Refinery Optimization: How to Run an Oil Refinery

Constraints

The following constraints are used in this example:

bounds on variables
for $i \in \text {NODES} \setminus \{ \text {‘source’},\text {‘sink’}\}$ ,

$\sum _{(i,j) \in \text {ARCS}} \Variable{Flow[i,j]} = \sum _{(j,i) \in \text {ARCS}} \Argument{arc\_ mult[j,i]} \cdot \Variable{Flow[j,i]}$
for $(i,j) \in \text {ARCS such that}\ i \in \text {CRUDES}$ ,

$\Variable{Flow[i,j]} = \Variable{CrudeDistilled[i]}$
for $(i,j) \in \text {ARCS such that}\ i \in \text {CRACKED}\mr{\_ }\text {OILS}$ ,

$\Variable{Flow[i,j]} = \Variable{OilCracked[i]}$
for $\text {petrol} \in \text {PETROLS}$ ,

$\frac{\sum \limits _{(i,\text {petrol}) \in \text {ARCS}} \Argument{octane[i]} \cdot \Argument{arc\_ mult[i,petrol]} \cdot \Variable{Flow[i,petrol]}}{\sum \limits _{(i,\text {petrol}) \in \text {ARCS}} \Argument{arc\_ mult[i,petrol]} \cdot \Variable{Flow[i,petrol]}} \ge \Argument{octane\_ lb[petrol]}$
$\displaystyle { \frac{\sum \limits _{(i,\text {‘jet}\mr{\_ }\text {fuel’}) \in \text {ARCS}} \Argument{vapour\_ pressure[i]} \cdot \Argument{arc\_ mult[i,`jet\_ fuel']} \cdot \Variable{Flow[i,`jet\_ fuel']}}{\sum _{(i,\text {‘jet}\mr{\_ }\text {fuel’}) \in \text {ARCS}} \Argument{arc\_ mult[i,`jet\_ fuel']} \cdot \Variable{Flow[i,`jet\_ fuel']}} \le \Argument{vapour\_ pressure\_ ub} }$
for $(i,\text {‘fuel}\mr{\_ }\text {oil’}) \in \text {ARCS}$ ,

$\frac{\Variable{Flow[i,`fuel\_ oil']}}{\sum \limits _{(j,\text {‘fuel}\mr{\_ }\text {oil’}) \in \text {ARCS}} \Variable{Flow[j,`fuel\_ oil']}} = \frac{\Argument{fuel\_ oil\_ coefficient[i]}}{\Argument{sum\_ fuel\_ oil\_ coefficient}}$
$\displaystyle { \sum _{i \in \text {CRUDES}} \Variable{CrudeDistilled[i]} \le \Argument{crude\_ total\_ ub} }$
$\displaystyle { \sum _{\substack{(i,\text {‘reformed}\mr{\_ }\text {gasoline’}) \in \text {ARCS}:\\ \text {index(}i\text {,‘naphtha’)} > 0}} \Variable{Flow[i,`reformed\_ gasoline']} \le \Argument{naphtha\_ ub} }$
$\displaystyle { \sum _{(i,\text {‘cracked}\mr{\_ }\text {oil’}) \in \text {ARCS}} \Variable{Flow[i,`cracked\_ oil']} \le \Argument{cracked\_ oil\_ ub} }$
$\displaystyle { \Argument{lube\_ oil\_ lb} \le \Variable{Flow[`lube\_ oil',`sink']} \le \Argument{lube\_ oil\_ ub} }$
$\displaystyle { \frac{\sum \limits _{(\text {‘premium}\mr{\_ }\text {petrol’},j) \in \text {ARCS}} \Variable{Flow[`premium\_ petrol',j]}}{\sum \limits _{(\text {‘regular}\mr{\_ }\text {petrol’},j) \in \text {ARCS}} \Variable{Flow[`regular\_ petrol',j]}} \ge \Argument{premium\_ ratio} }$