Lecture TOPSIS

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.