项目管理Project Mangement第2章

SEG5790 Project and TechnologyManagement•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 oftechnology–Forecasting of technology–Management of R&D projectsChapter 3. Multiple-criteria Methods forProject Selection§3.1 Project selection by using utility functions§3.2 Project selection under multiple criteria§3.1 Project selection by using utilityfunctions•Suppose you are asked to choose between two lotteries, L1 and L2, asfollows:• If you choose L1, you are guaranteed to get $10,000.• If you choose L2, your expected return is $15,000.• Which lottery would you like to choose ?L2L11/21/21$30,000$0$10,000§3.1 Project selection by using utilityfunctions• Although L2 has a larger expected return than L1, many people prefer L1 to L2.• The reason is, L1 offers the certainty to win.• In other words, we prefer L1 to L2, since L1 involves less risk than L2.L2L11/21$30,000$0$10,000How to measure the risk ?•Different people have different perception on risk.•Some people may be more risk averse, but some people may be more risk seeking.•How to measure the risk ? And how to evaluate and represent the degree of your acceptance to risk, if you are the decision maker ?•Your attitude toward risk will affect your decision to choose a project proposal.•Utility theory allows one to build his utility function to represent his attitude toward risk, and therefore to make the decision which he thinks right in situations involving uncertainties.Utility functions•Our goal is to determine a method that a person can use to choose between lotteries (alternatives) involving risks.•Suppose that she must choose to play L1 and L2 but not both.•We write– L1 i L2 if she is indifferent between L1 and L2.– L1 p L2 if she prefers L1 to L2.– L2 p L1 if she prefers L2 to L1.•We also say that L1 and L2 are equivalent lotteries, ifL1 i L2 .U (M )M M MU (M )U (M )(a ) Risk averse (b ) Risk seeker (c ) Risk neutral Utility functionsUtility functions•For a given lottery L=(p1, r1; p2, r2; …; p n, r n), define the expected utility of the lottery L, written E(U for L), byi=nE(U for L)= Σ p i u(r i).i=1•Fundamental Property ofUtility Function: Fundamental Property of Utility Function:Two lotteries are indifferent if they have the same expected utility.An approach to Generate utilityvalues1)Given three monetary values: M1, X, M2 (M1 < X < M2). Let u (M1) = 0, u (M2) = 1. Find u (X).2)Choose p so that the following two lotteries are indifferent :a. Get X with probability 1.b. Get M2 with probability p and M1 with probability (1-p ).Then u (X) = p . (Think about why ? )L2L1p 1-p1M2X M1§3.1 Project selection by using utilityfunctions•Example -- How to rank the following lotteries:L4L10.50.021-$10,000$0$10,000L31$00.98L20.5$500$30,000§3.1 Project selection by using utilityfunctions•The utility theory suggests to rank these lotteries as follows:–(1) Identify the most favorable ($30,000) and theleast favorable (-$10,000) outcomes that canoccur.–(2) For all possible outcomes r i (r1=$10,000,r2=500, and r3=$0), the decision maker is askedto determine a probability p i such that she isindifferent between:p i$30,0001r i1-p i-$10,000§3.1 Project selection by using utilityfunctionsSuppose that for r1=$10,000, the decision maker is indifferent between:0.90$30,0001$10,0000.10-$10,000§3.1 Project selection by using utilityfunctionsFor r2=$500, the decision maker is indifferent between:0.60$30,0001$00.40-$10,0000.62$30,0001$5000.38-$10,000For r3=$0, the decision maker is indifferent between :§3.1 Project selection by using utilityfunctionsTherefore, we can see:0.50$30,0001$10,0000.50L1L2”(i)0.90$30,0000.10-$10,000L1’0.50$30,0000.50$0L2$30,000-$10,0000.40.6(i)§3.1 Project selection by using utilityfunctions0.50$30,0000.50L2”-$10,000$30,0000.40.6 0.80$30,0000.20-$10,000L2’• • L’’ is a compound lottery.•It yields a chance of 0.5+0.5(0.6) =0.8 at $30,000,and a chance of 0.4(0.6)=0.2 at -$10,000. • Since L2 i L2” and L2” i L2’, we know L2 i L2’.(i)§3.1 Project selection by using utilityfunctions0.02$30,0000.98L4’’-$10,000-$10,0000.380.62 0.6076$30,0000.3924-$10,000L4’(i)1$0L30.60$30,0000.40L3’-$10,000(i)§3.1 Project selection by using utilityfunctions0.6076$30,0000.3924-$10,000L4’0.90$30,0000.10L1’-$10,0000.60$30,0000.40L3’-$10,0000.80$30,0000.20L2’-$10,000• We can see that L1’ p L2’ p L4’ p L3’.• Since L1 i L1’, L2 i L2’, L3 i L3’, and L4 i L4’ , we conclude that L1 p L2 p L4 p L3.§3.1 Project selection by using utilityfunctions•Generally, the utility of the reward r i , written u(r i ), is the number q i such that the decision maker isindifferent between the following two lotteries:Most favorable outcome11- q iLeast favorable outcomer iq i • That is, u(r i ) = q i .