BUS 2420 Management Science

1
BUS 2420Management Science

• Instructor Vincent WS Chow
• Office WLB 818
• Ext 7582
• E-mail vwschow_at_hkbu.edu.hk
• URL http//ww.hkbu.edu.hk/vwschow
• Office hours

(to p2)
2

• Refer to my website

(to p3)
3
Subject outline

• Subject 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 next week session.
• How you are being graded?

(to p4)
(to p5)
(to p6)
(lecture)
4
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

(to p3)
5
How you are being graded?

• Students will award marks if they show their
  works (by submission!) in the tutorial sessions
• Students are thus strongly encouraged to bring
  their works to show in tutorials or prepare
  materials for presentation ..
• Note you may like to approach me later to see
  how we could improve this process of grading!

(to p3)
6
Lecture 1Introduction to Management Science

• What is Management Science?
• How to apply Management Science technique?
• Types of Management Science Models/techniques
• We start with the most popular Management Science
  technique
• Linear Programming

(to p7)
(to p9)
Have we seen or used then before?
(to p11)
(to p13)
7
Management Science

• Management science uses a scientific approach to
  solving management problems.
• It is used in a variety of organizations to solve
  many different types of problems.
• It encompasses a logical mathematical approach to
  problem solving.
• History of Management Science

(to p8)
(to p6)
8
History of Management Science

• It was originated from two sources
• Operational Research
• Management Information Systems
• It is thus more emphasizing on the analysis of
  solution applications than learning their on how
  models were derived.
• Other names for management science quantitative
  methods, quantitative analysis and decision
  sciences.

(to p7)
9
Steps in applying Management Science teniques
(to p10)
(1)
(2)
(3)
(4)
In practice, this step is critical
(to p6)
(5)
10
Steps

1. Observation Identification of a problem that
   exists in the system or organisation.
2. Definition of the Problem Problem must be
   clearly and consistently defined showing its
   boundaries and interaction with the objectives of
   the organisation.
3. Model Construction Development of the
   functional mathematical relationships that
   describe the decision variables, objective
   function and constraints of the problem.
4. Model Solution Models solved using management
   science techniques.
5. Model Implementation Actual use of the model or
   its solution.

(to p9)
11
Models to be consideredin this subject









Their Characteristics
(to p6)
(to p12)
Topics that will cover in this subject!
12
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 as
  diagram deterministic or probabilistic.
• Forecasting and inventory analysis techniques
  probabilistic and deterministic methods in demand
  forecasting and inventory control.
• Other techniques variety of deterministic and
  probabilistic methods for specific types of
  problems.

(to p11)
13
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 formulations and its
  solutions in next lecture

(to p14)
(to p20)
(to p15)
(to p21)
(to p23)
(to p25)
14
Linear Programming - An Overview

• Objectives of business firms frequently include
  maximizing profit or minimizing costs, or denote
  as Max Z or Min Z
• Linear programming is an analysis technique in
  which linear algebraic relationships represent a
  firms decisions given a business 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.

(to p13)
15
4 Components of LP

1. Decision variables mathematical symbols
   representing levels of activity of a firm.
2. Objective function a linear mathematical
   relationship describing an objective of the firm,
   in terms of decision variables, that is maximized
   or minimized
3. Constraints restrictions placed on the firm by
   the operating environment stated in linear
   relationships of the decision variables.
4. Parameters numerical coefficients and constants
   used in the objective function and constraint
   equations.
5. Non-negativity (or necessary) constraints

(to p16)
(to p17)
(to p18)
(to p19)
(to p13)
16
Example of Decision Variables

• Decision Variables
• It is used to represent decision problem to be
  solve
• Let,
• x1number of bowls to produce/day
• x2 number of mugs to produce/day
• How of them are needed is depended on the
  nature of the problem!

(to p15)
17
Objective Functions

• It is used to represent the type of problems we
  are to solve
• In this subject, we only emphasize to either
• Maximizing a profit margin or
• Minimizing a production cost
• Example
• An Objective function
• maximize Z 40x1 50x2

(to p15)
Refer to how much we made for each x is produced
18
Constraints

• It is also referred to resource constraints
• They are to indicate how much resources made
  available in a firm
• Example
• Resource Constraints
• 1x1 2x2 ? 40
  hours of labor
• 4x1 3x2 ? 120
  pounds of clay

(to p15)
19
Non-negativity constraints

• We assumed that all decision variables are
  carried out positive values (why?)
• Example
• Non-negativity Constraints
• x1?0 x2 ? 0

(to p15)
20
Sample of LP
Decision variables

• 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 Z40x1 50x2
• subject to
• 1x1 2x2 ? 40 hours of labor
• 4x2 3x2 ? 120 pounds of clay
• x1, x2 ? 0

Cost
Objective function
Constraints
(to p13)
21
General LP format
Max/Min Z S cixi subject to
S aij xij (, , ) bj , j
1,., n xij 0, for
i1,,m, j1,,n

(to p22)
General steps for LP formulation
It means there are total of m decision variables
n
resource constraints
(to p13)
22
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

(to p21)
23
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 and
  skilled labour. The two products have the
  following resource requirements for production
  and profit per item produced (that is, the model
  parameters).
• Resource available 40 hours of labour per day
  and 120 pounds of clay per day. How many bowls
  and mugs should be produced to maximizing profits
  give these labour resources?
• LP formulation

(to p24)
24
Max LP problem

• Step 1 define decision variables
• Let x1number 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
• x1?0 x2 ? 0
• Complete Linear Programming Model
• \ maximize Z40x1
  50x2
• subject to
• 1x1 2x2 ? 40
• 4x2 3x2 ? 120

(to p13)
25
Example 2 Min Z

• A farmer is preparing to plant a crop in the
  spring. There are two brands of fertilizer to
  choose from, Supper-gro and Crop-quick. Each
  brand yields a specific 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 in order to minimize the total
  cost of fertilizing.
• LP formulation

(to p26)
26
Min Z

• Step 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 ? 3x2
• Step 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

(to p13)