{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

4120_lecture18-F10

# 4120_lecture18-F10 - Computational Methods for Management...

This preview shows pages 1–10. Sign up to view the full content.

Computational Methods for Management and Economics Carla Gomes Lecture 18 Reading: Section 11.1-11.3 of text book.

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

View Full Document
Outline Introduction to Integer Programming
Examples of Applications of Binary Variables Making “yes-or-no” type decisions Build a factory? Manufacture a product? Do a project? Assign a person to a task? Logical constraints Alternative constraints Conditional constraints Representing non-linear functions Fixed Charge Problem If a product is produced, must incur a fixed setup cost. If a warehouse is operated, must incur a fixed cost. Piecewise linear representation Diseconomies of scale Approximation of nonlinear functions Set-covering, and set partitioning Make a set of assignments that “cover” a set of requirements. Partition a set into subsets meeting given requirements

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

View Full Document
StockCompany Example Capital Budgeting Allocation Problem StockCompany is considering 6 investments. The cash required from each investment as well as the NPV of the investment is given next. The cash available for the investments is \$14,000. Stockco wants to maximize its NPV. What is the optimal strategy? An investment can be selected or not. One cannot select a fraction of an investment.
Data for the StockCompany Problem Investment 1 2 3 4 5 6 Cash Required (1000s) \$5 \$7 \$4 \$3 \$4 \$6 NPV added (1000s) \$16 \$22 \$12 \$8 \$11 \$19 Investment budget = \$14,000

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

View Full Document
Integer Programming Formulation Max 16x 1 + 22x 2 + 12x 3 + 8x 4 + 11x 5 + 19x 6 1 0 , if we invest in i 1,. ..,6, , else i x = = What are the decision variables? Objective and Constraints?
Capital Budgeting Allocation Problem (one resource) Knapsack Problem Why is a problem with the characteristics of the previous problem called the Knapsack Problem? It is an abstraction, considering the simple problem: A hiker trying to fill her knapsack to maximum total value. Each item she considers taking with her has a certain value and a certain weight. An overall weight limitation gives the single constraint. Practical applications: Project selection and capital budgeting allocation problems Storing a warehouse to maximum value given the indivisibility of goods and space limitations Sub-problem of other problems e.g., generation of columns for a given model in the course of optimization – cutting stock problem (beyond the scope of this course)

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

View Full Document
The previous constraints represent “economic indivisibilities”, either a project is selected, or it is not. There is no selecting of a fraction of a project. Similarly, integer variables can model logical requirements (e.g., if stock 2 is selected, then so is stock 1.)
How to model “logical” constraints Exactly 3 stocks are selected. If stock 2 is selected, then so is stock 1.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 41

4120_lecture18-F10 - Computational Methods for Management...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online