Quantitative Techniques for Decision Making in Construction

Answers to Selected Exercise Questions

Answers to Selected Exercise Questions Chapter 1 Question 2: It is important t o make sure that the levels are totally independent, and it should not be possible to merge any of the two or more levels. Her e are two examples of 5-Level hierarchy structures to evaluate construction engineering decision problems: Solution 1 QUANTITATIVE TECHNIQUE FOR DECISION MAKINGIN CONSTRUCTION Level 1 Goal: to determine the most suitable team for this project. Level 2 Components of the Project Fll: Departmenta l Offic e F12: Residential Hall F13: Scientific Laborator y Level 3 Individual component to be designed in each component F21: Air-conditioning system F22: Lighting system F23: Fire resisting system F24: Piping system Level 4 Factors affecting the works F31: Team's experience F32: Team's professional skill s F33: Duration for completing the project F34: Identifying ke y issues F35: Innovative idea Level 5 Team alternatives 1: Team A 2: Team B 3: Team C Answers to Selected Exercise Questions 18 7 Solution 2 Level 1 Goal: to rank the 3 applicants. Level 2 The 3 Assessors F21: Project manager from the client F22: Project directo r F23: Project engineer from the consultant 1 88 QUANTITATIV E TECHNIQUE FOR DECISION MAKING IN CONSTRUCTION Level 3 The 3 sources of information for the recruitment board to evaluate the abilities of the applicant s F31: Application package submitted by the applicant F32: The interviews F33: Past performance record s of the applicants working for the client Level 4 The 6 main factors that are considered by the recruitment boar d to assess the abilities of the applicant s F41: Relevant technical experience and knowledge F42: Monitoring of construction programm e F43: Resolving of contractual issues F44: Liaison with different governmen t departments and other agencies F45: Management of resident site staff F46: Management of the contractor Level 5 The 3 applicants: 1: Applicant A 2: Applicant B 3: Applicant C Chapter 2 Question 1: Belton and Gear used the following t o demonstrate their famous example s of rank reversal: Example 1 Suppose that the decision maker wishes to evaluate three options (A, B and C) on three criteria (a, b and c). Saaty' s approach is outlined in the following steps: Answers to Selected Exercise Questions Step ! : b y comparing option s on each criterion, th e following matrice s (consistent) are formed : Criterion a f \ % I s 9 1 9 UV . l j Criterion b f l 9 9 N y9 i i l'/9 1 l j Criterion c ' l % 8\ % 1 9 0/s l h 1 , Step 2 : calculate relative weightings of options on each criterion It can be shown that the normalised priority vectors are: Criterion Criterion Criterion a b c (Wl) (W2 ) (W3 ) A / i n 9/11 U/llJ ^ 9 / i n l / n U/llJ f8/l8\ 9/18 The weighting matrix (or composite matrix) W = (Wl, W2, W3) Step 3 : For the comparison of Level 2 with respect to Level 1, the three criteria are assumed to be of equal importance. Th e matrix therefore is (1/3, 1/3, 1/3)T . Step 4 : The overal l importanc e o f eac h optio n i s obtaine d b y multiplyin g th e composite matri x in Step 2 by the matrix in Step 3. Th e overall priorit y vector is (0.45, 0.47, 0.08). i.e. B > A > C. Example 2 Now suppose that there is an additional alternative D, which is exactly similar to B, is introduced to the problem and that the judgement matrices of Step 1 become: QUANTITATIVE TECHNIQUE FOR DECISION MAKING IN CONSTRUCTION Criterion a Cxitexion b Criterion c 9/20 1/20 U/20J f9/12> 1/12 1/12 L1/12 J ( 8121 \ 9/27 1/27 L 9/27 ) Since the criteria are still assumed to be of equal importance compared with respective t o Level 1 so the matrix is again (1/3 , 1/3, 1/3) T . Th e overall priority vector of the options is therefore calculated to be (0.37, 0.29, 0.06, 0.29), i.e. A > B ~ D > C . It can be observed that the rankings of Examples 1 and 2 are not consistent: the ranking of Options A and B is reversed after th e introduction of Option D, although the pairwise inputs connected with...