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BUS 2420Management Science

Instructor: Vincent WS Chow

Office: WLB 818

Ext: 7582 E-mail: vwschow@hkbu.edu.hk

URL: http://ww.hkbu.edu.hk/~vwschow

Office hours: (to p2)

mailto:vwschow@hkbu.edu.hkhttp://ww.hkbu.edu.hk/~vwschowhttp://ww.hkbu.edu.hk/~vwschowmailto:vwschow@hkbu.edu.hk

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2* Office hours

(subject outline)

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Mon

dayTues

dayWednes

dayThurs

dayFriday

8:30

9:30

10:30

11:30

12:30

13:30

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14:30

* *15:30 ISEM BUS

16:30

17:30

17:30-

18:30 * *

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Subject outlineSubject outline (see handout)

Textbook: Bernard W. Taylor III, Introduction to Management Science, 10th

Edition, Prentice Hall, 2010

Grading: Topics:

Refer to handout

Tutorials

Start from 3rd hr of 3rd week lecture Typically, we assign few questions in each lecture

and then taken them up for discussion in the nextweek session.

How you are being graded?

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Grading:

Assignments 15% Most likely be1-3 assignments

Group Memberships (refer to our web site)

Class Participation 15% Tutorial performance

Test 20% One mid-term exam

Examination 50% One final exam

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How you are being graded?

Students will award marks if they showtheir works (by submission!) in the tutorial sessions

Students are thus strongly encouraged tobring their works to show in tutorials orprepare materials for presentation ..

Note: you may like to approach me later to

see how we could improve this process ofgrading!

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Lecture 1Introduction to Management Science

What is Management Science?

How to apply Management Sciencetechnique?

Types of Management ScienceModels/techniques

We start with the most popularManagement Science technique:

Linear Programming

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Have we seen or used then before?

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Management Science

Management science uses a scientificapproach to solving managementproblems.

It is used in a variety of organizations tosolve many different types of problems.

It encompasses a logical mathematical

approach to problem solving. History of Management Science (to p8)

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History of Management Science

It was originated from two sources: Operational Research Management Information Systems

It is thus more emphasizing on the analysis ofsolution applications than learning their on howmodels were derived.

Other names for management science:quantitative methods, quantitative analysis anddecision sciences.

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Steps in applying ManagementScience teniques

(1)

(2)

(3)

(4)

(5)

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In practice, thisstep is critical

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Steps

1. Observation Identification of a problem that exists inthe system or organisation.

2. Definition of the Problem Problem must be clearlyand consistently defined showing its boundaries andinteraction with the objectives of the organisation.

3. Model Construction Development of the functionalmathematical relationships that describe the decisionvariables, objective function and constraints of theproblem.

4. Model Solution Models solved using managementscience techniques.

5. Model Implementation Actual use of the model or itssolution.

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Models to be consideredin this subject

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* Topics that will cover in this subject!

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Characteristics of Modeling Techniques

Linear mathematical programming: clear objective;restrictions on resources and requirements;parameters known with certainty.

Probabilistic techniques: results contain uncertainty.

Network techniques: model often formulated asdiagram; deterministic or probabilistic.

Forecasting and inventory analysis techniques:probabilistic and deterministic methods in demandforecasting and inventory control.

Other techniques: variety of deterministic andprobabilistic methods for specific types of problems.

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Linear Programming

Or denote as LP

Overview of LP

How does LP look like?

Components of LP

General LP format

Example 1: Maximizing Z

Example 2: Minimizing Z

We will talk about more LP formulationsand its solutions in next lecture

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Linear Programming - An Overview

Objectives of business firms frequently include maximizing profitor minimizing costs, or denote as Max Z or Min Z

Linear programming is an analysis technique in which linearalgebraic relationshipsrepresent a firms decisions given abusiness objective and resource constraints.

Steps in application:

1- Identify problem as solvable by linear programming.

2- Formulate a mathematical model of managerial problems.

3- Solve the model.

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4 Components of LP

1. Decision variables: mathematical symbolsrepresenting levels of activity of a firm.

2. Objective function: a linear mathematicalrelationship describing an objective of the firm,

in terms of decision variables, that is maximizedor minimized

3. Constraints: restrictions placed on the firm bythe operating environment stated in linear

relationships of the decision variables.4. Parameters: numerical coefficients andconstants used in the objective function andconstraint equations.

