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PROJECT MANAGEMENT
Project Selection
MULTIPLE CRITERIA IN PROJECTS
• Investment
• Return (IRR,…)
• Payback
• Net Present Value
• Risk
• Future growth prospects
• Similarity to existing business
• Environmental implications
EVALUATION OF PROJECTS
• Rarely would one project emerge as the best on all the chosen criteria
• If this happens it is the dominant project and should clearly be chosen
• In general there would be a set of non-dominated projects the choice out of which is not normally easy
• Management priorities to various criteria could help decision making
CRITERIA
TANGIBLE INTANGIBLE(measurable in (not measurable on Rs., percentage, a well defined scale)year, Rs/year, …)
DECISION MATRIX
Criteria C1 C2 C3 . . . Cn
Projects
P1 x11 x12 x13 x1n S1
P2 x21 x22 x23 x2n S2
Pm xm1 xm2 xm3 xmn Sm
NON DOMINATED SOLUTIONS
Return
NPV
P1
P2
P3
P4
P5
P6
P7
P8
WEIGHTAGES TO CRITERIA
The priorities or weights to the different criteria may be obtained by:
• Mutual consultations or opinion polls
• Pair wise comparison between criteria
• Establishing a hierarchy of priorities and using AHP (developed by Saaty)
CRITERIA FOR PROJECT SELECTION (Worst - Best)
C1 Investment (in lakhs of Rs) (10 - 2)
C2 IRR (percentage) (10 - 40)
C3 Payback (years) (10 - 2)
C4 Risk (v high, high, medium, low, v low)
C5 Future growth
( v poor, poor, medium, good, v good)
C6 Similarity to existing business
(v poor, poor, medium, good, v good)
PERFORMANCE OF COMPETING PROJECTS
Criteria
C1 C2 C3 C4 C5 C6
P1 10 40 8 high good v. good
P2 6 25 4 v.high medium good
P3 8 30 10 low v.good medium
P4 3 10 2 medium poor v.poor
P5 2 20 2 v.low v.poor poor
Fighter Aircraft Selection(An Example)
X1 Maximum speed (Mach number)
X2 Ferry range (Nautical miles)
X3 Maximum payload (Lbs)
X4 Acquisition cost (Million dollars)
X5 Reliability (High - low)
X6 Maneuverability ( High - low)
Fighter Aircraft Example(Decision Matrix)
X1 X2 X3 X4 X5 X6
A1 2.0 1500 20,000 5.5 avg. v.high
A2 2.5 2700 18,000 6.5 low avg
A3 1.8 2000 21,000 4.5 high high
A4 2.2 1800 20,000 5.0 avg avg
(X4 is a cost criterion, others are benefit criteria)
SCALE FOR INTANGIBLESCost attributes Benefit attributes
0
very high 1.0 1.0 very low
high 3.0 3.0 low
average 5.0 5.0 average
low 7.0 7.0 high
very low 9.0 9.0 very high
10
Technique for Order Preference using
Similarity to Ideal Solution (TOPSIS)Step 1 Obtain the decision matrix after
using a numerical scale for intangibles.
X1 X2 X3 X4 X5 X6
A1 2.0 1500 20,000 5.5 5 9
A2 2.5 2700 18,000 6.5 3 5
A3 1.8 2000 21,000 4.5 7 7
A4 2.2 1800 20,000 5.5 5 5
NORMALIZED DECISION MATRIX
Step 2 Obtain the normalized decision matrix, R, using the relationship
rij = xij/sq root (sum, i=1...m of xij2)
0.4671 0.3662 0.5056 0.5063 0.4811 0.6708
0.5839 0.6591 0.4550 0.5983 0.2887 0.3727
0.4204 0.4882 0.5308 0.4143 0.6736 0.5217
0.5139 0.4392 0.5056 0.4603 0.4811 0.3727
WEIGHTED DECISION MATRIX
Step 3 Obtain the weighted decision matrix V by multiplying each column of R by the corresponding weight.
