Eawag: Swiss Federal Institute of Aquatic Science and Technology

Multi-Criteria Decision AnalysisExercise

Judit Lienert

Lecture: Advanced Environmental AssessmentsStefanie Hellweg; Rolf Frischknecht / IfU – Ökologisches Systemdesign

25. October 2016, ETH Zürich Hönggerberg

Aims

Carry out own small MCDA

Demonstrate feasibility; using simple tools and Excel

(but lots of expensive software available)

Focus on elicitation of stakeholder preferences (single-attribute value functions, weights)

Preparation (hopefully already done)

1. Group task (if not prepared; max. 10–15 mins.)Define and set up decision problemDetermine objectives, attributes, and alternatives Choose environmental problem. Define: What is the problem?

What are objectives and main trade-offs between objectives? Who decides/ is affected? What are their interests?

Define 4 objectives (1, 2, 3, 4) and corresponding attributes

Define 4 decision alternatives (a, b, c, d)

Make predictions: for each alternative (a, b, c, d) what is the level of each objective / attribute? Fill in prediction matrix (Tab. 1); use Excel-file

Determine ranges: best-and worst case for each objective

For each alternative: How well are objectives achieved?Objective

Alternative

1. 2. 3. 4.

a.

b.

c.

d.

1. Define and set up decision problem: choose objectives, alternatives, fill in prediction matrix

2. Elicit single-attribute value function (15 mins.)

One person is interviewer, the other stakeholder (answers)

Use tool (word-file) to elicit a single-attribute value function

For the other three attributes transform attribute numbers to values using a linear value function

Fill in prediction matrix (Tab. 1) with values instead of attribute numbers

Fill in the Excel file

Q: Total biomass of trout in lower reaches of Wigger is?

A: xmin = 20 kg/ ha, xmax = 250 kg/ ha

A C

20 kg/ ha 250 kg/ ha

A: No way!

B

135 kg/ ha

115 kg 115 kg

Q: Is improvement from worst case (A) to 135 kg/ ha (B)equally good as improvement from 135 kg to best case (C)?

2. Elicit single-attribute value function withMidvalue splitting technique / Bisection method

Q: Where is midpoint (B) (x0.5) so that improvement from A to B is just as good as improvement from B to C?

A: ... well .... ca. 100 kg/ ha

80 kgA C

20 kg/ ha 250 kg/ ha

B

100 kg/ ha

150 kg

Q: Like this?A: ... yes ...

2. Elicit single-attribute value function withMidvalue splitting technique / Bisection method

Q: Same procedure for x(0.75) and x(0.25)

Q: Consistency checks with some other points(Should always be done – not here for time reasons)

x(0.75)

175

A C

20 250 (kg/ ha)

B

100

x(0.25)

60

A: x0.25 (= 60 kg/ ha) and x0.75 (= 175 kg / ha)

2. Elicit single-attribute value function withMidvalue splitting technique / Bisection method

10060 175

0.25

0.5

0.75

1

0

Value

Biomass adult trout (kg/ ha)25020 135

2. Elicit single-attribute value function withMidvalue splitting technique / Bisection method

Convert attribute level to value [0, 1] with help of value function2. Elicit single-attribute value function

Objective

Alternative

1. 2. 3. 4.

a.

v1(a1) = …. v2(a2) = …. v3(a3) = …. v4(a4) = ….

b.

v1(b1) = …. v2(b2) = …. v3(b3) = …. v4(b4) = ….

c.

v1(c1) = …. v2(c2) = …. v3(c3) = …. v4(c4) = ….

d.

v1(d1) = …. v2(d2) = …. v3(d3) = …. v4(d4) = ….

Preferences

Objective

Alternative

1. High flexibility

2. Good chemical state

3. Low time demand

4. Low costs

a. central, rehabilitate, high-tech

35%

v1(a1) = 0

0.77 (good)

v2(a2) = 0.86

0

v3(a3) = 1

863 CHF/p/yr

v4(a4) = 0

b. central,decay, “high-tech”

50%

v1(b1) = 0.28

0.3 (unsatisf.)

v2(b2) = 0

0

v3(b3) = 1

76 CHF/p/yr

v4(b4) = 1

c. decentral,low tech (e.g. reed beds)

70%

v1(c1) = 0.64

0.5 (moderate)

v2(c2) = 0.38

20 hrs/p/yr

v3(c3) = 0

400 CHF/p/yr

v4(c4) = 0.58

d. decentralhigh-tech (e.g. NoMix)

90%

v1(d1) = 1

0.85 (v. good)

v2(d2) = 1

10 hrs/p/yr

v3(d3) = 0.5

800 CHF/p/yr

v4(d4) = 0.08

1. Prediction matrix for decentral wastewater management (example from lecture)For each alternative: How well are objectives achieved?

