argument{frequency[i]}$
for $k \in \text {NODES}$ and $d \in \text {DAYS}$ ,

$\sum _{(i,j) \in \text {EDGES}: k \in \{ i,j\} } \Variable{UseEdge[i,j,d]} = 2 \cdot \Variable{UseNode[k,d]}$
for $d \in \text {DAYS} \setminus \{ 1\}$ ,

$\sum _{i \in \text {NODES}} \Variable{UseNode[i,d]} \le \sum _{i \in \text {NODES}} \Variable{UseNode[i,d}-\Variable{1]}$
for $s \in \{ 1, \dots , \Argument{num\_ subtours}\}$ and $k \in \text {SUBTOUR[s]}$ and $d \in \text {DAYS}$ ,

$\sum _{\substack {i \in \text {NODES} \setminus \text {SUBTOUR[s]},\\ j \in \text {SUBTOUR[s]}:\\ (i,j) \in \text {EDGES}}} \Variable{UseEdge[i,j,d]} + \sum _{\substack {i \in \text {SUBTOUR[s]},\\ j \in \text {NODES} \setminus \text {SUBTOUR[s]}:\\ (i,j) \in \text {EDGES}}} \Variable{UseEdge[i,j,d]} \ge 2 \cdot \Variable{UseNode[k,d]}$