• The definition forces u(least favorable outcome)=0and u(most favorable outcome)=1.§3.1 Project selection by using utilityfunctions•So, for our possible payoffs of $30,000, -$10,000, $0, $500, and $10,000, we have: u($30,000)=1, and u(-$10,000)=0.•From 0.90$30,0001$10,0000.10-$10,000we have u($10,000)=0.90.§3.1 Project selection by using utilityfunctions•From:0.60$30,0001$00.40-$10,0000.62$30,0001$5000.38-$10,000• From :we have u($500)=0.62.we have u($0)=0.60§3.1 Project selection by using utilityfunctions•For a given lottery L=(p1, r1; p2, r2; …; p n, r n), define the expected utility of the lottery L, written E(U for L), byi=nE(U for L)= Σ p i u(r i).i=1• Thus, in our example,E(U for L1) = 1(0.9) =0.9E(U for L2) = 0.5(1) + 0.5(0.6) = 0.8E(U for L3) = 1(0.6) =0.6E(U for L4) = 0.02(0) + 0.98(0.62)=0.6076.§3.1 Project selection by using utilityfunctions•From the example above, we can see that:E(U for L)Most favorable outcomeLi’1- E(U for L)Least favorable outcome• So, we know Li p Lj, if E(U for Li) > E(U for Lj)§3.1 Project selection by using utilityfunctions•More specifically,Li p Lj, if and only if E(U for Li) > E(U for Lj)Lj p Li, if and only if E(U for Lj) > E(U for Li)Li i Lj, if and only if E(U for Li) = E(U for Lj)Estimating an individual‘s utilityfunction•(1) We begin by assuming that the least favorable outcome (say, -$10,000) has a utility zero and the most favorable outcome (say, $30,000) has a utility one.•(2) Next we identity the number x1/2 having u(x1/2)=1/2.To determine x1/2, we ask the decision maker (DM) for the number x1/2 that makes her indifferent between:1/2$30,0001x1/21/2-$10,000 Suppose the DM states that x1/2=-$3400.Estimating an individual‘s utilityfunction•(3) Using x1/2 and the least favorable outcome (-$10,000) as the possible outcomes, we can construct a lottery that can be used to determine x1/4 (that is, u(x1/4)=1/4). The point x1/4 must be such that the DM is indifferent between1/2x1/2=-$34001x1/41/2-$10,000Suppose the DM states that x1/4=-$8000. This gives another point on the DM’s utility function.Estimating an individual‘s utilityfunction•(4) We can now use x1/2 and the most favorable outcome ($30,000) as the possible outcomes to construct a lottery that yields x3/4 with u(x3/4)=3/4. Again, the point x4/4 must be such that the DM is indifferent between1/2$30,0001x3/41/2x1/2=-$3400Suppose the DM states that x3/4= $8000. This gives one more point on the DM’s utility function.Estimating an individual‘s utilityfunction•(5) Gradually, we have a number of points:(-$10,000,0), (x1/8, 1/8), (x1/4 , 1/4), …, ($30,000, 1).•(6) The DM’s utility function can be approximated by drawing a smooth curve joining these points. (See below for the example).Chapter 3. Multiple-criteria Methods forProject Selection§3.1 Project selection by using utility functions§3.2 Project selection under multiple criteria§3.2 Project selection under multiplecriteria•In this section, we discuss the extension of utility theory to situations in which more than one attribute (criterion) affects the decision maker’s preferences and attitude toward risk.•When more than one attribute affects a decision maker’s 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.§3.2 Project selection under multiplecriteria•Suppose a decision maker’s preferences and attitude toward risk depend on two attributes, and letx i=level of attribute i, i=1,2.•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 maker’s preferences and attitude toward risk ?§3.2 Project selection undermultiple criteria•In general, determination of u(x1,x2) (or, in case of n attributes, determination of u(x1,x2,…, x n) is a difficult matter.•However, under certain conditions, the assessment of a utility function can be greatly simplified.§3.2.1 Properties of multi-attributeutility 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.§3.2.1 Properties of multi-attributeutility 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 Wivco’s pricing decision. Let:x1 = Wivco’s market sharex2 = Wivco’s profits (million of dollars)§3.2.1 Properties of multi-attribute utilityfunctions •Suppose that Wivco is indifferentbetween: L11/230%, $20L1’11/216%, $2010%, $20• If attribute 1 (market share) is ui of attribute 2 (profit), Wivco would also be indifferent betweenL11/230%, $5L1’11/216%, $510%, $5§3.2.1 Properties of multi-attribute utilityfunctions•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.§3.2.1 Properties of multi-attributeutility 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).§3.2.1 Properties of multi-attributeutility functions•Theorem 3.2.1 -- Attributes 1 and 2 are mui if and only if the decision maker’s 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 andu1(x1) and u2(x2) are utility functions of x1 and x2 , respectively.