EMSE_1b

EMSE_1b - EMSE 154 - 254: Applied Optimization Modeling...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
1 EMSE 154 - 254: Applied Optimization Modeling Lecture notes #1 Applied Optimization Modeling EMSE 154-254 EMSE 154 254 Hern á n Abeledo Fall 2008 1 EMSE 154 - 254: Applied Optimization Modeling Lecture notes #1 Today: Introduction to optimization modeling • Diet Problem • Financial Portfolios • Shift Scheduling • The modeling and optimization process • Blending problems 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 EMSE 154 - 254: Applied Optimization Modeling Lecture notes #1 Optimization Models: Diet Problem 3 EMSE 154 - 254: Applied Optimization Modeling Lecture notes #1 Diet Problem: Low Cost Satisfying Diet We need to buy food for one day. We want to guarantee that 100% of the recommended vitamin intakes are covered at a minimum cost. Code Name Cost / Packet B Beef $3.19 Ck Chicken $2.59 F Fish $2.29 4 H Ham $2.89 MC Macaroni $1.89 ML Meat Loaf $1.99 S Spaghetti $1.99 T Turkey $2.49
Background image of page 2
3 EMSE 154 - 254: Applied Optimization Modeling Lecture notes #1 Vitamin Contents % of daily vitamin requirements provided by each frozen dinner A CB 1 B 2 Beef 60 20 10 15 Chicken 8 0 20 20 Fish 8 1 01 51 0 Ham 40 40 35 10 5 Macaroni 15 35 15 15 Meat Loaf 70 30 15 15 Spaghetti 25 50 25 15 Turkey 60 20 15 10 EMSE 154 - 254: Applied Optimization Modeling Lecture notes #1 Optimization model components Decision variables: Quantities under our control: how many packages to buy. Parameters (data): Quantities not under our control: cost of packages, nutrient contents. Objective : minimize the dollars spent. 6 Constraints: satisfy vitamin requirements.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 EMSE 154 - 254: Applied Optimization Modeling Lecture notes #1 Formulation = Let packages of food to buy. i xi ++ + +++ + + + + + ++≥ + + min 3.19 2.59 2.29 2,89 1.89 1.99 1.99 2.49 subject to: 60 8 8 40 15 70 25 60 100 20 10 40 35 30 50 20 100 10 20 15 35 15 15 25 15 BC KFHM CM LST KF H M C M L S T BF HM LS xx xxx x x x x x x x xxxx x x + + 100 15 20 10 10 15 15 15 10 100 T x 7 0 for all i An optimization problem where the objective is a linear function and all the constraints are linear inequalities or equations is a linear program (LP). EMSE 154 - 254: Applied Optimization Modeling Lecture notes #1 Divisibility assumption of linear programs + + min 3.19 2.59 2.29 2,89 1.89 1.99 1.99 2.49 subject to: x + + + + + + 60 8 8 40 15 70 25 60 100 20 10 40 35 30 50 20 100 10 20 15 35 15 15 25 15 H M C M L S T x x x x x x x x + + 100 15 20 10 10 15 15 15 10 100 for all T i x • Decision variables can take fractional values. 8 Decision variables can take fractional values. • We need to determine if fractional values make sense for the problem that we are trying to solve. • Trade-off: model accuracy vs. solvability.
Background image of page 4
5 EMSE 154 - 254: Applied Optimization Modeling Lecture notes #1 Portfolio problem: description An investor is evaluating ten different securities (“shares”) for his investment. The table shows the country of origin, risk category (R: high risk N: low) and expected return (ROI) for a period of one high risk, N: low), and expected return (ROI) for a period of one year. The investor specifies the following constraints: (1) the investor wants to invest all his available capital (2) at most 30% of capital can be in a single share; (3) at least 50% of capital must be invested in North America; 9 (4) at most 40% of capital can be invested in high risk shares.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 20

EMSE_1b - EMSE 154 - 254: Applied Optimization Modeling...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online