W = ( 0.2, 0.1, 0.1, 0.1, 0.2, 0.3) 0.0934 0.0366 0.0506 0.0506 0.0962 0.2012
0.1168 0.0659 0.0455 0.0598 0.0577 0.1118
0.0841 0.0488 0.0531 0.0414 0.1347 0.1565
0.1028 0.0439 0.0506 0.0460 0.0962 0.1118
IDEAL & NEGATIVE IDEAL SOLUTIONS
Step 4 Obtain the ideal (A*) and the negative ideal (A-) solutions from the weighted decision matrix V.
A* =(0.1168, 0.0659, 0.0531, 0.0414, 0.1347, 0.2012)
A- =(0.0841, 0.0366, 0.0455, 0.0598, 0.0577, 0.1118)
SEPARATION MEASURES
Step 5 Compute the separation measures from the ideal (Si*) and the negative ideal (Si-) solutions for all alternatives, i=1,...,m.
Si* = Sq root ( sum of squares for j=1,...,n of (vij-vj*))
Si- = Sq root (sum of squares for j=1,...,n of (vij-vj-))
VALUES OF SEPARATION MEASURES
Separation measures from:
Ideal solution Negative ideal solution
S1* = 0.0545 S1- = 0.0983
S2* = 0.1197 S2- = 0.0439
S3* = 0.0580 S3- = 0.0920
S4* = 0.1009 S4- = 0.0458
RELATIVE CLOSENESS TO IDEAL SOLUTION
Step 6 For each alternative determine the relative closeness to the ideal solution
( Ci*, i=1,...,m) as
Ci*= Si- / (Si*+Si-) Ideal solution
Negative idealsolution
Alternative i
Si*
Si-
RELATIVE CLOSENESS VALUES
C1* = 0.643
C2* = 0.268
C3* = 0.613
C4* = 0.312
(Notice that the closeness rating is a number between 0 and 1, with 0 being the worst possible and 1 the best possible solution)
RANK THE PREFERENCE ORDER
Step 7 Determine the preference order by arranging the alternatives in the descending order of Ci*, i=1,...,m.
Thus the ranks for the alternatives in the fighter aircraft selection problem using TOPSIS emerge as
A1, A3, A4, A2
SIMPLE ADDITIVE WEIGHTIING (SAW)
Step 1: Obtain the decision matrix after converting intangibles to numbers
X1 X2 X3 X4 X5 X6
A1 2.0 1500 20,000 5.5 5 9
A2 2.5 2700 18,000 6.5 3 5
A3 1.8 2000 21,000 4.5 7 7
A4 2.2 1800 20,000 5.5 5 5
NORMALIZATION
Step 2: Obtain the normalized decision matrix R (rij, i= 1,..., m: j=1,...,n) using
rij = xij/ xj* , if the jth criterion is a benefit criterion, and
rij = xj-/ xij , if the jth criterion is a cost criterion
FINAL SCORES
Step 3: Using the weights for the different criteria obtain the weighted score for each alternative using the normalized decision matrix
Step 4: Based on the final scores, rank the alternatives for a decision by the decision maker
NORMALIZED DECISION MATRIX
A1 0.80 0.56 0.95 0.82 0.71 1.00 0.835
A2 1.00 1.00 0.86 0.69 0.43 0.56 0.709
A3 0.72 0.74 1.00 1.00 1.00 0.78 0.852
A4 0.88 0.67 0.95 0.90 0.71 0.36 0.738
W (0.2 0.1 0.1 0.1 0.2 0.3)
Ranking of alternatives with SAW :
A3, A1, A4, A2
SAW & TOPSIS(A Comparison)
Rankings obtained using two Multi attribute decision making techniques need not be identical.
For the Fighter Aircraft Selection Project
SAW gave a ranking A3, A1, A4, A2
TOPSIS gave a ranking A1, A3, A4, A2
SUMMARY
• Project selection involves consideration of multiple, often conflicting criteria among alternatives.
• Project appraisal leads to evaluations which may be tangible, incommensurate or intangible.
• Intangibles are evaluated on a numerical subjective scale.
SUMMARY (Continued)
• A decision matrix with numerical evaluations is the starting point for MADM methods.
• Different methods vary in their normalization schemes and in the manner in which scoring of alternatives is done.
• A fighter aircraft example was illustrated using both TOPSIS and SAW.