§3.2.1 Properties of multi-attribute utilityfunctions•Let x 1(best) or x 2(best) be the most favorable level of attribute 1 or 2 that can occur. Also, let x 1(worst) or x 2(worst) be the least favorable level of attribute 1 or 2 that can occur.•Definition - A decision maker’s utility function exhibits additive independence if the decisionmaker is indifferent between:L11/2L21/21/21/2x 1(best), x 2(worst)x 1(worst),x 2(worst)x 1(worst),x 2(best)x 1(best), x 2(best)§3.2.1 Properties of multi-attribute utilityfunctions•Corollary 3.2.1 -- If attributes 1 and 2 are mui and the decision maker’s utility function exhibits additive independence, then k3=0 and u(x1,x2)=k1u1(x1) + k2u2(x2).§3.2.1 Properties of multi-attribute utilityfunctions •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) k2This gives us k3 =0.§3.2.2 Assessment of multi-attributeutility 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 thatu(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.§3.2.2 Assessment of multi-attributeutility functions•Now, u(x 1, x 2)=k 1u 1(x 1) + k 2u 2(x 2) +k 3u 1(x 1)u 2(x 2) yieldsu(x 1(best), x 2(worst))= k 1(1)+ k 2(0)+ k 3(0)= k 1•Thus, k 1 can be determined from the fact that the decision maker is indifferent between L2L11- k 11x 1(worst),x 2(worst)x 1(best), x 2(worst)k 1x 1(best), x 2(best)§3.2.2 Assessment of multi-attributeutility functions•Similarly, u(x 1, x 2)=k 1u 1(x 1) + k 2u 2(x 2) + k 3u 1(x 1)u 2(x 2) yieldsu(x 1(worst), x 2(best))= k 1(0)+ k 2(1)+ k 3(0)= k 2•Thus, k 2 can be determined from the fact that the decision maker is indifferent between L2L11- k 21x 1(worst),x 2(worst)x 1(worst), x 2(best)k 2x 1(best),x 2(best)§3.2.2 Assessment of multi-attributeutility functions•To determine k 3, observeu(x 1(best), x 2(best)) = u 1(x 1(best))=u 2 (x 1(best))=1. •So, from u(x 1, x 2)=k 1u 1(x 1) + k 2u 2(x 2) + k 3u 1(x 1)u 2(x 2), we have1= u(x 1(best), x 2(best)) = k 1(1)+ k 2(1)+ k 3(1)= k 1 + k 2+ k 3•Thus, k 3= 1- k 1 - k 2•Of course, if the decision maker’s utility function exhibits additive independence, then k 3= 0.§3.2.2 Assessment of multi-attributeutility 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, DecisionMaking 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 additiveindependence) k3.–Step 5. Check if the assessed utility function is reallyconsistent with the decision maker’s preferences. Todo this, set up several lotteries and use the expectedutility of each lottery to rank the lotteries. If theassessed assessed utility function is consistent withthe decision maker’s preferences, the ranking underthe assessed utility function should be closelyassemble the decision maker’s ranking of lotteries.§3.2.2 Assessment of multi-attributeutility 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 Fruit’s multi-attribute utility function u(x1, x2), wherex1 = Fruit’s market share during 1999x2 = Fruit’s profits during 1999 (in millions of dollars)§3.2.2 Assessment of multi-attributeutility 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.§3.2.2 Assessment of multi-attribute utility functions •Step 2 - To check for additive independence. We must determine if Fruit is indifferentbetweenL11/2L21/21/21/250%, $510%, $510%, $3050%, $30• Suppose that Fruit is not indifferent between these lotteries. Then Fruit’s utility function will not exhibit additive independence.• We now know that u(x 1, x 2) takes the following form: u(x 1, x 2)=k 1u 1(x 1) + k 2u 2(x 2) + k 3u 1(x 1)u 2(x 2).§3.2.2 Assessment of multi-attributeutility functions•Step 3 - We now assess u1(x1) and u2(x2). Suppose we obtain the results as shown in the following figures.。

《项目管理知识体系指南》第二章节风险管理Project risk management is an essential aspect of project management. It involves identifying, assessing, and prioritizing risks to minimize potential negative impacts on a project. 项目风险管理是项目管理的一个重要方面。

它涉及识别、评估和优先考虑风险，以最小化对项目的潜在负面影响。

The first step in project risk management is to identify potential risks. This involves brainstorming with the project team to come up with a comprehensive list of possible risks that could affect the project. 项目风险管理的第一步是识别潜在风险。

这涉及与项目团队进行头脑风暴，以得出可能影响项目的全面风险清单。

Once potential risks have been identified, the next step is to assess their likelihood and potential impact. This involves assigning a probability and severity rating to each risk to determine which ones require the most attention. 一旦确定了潜在风险，下一步是评估它们的可能性和潜在影响。

这涉及为每个风险分配概率和严重性评级，以确定哪些风险需要最多的关注。

After assessing the risks, the project team should prioritize them based on their potential impact on the project. This will help the team focus on the most critical risks and allocate resources accordingly. 在评估风险之后，项目团队应根据其对项目的潜在影响对其进行优先排序。