Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Linear programming mohsin 21, Lecture notes of Quantitative Techniques

University of Central Punjab (UCP)Quantitative Techniques

Best topic on liner programing

Typology: Lecture notes

2014/2015

Uploaded on 12/10/2015

mohsin_bin_latif
mohsin_bin_latif 🇵🇰

4

(3)

1 document

1 / 5

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Linear Programming
By: MOHSIN RAZA
K5F14MCOM0021
Contents
1. Introduction
2. History
3. Applications
4. Linear programming model
5. Example of Linear Programming Problems
6. Sensitivity analysis
Introduction
▲Linear Programming is a mathematical modeling technique used to determine a level of
operational activity in order to achieve an objective.
▲Mathematical programming is used to find the best or optimal solution to a problem that
requires a decision or set of decisions about how best to use a set of limited resources to
achieve a state goal of objectives.
Steps involved in mathematical programming
✓Conversion of stated problem into a mathematical model that abstracts all the
essential elements of the problem.
✓Exploration of different solutions of the problem.
✓Find out the most suitable or optimum solution.
Linear programming requires that all the mathematical functions in the model be
linear functions.
LP Model Formulation
♦Decision variables
pf3
pf4
pf5

Partial preview of the text

Download Linear programming mohsin 21 and more Lecture notes Quantitative Techniques in PDF only on Docsity!

Linear Programming

By: MOHSIN RAZA

K5F14MCOM

Contents

1. Introduction

2. History

3. Applications

4. Linear programming model

5. Example of Linear Programming Problems

6. Sensitivity analysis

Introduction

▲ Linear Programming is a mathematical modeling technique used to determine a level of operational activity in order to achieve an objective. ▲ Mathematical programming is used to find the best or optimal solution to a problem that requires a decision or set of decisions about how best to use a set of limited resources to achieve a state goal of objectives.

Steps involved in mathematical programming

✓ Conversion of stated problem into a mathematical model that abstracts all the essential elements of the problem. ✓ Exploration of different solutions of the problem.

✓ Find out the most suitable or optimum solution.

Linear programming requires that all the mathematical functions in the model be

linear functions.

LP Model Formulation

♦ Decision variables

  • mathematical symbols representing levels of activity of an operation

♦ Objective function

  • a linear relationship reflecting the objective of an operation
  • most frequent objective of business firms is to maximize profit
  • most frequent objective of individual operational units (such as a production or packaging department) is to minimize cost

♦ Constraint

  • a linear relationship representing a restriction on decision making

History of linear programming

▲ It started in 1947 when G. B. Dantzig design the “simplex method” for solving linear programming formulations of U.S. Air Force planning problems.

▲ It soon became clear that a surprisingly wide range of apparently unrelated problems in production management could be stated in linear programming terms and solved by the simplex method.

Applications

♦ The Importance of Linear Programming

A. Hospital management

B. Diet management

C. Manufacturing

D. Finance (investment)

E. Advertising

F. Agriculture

G. Business industry

♦ The Bullhay shah Dying Business Industries Production

Problem

▲ Bullhay shah manufactures two sulphur green combination of same Canvas:

  • X
  • X
  • 3X 1 + 4X 2 £ 2400 (Production Time)
  • X 1 + X 2 £ 700 (Total production)
  • X 1 - X 2 £ 350 (Mix)
  • Xj> = 0, j = 1,2 (Non negativity)
  • (^) The Graphical Analysis of Linear Programming

The set of all points that satisfy all the constraints of the model is

called a

FEASIBLE REGION

♦ Sensitivity Analysis of the Optimal Solution

  • Is the optimal solution sensitive to changes in input parameters?
  • Possible reasons for asking this question:
    • Parameter values used were only best estimates.
    • Dynamic environment may cause changes.
    • “What-if” analysis may provide economical and operational information.

♦ Sensitivity Analysis of Objective Function Coefficients.

✓ Range of Optimality

▲ The optimal solution will remain unchanged as long as

  • An objective function coefficient lies within its range of optimality
  • (^) There are no changes in any other input parameters.
  • The value of the objective function will change if the coefficient multiplies a variable whose value is nonzero.

Conclusion

A linear programming model can provide an insight and an intelligent solution to

the problem.

REFERENCES

  • www.math.ucla.edu/~tom/LP.pdf
  • www.sce.carleton.ca/faculty/chinneck/po/Chapter2.
  • www.markschulze.net/LinearProgramming.pdf
  • web.ntpu.edu.tw/~juang/ms/Ch02.
  • cmp.felk.cvut.cz/~hlavac/Public/.../Linear%20Programming