For each alternative: How well are objectives achieved?Estimates adapted from SWIP (Zheng et al., 2016)

PredictionsMCDA – Examples predictions wastewater

Objective

Alternative

1. Lowfuture rehabilitation burden(% rehab. demand)

2. High flexibility(% flexib.extension/ deconstruction)

3. Good chemical state (0-1: Modularstream assessm.)

4. Nutrientrecovery (% phos-phate)

5. Efficientenergy consumption (kWh/p/yr)

6. Few gastro-int. infections dir. cont. (% pop. inf. 1x/ y)

7. Low time demand end-user (hr/p/yr)

8. Low area demand (m2 on propertyend-user)

9. Low annualized costs (CHF/p/yr)

a. central, rehabilitate, high-tech

80% 35% 0.77 (good)

0 250 2% 0 0 863 (1.3% of income)

b. central,decay, “high-tech”

0% 50% 0.3 (unsatis-factory)

0 60 10% 0 0 76 (0.07% of

income)

c. decen-tral, low tech (e.g. reed beds)

20% 70% 0.5 (moder-

ate)

60% 20 20% 20 10 400

d. decen-tral high-tech (e.g. NoMix)

100% 90% 0.85(very

good)

90% 40 5% 10 4 800

3. Determine stakeholders, elicit weights (20 mins.)

Define two stakeholders that likely have different interests

One person is interviewer, the other stakeholder (answers)

Elicit weights for one stakeholder using SWING method

If there is time, do same for second stakeholder

Use tool (word-file) to elicit weights with SWING

See instructions there

Fill weights into Excel file

SWING-method (“recipe”)1. Determine ranges of objectives2. Rank alternatives from best br to

worst a–

3. Allocate points: best br = 100 ptworst a– = 0 pt

4. Assign points to the remaining alternatives br such that the value differences are reflected

5. Calculate weights by normalizing the points: (convention: sum wr = 1)

6. Consistency checks m

ii

rr

t

tw

1

3. Elicit weights with SWING

1. For each objective: Range? (= best / worst-possible case?)Example: choosing a job (Eisenführ et al., 2010, p. 139 ff.)

Objective

Alternative

1. Salary 2. Working hours

3. Careerperspectives

4.

a. Consultancy 80’000 € 60 hrs / week Good

b. Universityassistant

50’000 € 40 hrs / week Excellent

c. Sailing instructor

30’000 € 20 hrs / week Bad

d.

3. Elicit weights with SWING

Alternative a = (€30'000, 60 hrs, bad)

Q: In alternative a all attributes are at their worst level. If you could move one to its best level, which would you choose?

2. Rank alternatives from best br to worst a–

Salary WorkinghoursCareer

perspectives

60 hrs bad€30'000

DM: I would certainly move the salary to it's highest level

(note: this is the preferred-alternative b1 and receives 100 pt.)

€80'000 20 hrs excellent

3. Elicit weights with SWING

Alternative a = (€30'000, 60 hrs, bad)

Q: Which attribute would you choose to move to its' best level as second option?

Salary WorkinghoursCareer

perspectives

60 hrs bad€30'000

DM: (think, think, ...) I suppose the working hours

(note: this is alternative b2)

€80'000 20 hrs excellent

2. Rank alternatives from best br to worst a–3. Elicit weights with SWING

Attribute Salary Hours Career Alternative Points (tr)Rank

1. b1 1002. b2

3. b3

4. a 0

Q: This means that the most-preferred alternative, with the salary at its best level (b1), receives 100 points. Note: this is not the best-possible alternative. The worst one (a) has zero points. Which points would you assign to b2 and b3, between 0 and 100 points, that correctly reflect the differences?

