Download presentation

Presentation is loading. Please wait.

Published byDarien Lavell Modified over 2 years ago

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

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

3
Summary 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) all parameters known goal is to minimize or maximize

4
What this course is/is not about 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 Not about: coding (computer programming) engineering (heuristics, trade-offs, best practice) stochastic problems (uncertainty, chance) solving problems on real-world data modeling risk, financial models, stock markets, strategic planning

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 Model Problem simplification Model formulation Algorithm selection Numerical calculation Interpretation Sensitivity analysis

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

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 Decision variables Objective Constraints Domains x 1, x 2, x 3, x 4 2x 2 + 3x 3 x 1 − 2x 2 + x 3 − 3x 4 ≤ 1 − x 1 + 3x 2 + 2x 3 + x 4 ≥ − 2 x 1 ≥ 0 x 3 in {0,1} x 4 in [0,1] Linear constraints Linear constraints Sign restriction + x 1 (1 − 2x 2 ) 2 (x 1 ) 2 + (x 2 ) 2 + (x 3 ) 2 + (x 4 ) 2 ≤ 2 − 2x 1 x 3 = 1 Linear objective Linear objective x 2 ≠ 0.5 Minimize

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

Similar presentations

OK

ISE420 Algorithmic Operations Research Asst.Prof.Dr. Arslan M. Örnek Industrial Systems Engineering.

ISE420 Algorithmic Operations Research Asst.Prof.Dr. Arslan M. Örnek Industrial Systems Engineering.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on c language functions Ppt on switching devices and timers Ppt on network interface card Ppt on cross-sectional study design Ppt on target marketing Ppt on condition monitoring of transformer Ppt on history of atomic model Ppt on teacher's day Ppt on wireless power supply Ppt on environmental protection act