ms lecture010 introduction to modeling sem2 2011

7/29/2019 MS Lecture010 Introduction to Modeling Sem2 2011

1/23

Introduction to Modeling

OPIM 101 Management Science


2/23

Semester 2 2011/20122

"We at Wealth Management Research UBS, we are economists analysts, sometimeseven a bit geeky, but generally we are all very enthusiastic football fans, so four yearsago, we thought why not apply the toolkit we have to analyze economies andapply it on to football and predict the World Cup winner, said Mr Thomas Kaegi,Head, Macroeconomic Research Asia Pacific UBS Wealth Management.

They applied pure quantitative analysis models to predict World Cup winners thesame statistical models that they normally use to predict market trends and makeinvestment decisions.

Who will win the next World Cup?


3/23

Semester 2 2011/20123

In the past, managers depended on intuition as the

primary vehicle for making decisions.

ManagementProblems Decision

intuition

QUESTION:

Is there a more systematic and optimal way to make thedecision?


4/23

Relating Our Intuition with Theory

Semester 2 2011/20124

Example:

Set A:

2 x chicken + fries + drinks = $2.95

Set B:

1 x chicken + 1 x fish + fries + drinks=$3.95

Set C:

1 x chicken + 4xshrimps + 1xfish + drinks=$5.95

Additional side dish:

1x chicken = $1.10

1x fish = $1.80

What is the most economical combination, assuming I want at least a 2 xchicken, 1 x fish and a drink? Lets suppose I want to go for at least a setmeal.


5/23

Relating Our Intuition with Theory

Semester 2 2011/20125

Combination 1:

Set A + 1 x fish = $2.95 + $1.80 = $4.75

Combination 2:

Set B + 1 x chicken = $3.95 + $1.10 = $5.05

Intuition: Go for Combination 1. Savings of $0.30.


6/23

Semester 2 2011/20126

ManagementProblems Decision

intuition

Analysis

Model

Results

Managers role

Management Scientists

role Interpretation of results


7/23

The Management Science Approach

Semester 2 2011/20127

Usually, the manager and management scientist are notthe same person.

Hence, a management scientist is responsible of not only

solving the problem, but explaining the benefits of thesolution.

Management science, also known as operations

research, quantitative methods, etc., involves aphilosophy of problem solving in a logical manner.


8/23

Semester 2 2011/20128

This direct decision-support use of models leads tobetter management decisions, because the manager must

address the following issues:

(a) what questions to ask(b) what alternatives to investigate

(c) where to focus attention


9/23

Applicability of Management Science

Semester 2 2011/20129

That is why you are learning Management Science.

There are now many computers and software tools available.

But the crucial first step is always to frame a management

situation as a mathematical model.

In this course you will be introduced to a variety of modelsalong with appropriate concepts.

Often, you will find these models to be overly-simplified ordifficult to apply to the real world.


10/23

Other uses

Semester 2 2011/201210

Solving suduko! Can be solved by integer programming. By solving it by hand, we are actually using our

intuition/experience to solve it.

- A skilled player will make better decisions based onexperience.


11/23

Back to Problem Formulation for the

most economical meal.

Semester 2 2011/201211

Problem: Choose the most economical combination withdrinks

Parameters: Cost of each set meal, side dish

Decision Variables:xa: number of set A

xb: number of set B

xc: number of set C

yc: number of additional chicken

yf: number of additional fish


12/23

Model

Min 2.95xa+ 3.95xb+ 5.95xc+ 1.10yc+ 1.80yf

s.t.

2xa + 1xb + 1xc+ 1yc 2 (chicken constraint)

1xb + 1xc+ 1yf 1 (fish constraint)

xa +xb + xc 1

(set meal constraint (only set meal comes with drinks))

xa,xb,xc,yc,yf 0

Semester 2 2011/2012 12


13/23

Questions

Is the model still valid if in constraint is changed

to =? What does this mean?

What does (xa,xb,xc,yc,yf)= (0,1,0,0,0) mean?

What if there is a promotion in set A which now gives

3 pieces of chicken for the same price?

Semester 2 2011/2012 13


14/23

Linear Programming: An Overview

Semester 2 2011/201214

Steps in application: Identify problem as solvable by linear programming.

Formulate a mathematical model of the unstructured problem.

Solve the model.

Implementation


15/23

Model Components: D.O.C.

Semester 2 2011/201215

Decision variables - mathematical symbols representing levels ofactivity of a firm.

Objective function - a linear mathematical relationship describing anobjective of the firm, in terms of decision variables - this function is to be

maximized or minimized.

Constraintsrequirements or restrictions placed on the firm by theoperating environment, stated in linear relationships of the decision

variables.


16/23

Model Components

Semester 2 2011/201216

Parameters - numerical coefficients and constants usedin the objective function and constraints.


17/23

Summary of Model Formulation

Steps: D.O.C.

Semester 2 2011/201217

Step 1 : Clearly define the Decision variables-very important. Spend more time on it.

Step 2 : Construct the Objective function

Step 3 : Formulate the Constraints


18/23

Practice: Taylor 10th Edition Chapter 2, Qn 2

Semester 2 2011/201218

A company produces two products that are processed on aassembly line with 100 available hours. Each product requires 10hours on the assembly line. The profit for product 1 is $6 per unitand profit for product 2 is $4 per unit.

Formulate a linear programming model for the problem.


19/23

PracticeEconomical Meal

Semester 2 2011/201219

Set A: 2 x chicken + fries + drinks = $2.95

Set B: 1 x chicken + 1 x fish + fries + drinks=$3.95

Set C: 1 x chicken + 4xshrimps + 1xfish + drinks=$5.95

Additional side dish:

1x chicken = $1.10

1x fish = $1.80

Additional drink: 1 x drink = $1.50

What is the most economical combination, assuming I want at least a

2 x chicken, 1 x fish, a drink?

Formulate a model to solve it.


20/23

Summary

Semester 2 2011/201220

An LP problem (or simply LP) is an optimization problem

where :

1. We maximize (or minimize) a linear function (called theobjective function) of the decision variables.

2. The values of the decision variables must satisfy a set ofconstraints. Each constraint must be a linear equation ( = ) orlinear inequality ( or ).

3. A sign restriction is associated with each decision variable.For each variablex, either x 0 or x 0orxmay beunrestricted in sign


21/23

Semester 2 2011/201221

Note:By convention, constraints are written such that all the

decision variables are on the LHS, while the constant is

on the RHS.

So far, we have only learn how to model the problem.We will learn how to solve in the next lecture.


22/23

Practice: Extension to Taylor 10th Edition Chapter

2, Qn 2

Semester 2 2011/201222

a) A company produces two products that are processed on twoassembly lines.

Line 1 has 100 available hours, and line 2 has 42 available hours.

Each product requires 10 hours on line 1, and on line 2, product 1

requires 7 hours and product 2 requires 3 hours.

The profit for product 1 is $6 per unit and profit for product 2 is $4per unit.

i) Formulate a linear programming model for the problem.

ii) Based on your model, what is a possible decision?


23/23

Practice: Taylor 10th Edition Chapter 2, Qn 3

Semester 2 2011/201223

The Munchies Cereal Company makes a cereal from several ingredients.

Two of the ingredients, oats and rice, provide vitamin A and B. The

company wants to know how many ounces of oats and rice it should

include in each box of cereal to meet the minimum requirements of 48

milligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost.

An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of

vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2milligrams of B. An ounce of oats costs $0.05, and an ounce of rice costs

$0.03.

Formulate a linear programming model for this problem.

ms lecture010 introduction to modeling sem2 2011

Documents