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Part 5 Mixed Integer Programming

Part 5 Mixed Integer Programming. 5.1 Introduction. Classification. Example 1: A Production Planning Problem. Example 1: MILP Formulation. Example 2: Minimum Number of Exchangers in HEN – MILP obtained by modifying the transportation model.

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Part 5 Mixed Integer Programming

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  1. Part 5 Mixed Integer Programming 5.1 Introduction

  2. Classification

  3. Example 1: A Production Planning Problem

  4. Example 1: MILP Formulation

  5. Example 2: Minimum Number of Exchangers in HEN– MILP obtained by modifying the transportation model

  6. Application – Minimum Utility Consumption Rates and Pinch Points Cerda, J., and Westerberg, A. W., “Synthesizing Heat Exchanger Networks Having Restricted Stream/Stream Matches Using Transportation Formulation,” Chemical Engineering Science, 38, 10, pp. 1723 – 1740 (1983).

  7. Definitions

  8. Transportation Formulation

  9. Cost Coefficients

  10. Additional Constraints

  11. Solution

  12. 5.2 Mixed Integer Linear Programming 5.2.1 Branch-and-Bound Algorithm

  13. Branch-and-Bound Algorithm

  14. Step 1: Solve the LP problem by assumingall variables are positive real numbers (Problem LP-1)

  15. Step 2: LP-1 is branched into 2 new problems

  16. No further branching needed!

  17. Step 3: LP-3 is branched into 2 new problems

  18. Computation Steps

  19. Example

  20. Node 0

  21. Node 1 Node 2

  22. Node 3 Node 4 3. Infeasible →fathomed

  23. Node 6 Node 5 3. Infeasible, fathomed

  24. 8 7 Node 7 Node 8

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