Multicriteria decision making for finding out the final performance

When there are more than one criterion involved in the decision making, the process of decision making becomes multicriteria decision making (MCDM). This is the multiple-criteria decision making technique combines the available, often completely different, performance indicators into a final performance indicator (FPI). Considering the nature of study and involvement of different parameters; the MCDM process needs to be used to find out the overall performance of the irrigation water management. Following the approach set out by Gorantiwar and Smout (2010), the selected MCDM technique for the study is compromise programming (CP) for first level.

Vairavamoorthy et al (2006) described compromise programming developed by Zeleny (1973) that employs single level non-normalized distance based methodology to rank a discrete set of solutions according to their distances from an ideal solution. This is reproduced below.

Compromise programming includes solutions that are closest to the ideal solution as determined by some measure of distance. It consists of identifying the different attributes or indicators or

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performance measures (for example, productivity, equity etc.) that contribute to “final performance index” (FPI) of irrigation management in an irrigation scheme. The weights are assigned to each performance measure that reflects the relative importance of that performance measure compared to other performance measures. The compromise programming also uses weights to reflect the importance of maximal deviation between the indices. This is called as balancing factor. The deviation is a measure of difference between the observed value of variable and some other variable. Balancing factor (p) is the degree of compromise between indicators

of the same group. The values of the indicators are obtained from the simulation-optimization modeling (AWAM model). The weights are obtained by analytical hierarchical process (AHP). In this study the balancing factor is considered as one meaning that the same importance was given for the maximal deviation between the indices. FPI is then obtained by calculating the distance that determines the closeness to the ideal solution with the help of ideal and worst values for each of the indicators, weights and balancing factors. FPIs are obtained for different alternatives or management options and the preferred option would be the one that is nearest to the ideal point in terms of the distance.

Compromise programming uses equation (3.15) (Zeleny1973) to rank a discrete set of solution according to their distance from an ideal solution. One compromise distance for each alternative of the problem is obtained. (In this case different alternatives are irrigation strategies).

p n i p w i b i w i i p i j f f f f w L 1 1                       − − =

∑

whereLjis distance metric of alternative, wiis weight of indictor I, p is balance factor

(described below), b i

f is best value for indictor I, f_iw is worst value for indictor I and f_i is

actual value for indictor i

However for multi level problem (as in this study), the entire problem needs to be arranged in hierarchal way (Figure 3.1) and compromise programming needs to be used at each level. Using compromise programming at multi-level forms the composite programming.

Bardossy et al. (1985) developed composite programming that deals with problems of a hierarchical

nature at different levels (i.e., when certain criteria contain a number of sub-criteria). Composite programming extends a compromise programming to a normalised multilevel methodology.

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Composite programming generates distance metrics of each sub-criterion within the same group, and then combines the distance metrics of each sub-criterion to form a single composite distance metric. Then the process sequentially proceeds with the successive levels until final level composite distance metric is reached. In this way one composite distance metric is obtained for each alternative. Mathematical representation of the composite programming (Bardossy et al.1985) is given below.

Normalization that is needed to consider different levels is performed by equation (3.16).

w i b i w i i i f f f f S − − = (3.16)

Composite distance for jth _{group of indictors is obtained by substituting equation (3.16) into}

equation (3.15), and ignoring the exponent p on the weight w (Bardossy and Duckstein 1992).

The composite distance, L_j, is the distance between the actual point of indicator and the ideal

one (Woldt and Bogardi 1992):

j j j p n i p i j i j j w S L / 1 1 , ,         =

∑

Where Lj= composite distance metric for B+1 level group j of B level indicators; Sj,i= normalized value of the B level indictor i in the B+1 level group j of B level indicators;

j

n =number of B level indicators in group j; w_j,i=weights expressing the relative importance of

B level indicators in group j such that their sum is 1; and pj=balancing factors among indicators for group j.

The value of Lj at final level is the final performance index (FPI).

Balance factors: Balance factor (p in equation 3.15) determines the degree of compromise between indicators of the same group. Low balance factors are used for a high level of compromise among indicators of the same group (Jones and Barnes 2000). The guidelines for using balance factor is given below (Jones and Barnes, 2000)

• A balance factor of 1 for a perfect compromise between indicators of that group. • A balance factor of 2 for the moderate level of compromise

• A balance factor greater than 3 for minimal compromise.

AHP method allows the subjective evaluation of different elements. In this study AHP method was used.

94 3.3 Analysis of Performance Results

Gorantiwar and Smout (2010) developed different management scenarios. These scenarios will be used in this study for finding out the performance results. These are described below.

The performance results will be obtained for different management scenarios (for example on the irrigation interval) and irrigation strategies (for example existing against the improved). In the management scenario, the combination of different irrigation intervals (7, 14, 21, 28, 35 days) in

Rabi season and summer season will be considered. In the irrigation strategy different depths of

irrigation and different water distribution options will be considered for free and fixed cropping distribution. These include:

Irrigation amount: The following options were considered: 1. Full irrigation (Fl-I):

2. Fixed depth irrigation (Fx-I) 3. Optimized deficit irrigation (ODI)

Irrigation frequency: Different combinations of irrigation interval (7, 14, 21, 28, 35 days) in Rabi season and Summer season

Water distribution: The following options were considered: 1. Free water distribution (FWD)

2. Equitable distribution of seasonal water allocation based on CCA of AU (EDSW) 3. Equitable distribution of intraseasonal water based on CCA of AU (EDIW) Cropping distribution: The following two options were considered.

1. Free cropping distribution 2. Fixed cropping distribution

The results will be obtained at scheme level, main canal (right bank) level, secondary and tertiary levels. The performance results will be analyzed in terms of productivity, equity, adequacy and excess for knowing whether these performance measures conflict with each other.