Decision Analysis Lecture 1

1
Decision Analysis - Lecture 1

• Course Overview
• Expectations and Assessment
• Case Preparation
• Karma Computers
• Introduction to Linear Programming

2
Contact Info

• Dr Jennifer George (Jenny)
• Office 119
• Phone [phone]
• Email j.george_at_mbs.edu
• Class web page www.mbs.edu/da/

3
Course Overview

• Topics
• Linear Programming
• Queueing and Simulation
• Decision Analysis and Risk

4
Course Overview

• Modelling steps
• Problem Recognition
• Formulation
• Solution
• Sensitivity Analysis
• Implementation

5
Expectations

• Come to class prepared
• Notify if late or absent
• Switch off mobile phones/beepers
• Spend about 6 hours outside class per week
• Pull your weight in group work
• Important to keep up with the topics (do
  numerical exercises in texts on your own)

6
Expectations

• Ask questions/talk to me early in course about
  any problems
• I will work hard to make this course valuable and
  interesting for you
• Feedback sheets in back of course reader

7
Assessment

• Assignment 15
• Midterm 30
• Final 40
• Participation 15

8
Assignment

• Groups of 3 or 4
• Please complete and hand in the survey sheet in
  course reader
• Describe a problem and give a solution for a
  topic that we cover in class, i.e. LP, queue,
  simulation or decision analysis/risk
• 1500 words plus exhibits

9
Test and Exam

• Midterm - 1.5 hours in class. Covers linear
  programming
• Final - 2 hours at end of term. Covers everything
  after linear programming

10
Participation

• Each class marked out of 4.
• Absent 0 or 2 if you have reason that school
  accepts for special consideration.

11
Case Preparation

• Case Preparation sheets in course reader
• Learning with Cases on reserve in library
• Short Cycle Process (10-15 minutes)
• Long Cycle Process (30-60 minutes)
• Small Group Discussion (15-20 minutes)

12
Karma Computers

• Suppose new disk drives are now being
  manufactured that will be assembled on slightly
  different chassis. Karma wants to make the
  maximum profit possible by using up its old
  inventory.
• How many deluxe and standard model computers
  should Karma produce?

13
General problem features

• Objective
• what is your aim?
• Variables
• what can you control?
• Constraints
• what are your limitations?
• (you cant have an infinite amount of a good
  thing)

14
Karma Computers

• Objective
• Variables
• Constraints

15
Karma Computers

• Variables
• Objective
• Constraints

16
Linear Programming

• Formulation
• objective, variables, constraints
• objective and constraints must be linear
• Solution
• graphical (if only two variables) or spreadsheet
• Sensitivity Analysis
• Implementation

17
Karma Computers

• In pairs, try to draw the equations for the Karma
  problem on a piece of graph paper
• What is the best solution?
• Is this what you expected?
• Why or why not?

18
Karma Computers
Deluxe
Standard
19
Deluxe
50
30
Standard
20
60
20
Solution
21
What can go wrong?

• No feasible solution
• there is no feasible region
• ? constraints are too restrictive/incompatible
• Unbounded
• keep pushing the profit line up and up to
  infinity
• ? a constraint is missing (you cant have an
  infinite amount of a good thing)

22
Sensitivity Analysis

• What if...?
• Profit on deluxe computers went up to 450?
• An extra 20 disk drives are suddenly found?
• An extra 10 deluxe chassis are suddenly found?
• Work in pairs, using your graphs, to answer these
  questions

23
Profit for deluxe rises to 450
Deluxe
50
30
Standard
20
60
24
Find an extra 20 disk drives
25
Find an extra 10 deluxe chassis
Deluxe
50
30
Standard
20
60
26
Constraints

• Constraints are either slack or binding.
• Deluxe Chassis inventory is a slack constraint.
• another deluxe chassis would not change the
  solution.
• so one more deluxe chassis is worthless to Karma
• Standard Chassis and Disk Drive inventory are
  binding constraints.
• there would be value in having more of these

27
Shadow Prices

• How much would you pay for an extra unit of
  inventory? This is the shadow price.
• Shadow price of an extra dlx chassis 0 (We saw
  this when we added an extra 10 deluxe chassis.
  The solution did not change.)
• Shadow price of an extra std chassis 100
• Shadow price of an extra disk drive 200 (We
  saw this when we added an extra 20 drives. The
  profit went up 4000.)

28
Changes in profit contribution

• How much would the profit contributions of each
  type of computer have to change before the
  solution changed?
• Otherwise, production will be the same

29
More than two variables

• With more than two variables cant solve
  graphically.
• Same ideas
• constraints form a feasible region
• move objective function until get best solution.

30
George Dantzig

• In the 1950s, Dantzig had a brilliant idea.
• Realised that the solution for a linear program
  would always be at a corner point. (Why?)
• Developed a method called the Simplex method that
  only searched through corner points instead of
  through the whole feasible region.

31
Computer solutions

• Simplex method - basis of computer solution
  methods (can also do it by hand)
• Dantzig did his first few major applications on
  one of the 3 or 4 computers that then existed in
  the world
• Hundreds of times that power now available in
  Excel on every desktop

32
Limitations

• Dantzig versus Von Neumann
• Linear Programs
• are deterministic (no chance involved)
• are linear (always same proportions, same profit
  contributions or costs regardless of quantities
  and so on)
• require costs/profits and constraints to be known
  and well defined

33
LP - when is it a good choice?
34
Next lecture

• Read text (either BHB or AWZ)
• Formulate Ebel Mining Company. Identify
  objective, variables and constraints (in words).
  Write them out in algebra.
• Try problems 2-6 and 2-7 from BHB (provided in
  course reader). We will go over these in class
  next week.