Lecture aims to familiarize the subject of Management Science. It starts with a question and then attempts to describe why the subject is so important for decision making. Then it explain introductory concepts of linear programming. It explain formulation of Linear Programming Problem (LPP) using examples.

1. Dr. Kishore Morya
(Do I REALLY Have to Know This Stuff?)
An Introduction to Management
Science/Operations Research

2. Problem Solving
Problem solving is a process of identifying a
difference between the actual and desired
state of affairs and then taking action to
resolve the difference
Problem should be important enough to justify
cost, time, and efforts of careful analysis

3. Steps in Problem Solving
• Identify and define the problem
• Determine the set of alternative solutions
• Determine the criterion or criteria that will used to
evaluate the alternatives
• Evaluate the alternatives
• Choose an alternative
• Implement the skeleton alternative
• Evaluate the results to determine whether a
satisfactory solution has been obtained

4. Decision Making
Decision Making is the term generally associated
with the first five steps of the problems
solving process
First step is to identify and define the problem
Decision Making ends with the choosing of an
alternative, which the act of making decision

5. Example
• Assume that you want to get employed. You
like a position that will lead to a satisfying
career.
• Suppose that your job research has resulted in
offers from companies in
- Rochester – New York
- Dallas – Texas
- Greensboro – North Carolina
- Pittsburgh - Pennsylvania

6. Alternatives for your decision problems
• Accept the position in Rochester
• Accept the position in Dallas
• Accept the position in Greensboro
• Accept the position in Pittsburgh

7. Determining the Criteria
• Starting Salary
• Potential of Advancement
• Location of the Job
One criterion – Single-Criterion Decision Problems
More than one criterion – Multi-criteria Decision
Problems

8. Evaluate Each of the Alternatives
Alternatives Starting Salary Potential for
Advancement
Job Location
Rochester $38500 Average Average
Dallas $36000 Excellent Good
Greensboro $36000 Good Excellent
Pittsburgh $37000 Average Good
You are now ready to make choice!
Are you?

9. The Choice is Difficult
The criteria are probably not all equally
important, and no alternative is “best” with
regards to all criteria
If you select any choice, let it be alternative 3
Alternative 3 thus referred to as the decision

10. Quantitative Analysis and Decision Making
Prob-
• Define the Problem
• Identify the Alternatives
-lem
• Determine the criteria
• Evaluate the Alternatives
Sol-
• Choose an Alternative
-vi
• Implement the Decision
• Evaluate the Results
-ng
• Results are according to expectation, stop the process
• Otherwise go back to the first stage
Decision Making
Decision

11. Quantitative analysis and Decision Making
Define
the
problem
Identify
the
alternati
ves
Make the
Decision
Summary
and
Evaluation
Quantitative
Analysis
Qualitative
Analysis
Determin
e the
Criteria
Structuring the problem
Analysing the problem

12. Model Development
• Iconic Model
- Physical replicas of real model, a scale model of an
airplane is a representation of a real airplane
• Analog Model
- Do not have the physical appearance as the object
being modeled
• Mathematical Model
- Representation of a problem by a system of
symbols and mathematical relationships or
expressions

13. Model…
• Objective Function
P = 10x
x represents the quantity sold
$10 is the profit per unit sold
P is the total profit
• Constraints
- 5 hours are required to produce each unit
- 40 hours of production time is available
Production Time constraint is given by
5x ≤ 40

14. Complete Mathematical Model
Maximize P = 10x
s. t.
5x ≤ 40 constraints
x ≥ 0

15. Model of Cost, Revenue, Profit,
• Cost and Volume Model
C(x) = 3000 + 2x
x = production volume in units
C(x) = total cost of producing x units
• Revenue and Volume Model
R(x) = 5x
x = sales volume in units
R(x) = total revenue associated with selling x
units
• Profit and Volume Model
P(x) = R(x) – C(x)
= 5x – (3000 + 2x) = - 3000 + 3x

16. Management Science Techniques
1. Linear Programming
2. Decision Analysis
3. Forecasting
4. Stock Control
5. Simulation
6. Network Modelling
7. Waiting Line or Queuing Models
8. Goal Programming
9. Dynamic Programming
10.Markov Process Models

