ABSTRACT
The ROV method, developed by Yakowitz et al. [1], is a simple MCDM approach with uncomplicated mathematical formulations, and is applied for ranking of the competing alternatives from the best to the worst based on a set of conflicting criteria. Its application involves the following procedural steps [2, 3]:
Step 1: Development of the Initial Decision Matrix: https://www.w3.org/1998/Math/MathML"> X = [ x i j ] m × n = [ x 11 x 12 … x 1 n x 21 x 22 … x 2 n … … … … x m 1 x m 2 … x m n ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377030/d9605bd9-7b4d-4c40-a5a9-8fc61b88ce2e/content/math19_231_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
where; xij is the performance of i th alternative (i = 1, 2, …, m) for j th criterion (j = 1, 2, …, n).
Step 2: Normalize the Decision Matrix: Depending on the type of the criterion under consideration, the following equations can be adopted to convert all the entities of the decision matrix into dimensionless elements.
for Beneficial Criterion: https://www.w3.org/1998/Math/MathML"> r i j = [ x i j − min ( x i j ) ] / [ max ( x i j ) − min ( x i j ) ] ( i = 1 , 2 , … , m ; j = 1 , 2 , … , n ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377030/d9605bd9-7b4d-4c40-a5a9-8fc61b88ce2e/content/math19_231_2_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
for Non-Beneficial (Cost) Criterion: https://www.w3.org/1998/Math/MathML"> r i j = [ max ( x i j ) − x i j ] / [ max ( x i j ) − min ( x i j ) ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377030/d9605bd9-7b4d-4c40-a5a9-8fc61b88ce2e/content/math19_231_3_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
Step 3: Determine the Best and the Worst Utility Functions: In this step, the best and the worst utility functions of each alternative are separately computed taking into consideration both the beneficial and cost criteria. Utility functions for beneficial criteria ( https://www.w3.org/1998/Math/MathML"> u i + https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377030/d9605bd9-7b4d-4c40-a5a9-8fc61b88ce2e/content/math19_235_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ) and cost criteria ( https://www.w3.org/1998/Math/MathML"> u i − https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377030/d9605bd9-7b4d-4c40-a5a9-8fc61b88ce2e/content/math19_235_2_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ) are calculated based on the following equations: https://www.w3.org/1998/Math/MathML"> M a x i m i z e : u i + = ∑ j = 1 n w j × r i j https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377030/d9605bd9-7b4d-4c40-a5a9-8fc61b88ce2e/content/math19_232_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> M a x i m i z e : u i − = ∑ j = 1 n w j × r i j https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377030/d9605bd9-7b4d-4c40-a5a9-8fc61b88ce2e/content/math19_232_2_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
where; wj is the weight of j th criterion.
To rank the alternatives, the average utility function (ui ) is estimated. The best alternative should have the maximum value of ui . https://www.w3.org/1998/Math/MathML"> u i = u i + + u i − 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377030/d9605bd9-7b4d-4c40-a5a9-8fc61b88ce2e/content/math19_232_3_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
