SEG7490 Project and Technology Management

1
SEG7490 Project and Technology Management

• Part I Project Management
• Overview.
• Project screening and selection.
• Multiple-criteria methods for evaluation.
• Project structuring
• Project scheduling
• Budgeting and resource management.
• Life-cycle costing.
• Project control.
• Computer support for project management.
• Part II Technology Management
• Strategic and operational considerations of
  technology
• Forecasting of technology
• Management of RD projects

2
Chapter 3. Multiple-criteria Methods for
Project Selection

• 3.1 Project selection by using utility
  functions
• 3.2 Project selection under multiple criteria

3
3.2 Project selection under multiple criteria

• In this section, we discuss the extension of
  utility theory to situations in which more than
  one attribute (criterion) affects the decision
  makers preferences and attitude toward risk.
• When more than one attribute affects a decision
  makers preferences, her utility function is
  called a multi-attribute utility function.
• In the following we restrict our discussion to
  multi-attribute functions with only two
  attributes.

4
3.2 Project selection under multiple criteria

• Suppose a decision makers preferences and
  attitude toward risk depend on two attributes,
  and let
• xilevel of attribute i, i1,2.
• Then,
• u(x1, x2) utility associated with
  level x1 and x2.
• How can we find a utility function u(x1, x2) such
  that choosing a lottery or alternative that
  maximizes the expected value of u(x1, x2) will
  yield a decision consistent with the decision
  makers preferences and attitude toward risk ?

5
3.2 Project selection under multiple criteria

• In general, determination of u(x1, x2) (or, in
  case of n attributes, determination of u(x1, x2,
  , xn) is a difficult matter.
• However, under certain conditions, the assessment
  of a utility function can be greatly simplified.

6
3.2.1 Properties of multi-attribute utility
functions

• Definition - Attribute 1 is utility independent
  (ui) of attribute 2 if preferences for lotteries
  involving different levels of attribute 1 do not
  depend on the level of attributes 2.

7
3.2.1 Properties of multi-attribute utility
functions

• Example - The Wivco Toy Co. is to introduce a
  new product (a gobot) and must determine the
  price to charge for each gobot. Two factors
  (market share and profits) will affect Wivcos
  pricing decision. Let
• x1 Wivcos market share
• x2 Wivcos profits (million of dollars)

8
3.2.1 Properties of multi-attribute utility
functions

• Suppose that Wivco is indifferent between

1/2
10, 5
L1
1
L1
1/2
16, 5
30, 5

• If attribute 1 (market share) is ui of
  attribute 2 (profit),
• Wivco would also be indifferent between

1/2
10, 20
L1
1
L1
1/2
16, 20
30, 20
9
3.2.1 Properties of multi-attribute utility
functions

• In short, if market share is ui of profit, then
  for any level of profits, a 1/2 chance at a 10
  market share and a 1/2 chance at a 30 market
  share has a certainty equivalent of a 16 market
  share.

10
3.2.1 Properties of multi-attribute utility
functions

• Definition - If attribute 1 is ui of attribute
  2, and attribute 2 is ui of attribute 1, then
  attributes 1 and 2 are mutually utility
  independent (mui).

11
3.2.1 Properties of multi-attribute utility
functions

• Theorem 3.2.1 -- Attributes 1 and 2 are mui if
  and only if the decision makers utility function
  u(x1, x2) is a multi-linear utility function of
  the following form
• u(x1, x2)k1u1(x1) k2u2(x2)
  k3u1(x1)u2(x2),
• where k1, k2 and k3 are constants and u1(x1)
  and u2(x2) are utility functions of x1 and x2 ,
  respectively.

12
3.2.1 Properties of multi-attribute utility
functions

• Let x1(best) or x2(best) be the most favorable
  level of attribute 1 or 2 that can occur. Also,
  let x1(worst) or x2(worst) be the least favorable
  level of attribute 1 or 2 that can occur.
• Definition - A decision makers utility function
  exhibits additive independence if the decision
  maker is indifferent between

x1(best), x2(worst)
1/2
1/2
x1(best), x2(best)
L1
L2
1/2
1/2
x1(worst), x2(worst)
x1(worst), x2(best)
13
3.2.1 Properties of multi-attribute utility
functions

• Corollary 3.2.1 -- If attributes 1 and 2 are mui
  and the decision makers utility function
  exhibits additive independence, then k30 and
• u(x1, x2)k1u1(x1) k2u2(x2).