DM: I think, b2 would receive 70 points and b3 maybe 60(Now normalize points so that weights sum up to 1)

70

60

3./4. Assign points: b1 = 100 / 1 = 0 / rest = value differences3. Elicit weights with SWING

4. Carry out MCDA, rank alternatives (15 mins.) Use Excel to help with calculations

If you prefer: do it “by hand” (with calculator) Fill in all required parts: prediction matrix, replace attribute

levels with values between [0, 1], weights of main objectives For each alternative: calculate the total value with the

additive aggregation model Rank the alternatives from best to worst Discuss: Does ranking make sense? Reason for good (bad)

rank of “best” (“worst”) alternative? What if you use different weights?

If time: analyze in detail; produce graphs; explain results (weights? performance w.r.t achievement of objectives?, etc.)

If you had time to elicit weights for another stakeholder: is the ranking different?

Additive aggregation: Multi-attribute value function = weighted sum of single-attribute value functions

m

iiii avwav

1

v(a) = total value of alternative a= weighted sum of single values of

each attribute i of alternative aai = attribute level of attribute i for

alternative avi(ai) = value of attribute level of attribute i

for alternative awi = weighting factor of attribute i,

where wi = 1

4. Carry out MCDA with additive model

Objective Alternat.

1.

w1 = ….

2.

w2 = …

3.

w3 = …

4.

w4 = …

Total value v of each alternative

a.v1(a1) = …. v2(a2) = …. v3(a3) = …. v4(a4) = …. v(a) = ….

b.v1(b1) = …. v2(b2) = …. v3(b3) = …. v4(b4) = …. v(b) = ….

c.v1(c1) = …. v2(c2) = …. v3(c3) = …. v4(c4) = …. v(c) = ….

d.v1(d1) = …. v2(d2) = …. v3(d3) = …. v4(d4) = …. v(d) = ….

)(...)()( 222111

1 mmm

m

iiii avwavwavwavwav

4. Carry out MCDA with additive model

Single-attribute value functions, example High flexibility (%)

Preferences

0.25

0.5

0.75

40; 0.25

45; 0.5

55; 0.75

35; 0

90; 1

00.10.20.30.40.50.60.70.80.9

1

35 45 55 65 75 85Attribute (%)

Value function high flexibility (% flexibility of technical extension or deconstruction)

Linearcase1stelicitation

Value

0.62

50%(alternative

b. central, decay)

70%(alternative

c. decentral, low-tech)

0.86

MCDA – Preferences (value functions)

Weights of Eawag and the public (N=314)

Equity Resources W-water Social Costs

Wei

ghts

(ave

rage

)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Example SWIP; weights from stakeholdersExample: weights main objectives, elicited three times independently

Weights of ten wastewater experts

Equity Resources W-water Social Costs

Wei

ghts

(ave

rage

)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Weights of ten water supply experts

Equity Resourc. Wat.Supp. Social Costs

Wei

ghts

(ave

rage

)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ten water supply experts Ten wastewater experts General public, Eawag (N=314)

Protection ofwater & other resources

Good water supply

Safe waste-wat. disposal

High social acceptance

Low costs

Intergener-ational equity

Similar average preferences from ten interviews (local / cantonal / national stakeholders) and from public (survey) But large individual differences Question: do different preferences change the results (i.e. the

recommendations about best-performing alternative)?

Wei

ghts

(ave

rage

)

Lienert, J., Duygan, M., Zheng, J. (2016) Preference stability over time with multiple elicitation methods to support wastewater infrastructure decision-making. European Journal of Operational Research 253 (3): 746-760.

SWIP for wastewater infrastructure planning (Jun Zheng)

• A7: Decentral high-tech (e.g. NoMix)(our alternative d)

MCDA – Model / results Model

• A4: Decaying central infrastructure(our alternative b)

• A8d: Super central WWTP(similar to our alternative a)

Zheng, J., Egger, C., Lienert, J. (2016) A scenario-based MCDA framework for wastewater infrastructure planning under uncertainty. Journal of Environmental Management 183 (3): 895-908.

5. Plenum: Elevator pitch (5 – 10 mins.)

Each group chooses one person to present main insights

You are in the elevator with your boss: it takes 2 mins. to reach her floor

Present your decision problem, main insights from elicitation, and MCDA-result

Remember: it is important to you that she gets a good impression!