1. 5.2 Mixed Integer Linear Programming
5.2.3 Logic Inference

2. Reaction Path Synthesis
Assume that it is desired to manufacture acetone. The raw materials available are ethyl alcohol (CH3CH2OH) and methane (CH4). Assume that all the inorganic chemicals and catalysts required are available except for CrO3 and O3. At the preliminary design phase, determine if it is feasible to produce acetone from given raw materials. If yes, specify a reaction path.

4. Step 1: Express all reactions in the form of propositional logic

5. Step 2: Convert to conjunctive normal form

6. Example
Each term within brackets is called a clause.

7. Example

8. Step 3: Solve MILP Binary variable for the chemical to be synthesized
Chemical u can always be synthesized if Z=1 after solving the IP problem.
All possible reactions
Binary variables for the available raw materials and catalysts
(1 if available, 0 if not)

10. Logical OR, Exclusive OR and Logical AND

11. Implication and Equivalence

12. Selection between two (or more) mutually exclusive scenarios
If select reactor 1, then pressure P must lie between 5 and 10 atmospheres.
If select reactor 2, then pressure P must lie between 20 and 30 atmospheres.

13. Linear Disjunctions

14. “Big-M” Constraints

15. Convex Hull Formulation

16. Another Example

17. Example 3: Minimum Number of Exchangers in HEN (MILP)