14
3.2.1 Properties of multi-attribute utility
functions

• Justification
• We can scale u1(x1) and u2(x2) so that
  u1(x1(best))1, u1(x1(worst))0, u2(x2(best))1,
  and u2(x2(worst))0.
• So u(x1, x2)k1u1(x1) k2u2(x2) k3u1(x1)u2(x2)
  implies
• u(x1(best), x2(best)) k1 k2 k3,
  u(x1(worst), x2(worst))0,
• u(x1(best), x2(worst)) k1,
  u(x1(worst), x2(best)) k2.
• Then additive independence implies that
• (1/2)(k1 k2 k3)(1/2)(0)(1/2) k1 (1/2) k2
• This gives us k3 0.

15
3.2.2 Assessment of multi-attribute utility
functions

• We have known that, if attributes 1 and 2 are
  mui, then
• u(x1, x2)k1u1(x1) k2u2(x2)
  k3u1(x1)u2(x2).
• Now the question is, how can we determine u1(x1),
  u2(x2), k1, k2 and k3, so as to determine u(x1,
  x2) ?
• To find u1(x1), u2(x2), we can use the technique
  for assess single-attribute utility functions as
  introduced in 3.1.
• To find k1, k2 and k3, we begin by rescaling
  u1(x1), u2(x2) and u(x1, x2) so that
• u(x1(best), x2(best))1, u(x1(worst),
  x2(worst))0, u1(x1(best))1,
  u1(x1(worst))0,
• u2 (x1(best))1,
  u2(x2(worst))0.

16
3.2.2 Assessment of multi-attribute utility
functions

• Now, u(x1, x2)k1u1(x1) k2u2(x2)
  k3u1(x1)u2(x2) yields
• u(x1(best), x2(worst)) k1(1) k2(0)
  k3(0) k1
• Thus, k1 can be determined from the fact that the
  decision maker is indifferent between

k1
x1(best), x2(best)
1
x1(best), x2(worst)
L1
L2
1- k1
x1(worst), x2(worst)
17
3.2.2 Assessment of multi-attribute utility
functions

• Similarly, u(x1, x2)k1u1(x1) k2u2(x2)
  k3u1(x1)u2(x2) yields
• u(x1(worst), x2(best)) k1(0) k2(1)
  k3(0) k2
• Thus, k2 can be determined from the fact that the
  decision maker is indifferent between

k2
x1(best), x2(best)
1
x1(worst), x2(best)
L1
L2
1- k2
x1(worst), x2(worst)
18
3.2.2 Assessment of multi-attribute utility
functions

• To determine k3, observe
• u(x1(best), x2(best)) u1(x1(best))u2
  (x1(best))1.
• So, from u(x1, x2)k1u1(x1) k2u2(x2)
  k3u1(x1)u2(x2), we have
• 1 u(x1(best), x2(best)) k1(1) k2(1)
  k3(1) k1 k2 k3
• Thus, k3 1- k1 - k2
• Of course, if the decision makers utility
  function exhibits additive independence, then k3
  0.

19
3.2.2 Assessment of multi-attribute utility
functions

• The procedure to assess a multi-attribute utility
  function
• Step 1. Check if attributes 1 and 2 are mui. If
  yes, go to Step 2. (If no, see Keeney and
  Raiffa, Decision Making with Multiple Objective,
  Wiley, Section 5.7, 1976).
• Step 2. Check for additive independence.
• Step 3. Assess u1(x1) and u2(x2).
• Step 4. Determine k1, k2 and (if there is no
  additive independence) k3.
• Step 5. Check if the assessed utility function is
  really consistent with the decision makers
  preferences. To do this, set up several
  lotteries and use the expected utility of each
  lottery to rank the lotteries. If the assessed
  assessed utility function is consistent with the
  decision makers preferences, the ranking under
  the assessed utility function should be closely
  assemble the decision makers ranking of
  lotteries.

20
3.2.2 Assessment of multi-attribute utility
functions

• Example 1a - Assume the current year is 1998.
  Fruit Computer Company is certain that during the
  next year 1999 its market share will be between
  10 and 50 percent of the microcomputer market.
  Fruit is also sure that its profits during 1999
  will be between 5 million and 30 million.
  Assess Fruits multi-attribute utility function
  u(x1, x2), where
• x1 Fruits market share during 1999
• x2 Fruits profits during 1999 (in
  millions of dollars)

21
3.2.2 Assessment of multi-attribute utility
functions

• Step 1 - We begin by checking for mui. To
  check if attribute 1 is ui of attribute 2, we set
  x2 at different levels, and see whether the
  lottery w.r.t. x1 is affected or not. Similar
  experiments can be conducted to check if
  attribute 2 is ui of attribute 1. Assume that we
  have found that in this example attributes 1 and
  2 are (at least approximately) mui.

