COB 291. An Introduction to Management Science Dr. Mike Busing College of Business, James Madison University. Agenda. Syllabus Review Algebra Review Quiz Introduction to Models/Modeling Introduction to Linear Programming (LP) Graphical Solution to LP. Announcements.
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An Introduction to Management Science
Dr. Mike Busing
College of Business, James Madison University
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Used to solve problems where there is
no uncertainty about the future.
The GOAL of LP is to identify the decision that gives
me the best outcome.
However, there are millions of decision possibilities
LP is a searching mechanism that sifts through all the
possible (feasible) solutions to find the “best” solution.
LP is a very efficient search technique
BMW must produce cars such that they satisfy the
constraints of the production plan, the marketing plan,
the finance plan, etc. In addition, this plan should
generate the most profit, given the constraints of the
various functional business areas.
“x” million 3 series
“x” million 5 series
“x” million 7 series
“x” million 8 series
“x” million Z series
“x” million SUV
Advertising: Limited amount of money to invest
in different advertising mediums
“x” million dollars in radio spots
“x” million dollars in television spots
“x” million dollars in newspaper ads
“x” million dollars in magazine ads
“x” million dollars in billboards
Finance: As a mutual fund manager, you must
take all the money and invest it in various
“x” million dollars in stocks
“x” million dollars in fixed income bonds
“x” million dollars in money funds
“x” million dollars in annuities
“x” million dollars in cash
Seuss’s Sandwich Shop sells two types of sandwiches:
green eggs and ham (GEH) and ham and cheese (HC).
A green eggs and ham sandwich consists of 2 slices
bread, 1 green egg, and 1 slice ham. It takes an
employee 3 minutes to make one of these sandwiches.
A ham and cheese sandwich consists of 2 slices bread,
2 slices ham, and 1 slice cheese. It takes 2 minutes
to make a ham and cheese sandwich. The Sandwich
Shop presently has available 400 slices of bread, 80
slices of cheese, 120 green eggs and 200 slices of ham.
The shop also has one employee scheduled for 7 hours
to make all of the sandwiches. If a green egg and ham
sandwich sells for $5 and a ham and cheese sandwich sells
for $4, how many of each type should be prepared to maximize
sales revenue? (Assume that demand is great enough to ensure
that all sandwiches made will be sold.)
We will figure out how to represent the English sentences
in the problem via convenient mathematical equations. This
is the most important part of linear programming.
3 steps in all LP formulations:
1st: Decision Variables
- why am I solving this problem?
- what are the unknown quantities in the problem?
- the minimum number of decision variables is 2
and the maximum is several hundred thousand in
3 steps in all LP formulations:
2nd: Objective Function
- what is the motivation behind this problem?
(e.g., maximize profit or minimize cost?)
- issues that force decision variables from taking
on -¥ to +¥ values.
- no restriction on number of constraints.
- non-negativity is extremely important.
So why do we call it “Linear” Programming?
1. Identify the objective function, z.
2. Identify the constraints.
3. Identify what we mean by “feasible solution”
4. Identify the “optimal solution”
5. Identify the “binding constraints”
GRAPHICAL SOLUTION TO PROBLEM