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IEOR 4004: Introduction to Operations Research Deterministic Models

IEOR 4004: Introduction to Operations Research Deterministic Models. January 22, 2014. Syllabus. 1 st homework is already available on Courseworks. 20% homework assignments 40% midterm 40% final exam Lectures Monday, Wednesday 7:10pm-8:25pm Recitations: Friday 12:30pm-2pm

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IEOR 4004: Introduction to Operations Research Deterministic Models

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  1. IEOR 4004: Introduction to Operations Research Deterministic Models January 22, 2014

  2. Syllabus 1st homework is already available on Courseworks • 20% homework assignments • 40% midterm • 40% final exam • Lectures Monday, Wednesday 7:10pm-8:25pm • Recitations: Friday 12:30pm-2pm • Instructor: JurajStacho (myself) • office hours: Tuesday 1pm-2pm • Teaching assistant (TA): ItaiFeigenbaum • office hours: Friday, after recitations 2:15pm-3:15pm

  3. Summary all parameters known goal is to minimize or maximize Goal of the course: Learn foundations of mathematical modeling of (deterministic) optimization problems • Linear programming – problem formulation(2 weeks) • Solving LPs – Simplex method (4 weeks) • Network problems (2 weeks) • Integer Programming (1.5 weeks) • Dynamic Programming (1.5 weeks) • Non-linear Programming (1 week time permitting) • 2 weeks reserved for review (1 before midterm)

  4. What this course is/is not about Not about: • coding (computer programming) • engineering (heuristics, trade-offs, best practice) • stochastic problems (uncertainty, chance) • solving problems onreal-world data • modeling risk, financial models, stock markets, strategic planning Is about: • mathematical modeling (problem abstraction, simplification, model selection, solution) • algorithms • foundations of optimization • deterministic models • example real-world models • typical model: medium-term production/financial planning/scheduling

  5. Mathematical modeling • Simplified (idealized) formulation • Limitations • Only as good as our assumptions/input data • Cannot make predictions beyond the assumptions We need more maps

  6. Mathematical modeling Problem simplification Model formulation Model Algorithm selection Numerical calculation Problem Solution Interpretation Sensitivity analysis

  7. Model selection • trade-off betweenand accuracy (predictive power) model simplicity (being able to solve it) Predictivepower (quality of prediction) Low High Complex Model Simple Hard (if not impossible) to compute a solution (lifetime of the universe) Easy to compute a solution (seconds) Solving Linear programming Network algorithms Integer programming Dynamic programming

  8. Modeling optimization problems • Optimization problem • decisions • goal (objective) • constraints • Mathematical model • decision variables • objective function • constraint equations

  9. Formulating an optimization problem Linear program Linear objective • Decision variables • Objective • Constraints • Domains x1, x2, x3, x4 x1 (1 − 2x2)2 Minimize + 2x2 + 3x3 (x1)2 + (x2)2 + (x3)2 + (x4)2 ≤ 2 x1 − 2x2 + x3 −3x4≤ 1 − x1 + 3x2 + 2x3 + x4≥ − 2 − 2x1x3 = 1 Linear constraints x3 in {0,1} x4 in [0,1] x1≥ 0 x2 ≠ 0.5 Sign restriction

  10. Mathematical modeling • Deterministic= values known with certainty • Stochastic= involves chance, uncertainty • Linear, non-linear, convex, semi-definite

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