CHALLENGES OF SETTING THE DECISION MAKERS IMPORTANCE WEIGHTS WITHIN GROUP DECISION MAKING CONTEXTS

BALWOIS 2010 CHALLENGES OF SETTING THE DECISION MAKERS IMPORTANCE WEIGHTS WITHIN GROUP DECISION MAKING CONTEXTS B. Srdjevic, Z. Srdjevic, B. Blagojevic, K. Suvocarev Department of Water Management, Faculty of Agriculture, University of Novi Sad, SERBIA

SERBIA: Main Facts Located in South-Eastern Europe Area – 88.361 km2 Population - 7.397.651 (without Kosovo)

NOVI SAD DEPARTMENT OF WATER MANAGEMENT

DEFINITION OF THE PROBLEM GOAL: Select the most suitable irrigation technology CRITERIA: 1.Investments (€/ha) 2. Exploitation period (years) 3. Energy consumption (kW/ha) 4. Labor consumption (h/ha) 5. Water use efficiency (%)

DEFINITION OF THE PROBLEM ALTERNATIVES: V1 – wheel line irrigation,V2 – microsprinkler irrigation, V3 – traveling sprinkler, V4 – center pivot, V5 – linear drip irrigation, K1 – row irrigation, K2 – strip irrigation • DECISION MAKERS: • expert in irrigation technologies – DM1 • (2) expert in water resources economy – DM2 and • (3) expert in water resources system analysis – DM3

Evaluation parameters for irrigation technologies Table 1. Evaluation parameters for irrigation technologies

Solving problem in few steps Step 1. AHP Step 2. Decision makers’ importance weights and the final group decisions Step 3. SAW Step 4. SPW Step 5. TOPSIS Step 6. CP Step 7. Discussion of result

Step 1. AHP ANALYTIC HIERARCHY PROCESS Table 2. Saaty’s scale For each DMs, AHP starts by performing a sequence of Mx(M-1)/2 pair wise comparisons of criterions (only criterions) with respect to goal by using the standard (crisp) 9-point Saaty’s scale as defined in Table 2. This way a judgment matrix is created. Criteria set is assessed in pair-wise manner by the three decision makers.

Step 1. AHP ANALYTIC HIERARCHY PROCESS Results of AHP : Table 3. Criteria weights derived from three DM evaluations Table 4. Weights and ranking of alternatives

Step 2.Decision makers’importance weights and the final group decisions The key issues is how setting of different importance weights to the decision makers affects a group synthesis of individual valuations and is it possible to recognize an impact of such setting on the final ranking, including possible preorder of alternatives. For this purpose we used SAW, SPW, TOPSIS and CP Method with 6 variants of DMs weights distributions. Table 5. Different distributions of DMs’ weights

Step 3. SAW method The SAW method is one of the most simple, but good decision making methods . The method is comprised of three basic steps: 1 - scale the scores to make them comparable, 2 - apply weights, and 3 - sum up the values for each source. The final preference score for each alternative is: The best alternative is the one with maximum value of Si.

Step 4. SPW method The SPW method is similar to SAW. Scaling is not necessary, as well as normalization. The final preference score for each alternative is: The best alternative is the one with maximum value of Si

Step 5.TOPSIS method TOPSIS is based on the shortest distance from the ideal solution and the farthest from the negative ideal solution . It evaluates the decision matrix (1) in 6 steps: Step 1: Normalize decision matrix Step 2: Create weighted normalized decision matrix. Step 3: Determine ideal solutions. Step 4: Calculate the n–dimensional Euclidean distances from ideal solutions for all alternatives Step 5: Calculate relative closeness to the ideal solution for each alternative Step 6: Rank alternatives.(The best alternative is the one with the shortest distance to the ideal solution)

Step 6. CP CP (Compromise Programming) is a technique which ranks alternatives according to their closeness to ideal point. The best alternative is the one whose point is at the least distance from an ideal point in the set of efficient solutions. The distance measure used in CP is the family of Lp–metrics given as : - Lp(i) is the Lp–metric for alternative Ai; rij is the rating of alternative Ai for criterion Cj; - rj* and rj** are the best and the worst values respecively over the set of all alternatives for criterion Cj; -p is the parameter reflecting an attitude of the decison maker. An alternative with minimum Lp–metric is considered as the best.

Step 7. Discussion of result Final ranking of alternatives obtained with SAW and SPW for different distributions of DMs’ weights Final ranking of alternatives obtained with TOPSIS and CP (p=2) for different distributions of DMs’ weights

Discussion of result It is noticed that small variability in weights of DMs is not relevant to cause change in order of rankings of alternatives. To make distinct change in alternative rankings great importance (0.8) should be given to DM2 and very small to rest of the group. And even this is not enough to change importance of first ranked and last ranked alternative. Reason for this is in the similar preferences for criteria and alternatives for each DM. Also we can notice that in a group context all methods (SAW, SPW, CP and TOPSIS) point as the best one a Wheel line technology.

CHALLENGES OF SETTING THE DECISION MAKERS IMPORTANCE WEIGHTS WITHIN GROUP DECISION MAKING CONTEXTS