17. Linear Programming
Linear Programming is a problem solving approach
developed to help managers make decisions
e.g.
GE Capital uses Linear Programming to help
determine optimal lease structuring.
Marathon Oil Company uses Linear Programming
for Gasoline blending and to evaluate the
economics of new terminal or pipelines

18. Situations where LP can be used
• A manufacturer wants to develop a production
schedule and an inventory policy that will satisfy
sales demand in future periods. Ideally, the
schedule and policy will enable company to satisfy
demand and at the time minimize the total
production and inventory costs
• A financial analyst must select an investment
portfolio from a variety of stock and bond
investment alternatives. The analyst would like to
establish the portfolio that maximizes the return
on investment

19. • A marketing manager wants to determine how
best to allocate a fixed advertising budget among
alternative advertising media such as radio,
television, newspaper, and magazine. The
manager would like to determine the media mix
that maximizes advertising effectiveness.
• A company has warehouses in number of
locations throughout Unites States. For a set of
customer demand, the company would like to
determine how much each warehouses should
ship to each customer so that transportation
costs are minimized.

20. Commonality
• Maximizing
• Minimizing
Some quantity
Objective of LP is to Maximize or Minimize some
quantity.

21. Maximizing
• Par, Inc. is a small manufacturer of golf
equipment and supplies.
• Management has decided to move in to the
market for medium and high priced golf bags
• Par’s distributor is enthusiastic about the new
product line and has agreed to buy all the golf
bags Par produces over the next three months.
After a thorough investigation of the steps
involved in manufacturing a golf bag, managers
determined that each golf bag produced will
require the following operations

22. Par, Inc.
• Cutting and Dying the Material
• Sewing
• Finishing (inserting umbrella holder, club
separators, etc)
• Inspection and Packaging

23. Production Requirements per golf bag
Department Production time (Hours) Total Time
Available
Standard Bag Deluxe Bag (Hours)
Cutting and Dying 7/10 1 630
Sewing ½ 5/6 600
Finishing 1 2/3 708
Inspection and Packaging 1/10 1/4 135
Profit Contribution
Standard Bag $10/unit
Deluxe Bag $ 9/unit

24. Problem Formulation
• Understanding the Problem Thoroughly
• Describe the Objective
• Describe each constraint
- Constraint 1
- Constraint 2
- Constraint 3
- Constraint 4

25. • Define the decision variables
• Write the objective in terms of the decision
variables
• Write the constraint in terms of the decision
variables
Mathematical Statement of the Par, Inc.
Problem

26. Max 10S + 9D
subject to (s.t.)
7/10 S + 1 D ≤ 630
1/2 S + 5/6 D ≤ 600
1 S + 2/3 D≤ 708
1/10 S + 1/4 D ≤ 135
S, D ≥ 0

27. A Simple Minimization Problem
• M & D Chemicals produces Product A & Product B
that are sold to companies manufacturing both
soaps and laundry detergents. Based on an
analysis of current inventory levels and potential
demand for the coming month, M & D chemical
management specified that the combined
production for Product A and B must total at least
350 gallons.
Separately, a major customer’s order for 125
gallons of product A must also be satisfied

28. • Product A requires 2 hrs of processing time
per gallon and product B requires 1 hr of
processing time per gallon. For the coming
month, 600 hrs of processing time are
available.
• M & D’s objective is to satisfy these
requirements at a minimum total production
cost. Production costs are $2 per gallon for
product A and $3 per gallon for product B.

29. • Objective Function
Min. Z = 2x1 + 3x2
Constraints
s. t.
x1 ≥ 125 Customer Order’s Constraint
x1 + x2 ≥ 350 Production Constraint
2x1 + x2 ≤ 600 Processing Time Constraint
x1, x2 ≥ 0

30. • Infeasibility
No solution to the linear programming problem
satisfies all the constraints, including the non-negativity
conditions. Graphically, infeasibility means that a
feasible region does not exist; that is no points satisfy
all the conditions
• Unbounded
The solution to a maximizing linear programming
problem is unbounded if the value of the solution may
be made infinitely large without violating any of the
constraints. For a minimization problem, the solution is
unbounded if the value may be infinitely small.