5. Non-negativity (or necessary) constraints

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Example of Decision Variables

Decision Variables: It is used to represent decision problem to be

solve

Let,

x1=number of bowls to produce/dayx2= number of mugs to produce/day

How of them are needed is depended on thenature of the problem!

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Objective Functions

It is used to represent the type ofproblems we are to solve

In this subject, we only emphasize to either

1. Maximizing a profit margin or

2. Minimizing a production cost

Example:

An Objective functionmaximize Z = $40x1 + 50x2

Refer to how much we made for each x is produced

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Constraints

It is also referred to resource constraints

They are to indicate how much resourcesmade available in a firm

Example:

Resource Constraints:

1x1 + 2x2 40 hours of labor

4x1 + 3x2 120 pounds of clay

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Non-negativity constraints

We assumed that all decision variablesare carried out positive values (why?)

Example:

Non-negativity Constraints:

x10; x2 0

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Sample of LP

Let xi be denoted as xi product to be produced, and

i = 1, 2

or

Let x1 be numbers of product x1 to be produced

and x2 be numbers of product 21 to be produced

Maximize Z=$40x1 + 50x2

subject to

1x1 + 2x2 40 hours of labor4x2 + 3x2 120 pounds of clay

x1, x2 0

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Objectivefunction

Constraints

Decisionvariables

Cost

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Max/Min Z : cixi

subject to

aij xij (=, , ) bj, j = 1,., n

xij 0, for i=1,,m, j=1,,n

General LP format

It means there are total of m decision variablesn resource constraints

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General steps for LP formulation(to p22)

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Steps for LP formulation

Step 1: define decision variables

Step 2: define the objective function

Step 3: state all the resource constraints Step 4: define non-negativity constraints

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Example 1: Max Problem

A Maximisation Model Example The Beaver Creek Pottery Company produces bowls and

mugs. The two primary resources used are special pottery clay andskilled labour. The two products have the following resource

requirements for production and profit per item produced (that is, themodel parameters).

Resource available: 40 hours of labour per day and 120 pounds ofclay per day. How many bowls and mugs should be produced tomaximizing profits give these labour resources?

LP formulation

Resource Requirements

Product Labor(hr/unit)

Clay(lb/unit)

Profit($/unit)

Bowl 1 4 40

Mug 2 3 50

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Max LP problem

Step 1: define decision variables

Let x1=number of bowls to produce/day

x2= number of mugs to produce/day

Step 2: define the objective function

maximize Z = $40x1 + 50x2

where Z= profit per day

Step 3: state all the resource constraints

1x1 + 2x2 40 hours of labor ( resource constraint 1)

4x1 + 3x2 120 pounds of clay (resource constraint 2)

Step 4: define non-negativity constraints

x10; x2 0

Complete Linear Programming Model:

\ maximize Z=$40x1 + 50x2

subject to

1x1 + 2x2 40

4x2 + 3x2 120

x1, x2 0

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Example 2: Min Z

A farmer is preparing to plant a crop in the spring. There are two brands offertilizer to choose from, Supper-gro and Crop-quick. Each brand yields aspecific amount of nitrogen and phosphate, as follows:

The farmers field requires at least 16 pounds of nitrogen and 24 pounds of

phosphate. Super-gro costs $6 per bag and Crop-quick costs $3 per bag.The farmer wants to know how many bags of each brand to purchase inorder to minimize the total cost of fertilizing.

LP formulation

Chemical Contribution

Brand

Nitrogen

(lb/bag)

Phosphate

(lb/bag)

Super-gro 2 4

Crop-quick 4 3

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Min ZStep 1: define their decision variables

x1 number of bags of Super-gro,

x2 number of bags of Crop-quick.Step 2: define the objective function

Minimise Z 6x1 3x2Step 3: state all the resource constraints

2x1 4x2 16, (resource 1)

4x1 3x2 24 (resource 2)Step 4: define the non-negativity constraints

x1 0, x2 0

Overall LP: Minimise Z 6x1 3x2

subject to

2x1 4x2 16,

4x1 3x2 24,

x1 0, x2 0

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