22
3.2.2 Assessment of multi-attribute utility
functions

• Step 2 - To check for additive independence. We
  must determine if Fruit is indifferent between

1/2
1/2
50, 30
50, 5
L1
L2
1/2
1/2
10, 5
10, 30

• Suppose that Fruit is not indifferent between
  these
• lotteries. Then Fruits utility function will
  not exhibit
• additive independence.
• We now know that u(x1, x2) takes the following
  form
• u(x1, x2)k1u1(x1) k2u2(x2)
  k3u1(x1)u2(x2).

23
3.2.2 Assessment of multi-attribute utility
functions

• Step 3 - We now assess u1(x1) and u2(x2).
  Suppose we obtain the results as shown in the
  following figures.

24
(No Transcript)
25
(No Transcript)
26
3.2.2 Assessment of multi-attribute utility
functions

• Step 4 - Determine k1, k2 and k3. To find k1, we
  ask Fruit to determine the number k1 so that the
  following lotteries are indifferent

k1
50, 30
1
50, 5
L1
L2
1- k1
10,5
Suppose that for k10.6, Fruit is indifferent
between the two lotteries.
27
3.2.2 Assessment of multi-attribute utility
functions

• Similarly, to find k2, we ask Fruit to determine
  the number k2 so that the following lotteries are
  indifferent

k2
50, 30
1
10, 30
L1
L2
1- k2
10,5
Suppose that for k20.5, Fruit is indifferent
between the two lotteries.
28
3.2.2 Assessment of multi-attribute utility
functions

• Thus, k3 1- k1 - k2 1-0.6-0.5-0.1.
  Consequently,
• u(x1, x2)0.6u1(x1) 0.5u2(x2) -0.1
  u1(x1)u2(x2),
• where u1(x1) and u2(x2) are sketched as in
  the figures above.
• This completes the development of Fruits utility
  function.

29
3.2.3 Application of multi-attribute utility
functions

• Example 1b - Suppose that Fruit must determine
  whether to mount a small or large advertising
  campaign during the coming year. The management
  of Fruit believes there is a 1/2 probability that
  its main rival, CSL Computers, will mount a small
  TV ad campaign and a 1/2 probability that CSL
  will mount a large TV ad campaign. Find the
  optimal strategy for Fruit.

30
3.2.3 Application of multi-attribute utility
functions

• At the end of the year Fruits market share and
  profits (in million dollars) will be as shown
  below
• ---------------------------------------------
  ------------------------
• CSL chooses
• Fruit chooses small TV ad
  large TV ad
• ----------------------------------------------
  ------------------------
• small ad campaign 25, 16
  15, 12
• large ad campaign 35, 8
  25, 10
• ----------------------------------------------
  -------------------------

31
3.2.3 Application of multi-attribute utility
functions

• Fruit must determine which of the following
  lotteries should be chosen

1/2
25, 16
Small ad campaign
1/2
15,12
1/2
35, 8
Large ad campaign
1/2
25,10
32
3.2.3 Application of multi-attribute utility
functions

• First, from the figures of u1(x1) and u2(x2), we
  find
• u1(15) 0.125, u1(25) 0.375, u1(35)
  0.625,
• u2(8) 0.45, u2(10) 0.53, u2(12) 0.58,
  u2(16) 0.70.
• So,
• u(25, 16)0.6(.375)0.5(.7)-0.1(.375)(.7)0.
  549
• u(15, 12)0.6(.125)0.5(.58)-0.1(.125)(.58)
  0.358
• u(35, 8)0.6(.625)0.5(.45)-0.1(.625)(.45)0
  .572
• u(25, 10)0.6(.375)0.5(.53)-0.1(.375)(.53)
  0.470
• Then, E(U for small campaign)(1/2)(.549)(1/2)(
  .358)0.454
• E(U for large campaign)(1/2)(.572)
  (1/2)(.470)0.521
• Therefore, the optimal decision is Fruit should
  mount a large ad campaign.