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How LINGO diagnoses solution issues LINDO Systems lindo

LSL3-1. How LINGO diagnoses solution issues LINDO Systems www.lindo.com. Optimization Problems in General, Solution Issues. LSL3-2. When we try to solve a problem , Possible Outcomes: Infeasible Feasible Optimum(Finite/Infinite)

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How LINGO diagnoses solution issues LINDO Systems lindo

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  1. LSL3-1 How LINGO diagnoses solution issues LINDO Systems www.lindo.com

  2. Optimization Problems in General, Solution Issues LSL3-2 When we try to solve a problem, Possible Outcomes: Infeasible Feasible Optimum(Finite/Infinite) Unbounded

  3. LSL3-3 Formulations with Anomalies 1) Unbounded, Clearly a mistake.     2) Infeasible, Could be a mistake, but could be a misunderstanding of what is simultaneously possible.     3)  Multiple or Alternative Optima Quite common, but not good. God’s way of telling us to put more detail into the objective function. Real people are not indifferent between alternatives.

  4. LSL3-4 Example #1: Unique Solution • Unique, bounded objective function value z*=104 • Nonempty, bounded feasible region 4

  5. LSL3-5 LINGO Model

  6. LSL3-6 Example #2: Unique Solution • Unique, bounded objective function value z*=5.33 • Nonempty, unbounded feasible region 6

  7. LINGO Model LSL3-7

  8. LSL3-8 Example #3: No Solutions: Infeasible • First two inequalities are inconsistentempty feasible region • z* does not exist 8

  9. LINGO Model LSL3-9 max=x1; x1+x2<=2; 2*x1+2*x2>=8;

  10. LSL3-10 Example #4: No Solution: Unbound • Unbounded objective function value • Unbounded feasible region • Note: unbounded objective function value unbounded feasible region, but the reverse is not true (see the next example) 10

  11. LINGO Model LSL3-11 max = -x1+x2; x1<=2;

  12. LSL3-12 Example #5: Infinite # of Solutions • Infinite # of solutions along the edge between x1 and x2 • Nonempty, bounded feasible region 12

  13. LINGO Model LSL3-13

  14. Thank you for your attention. For more information, please visit www.m-focus.co.th or Call 02-513-9892

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