Ordinal priority approach

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Ordinal priority approach (OPA) is a multiple-criteria decision analysis method that aids in solving the group decision-making problems based on preference relations.

Contents

Description

Various methods have been proposed to solve multi-criteria decision-making problems. [1] The basis of methods such as analytic hierarchy process and analytic network process is pairwise comparison matrix. [2] The advantages and disadvantages of the pairwise comparison matrix were discussed by Munier and Hontoria in their book. [3] In recent years, the OPA method was proposed to solve the multi-criteria decision-making problems based on the ordinal data instead of using the pairwise comparison matrix. [4] The OPA method is a major part of Dr. Amin Mahmoudi's PhD thesis from the Southeast University of China. [4]

Decision-making components Decision Making components.jpg
Decision-making components

This method uses linear programming approach to compute the weights of experts, criteria, and alternatives simultaneously. [5] The main reason for using ordinal data in the OPA method is the accessibility and accuracy of the ordinal data compared with exact ratios used in group decision-making problems involved with humans. [6]

In real-world situations, the experts might not have enough knowledge regarding one alternative or criterion. In this case, the input data of the problem is incomplete, which needs to be incorporated into the linear programming of the OPA. To handle the incomplete input data in the OPA method, the constraints related to the criteria or alternatives should be removed from the OPA linear-programming model. [7]

Various types of data normalization methods have been employed in multi-criteria decision-making methods in recent years. Palczewski and Sałabun showed that using various data normalization methods can change the final ranks of the multi-criteria decision-making methods. [8] Javed and colleagues showed that a multiple-criteria decision-making problem can be solved by avoiding the data normalization. [9] There is no need to normalize the preference relations and thus, the OPA method does not require data normalization. [10]

The OPA method

The OPA model is a linear programming model, which can be solved using a simplex algorithm. The steps of this method are as follows: [11]

Step 1: Identifying the experts and determining the preference of experts based on their working experience, educational qualification, etc.

Step 2: identifying the criteria and determining the preference of the criteria by each expert.

Step 3: identifying the alternatives and determining the preference of the alternatives in each criterion by each expert.

Step 4: Constructing the following linear programming model and solving it by an appropriate optimization software such as LINGO, GAMS, MATLAB, etc.

In the above model, represents the rank of expert , represents the rank of criterion , represents the rank of alternative , and represents the weight of alternative in criterion by expert . After solving the OPA linear programming model, the weight of each alternative is calculated by the following equation:

The weight of each criterion is calculated by the following equation:

And the weight of each expert is calculated by the following equation:

Example

Decision problem of the example Decision Problem of the OPA.jpg
Decision problem of the example

Suppose that we are going to investigate the issue of buying a house. There are two experts in this decision problem. Also, there are two criteria called cost (c), and construction quality (q) for buying the house. On the other hand, there are three houses (h1, h2, h3) for purchasing. The first expert (x) has three years of working experience and the second expert (y) has two years of working experience. The structure of the problem is shown in the figure.

Step 1: The first expert (x) has more experience than expert (y), hence x > y.

Step 2: The criteria and their preference are summarized in the following table:

Experts’ opinions regarding criteria
CriteriaExpert (x)Expert (y)
c12
q21

Step 3: The alternatives and their preference are summarized in the following table:

Experts' opinions regarding alternatives
AlternativesExpert (x)Expert (y)
cqcq
h11213
h23121
h32332

Step 4: The OPA linear programming model is formed based on the input data as follows:

After solving the above model using optimization software, the weights of experts, criteria and alternatives are obtained as follows:

Therefore, House 1 (h1) is considered as the best alternative. Moreover, we can understand that criterion cost (c) is more important than criterion construction quality (q). Also, based on the experts' weights, we can understand that expert (x) has a higher impact on final selection compared with expert (y).

Applications

The applications of the OPA method in various field of studies are summarized as follows:

Agriculture, manufacturing, services

Construction industry

Energy and environment

Healthcare

Information technology

Transportation

Extensions

Several extensions of the OPA method are listed as follows:

Software

The following non-profit tools are available to solve the MCDM problems using the OPA method:

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References

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  41. ↑ Bouraima, Mouhamed Bayane; Qiu, Yanjun; Kiptum, Clement Kiprotich; Ndiema, Kevin Maraka (2022-08-17). "Evaluation of Factors Affecting Road Maintenance in Kenyan Counties Using the Ordinal Priority Approach". Journal of Computational and Cognitive Engineering. doi: 10.47852/bonviewJCCE2202272 . ISSN   2810-9503. Archived from the original on 2022-09-23. Retrieved 2022-09-19.
  42. ↑ Mahmoudi, Amin; Javed, Saad Ahmed (2023). "Uncertainty Analysis in Group Decisions through Interval Ordinal Priority Approach". Group Decision and Negotiation. 32 (4): 807–833. doi:10.1007/s10726-023-09825-1. ISSN   0926-2644. S2CID   258205868.
  43. ↑ Mahmoudi, Amin; Javed, Saad Ahmed (2023). "Strict and weak ordinal relations for estimating the criteria weights in Ordinal Priority Approach (OPA)". MethodsX. 11: 102389. doi:10.1016/j.mex.2023.102389. PMC   10542415 .
  44. ↑ Abdel-Basset, Mohamed; Mohamed, Mai; Abdel-monem, Ahmed; Elfattah, Mohamed Abd (2022-04-29). "New extension of ordinal priority approach for multiple attribute decision-making problems: design and analysis". Complex & Intelligent Systems. 8 (6): 4955–4970. doi:10.1007/s40747-022-00721-w. ISSN   2199-4536. PMC   9051802 . PMID   35505994. Archived from the original on 2022-09-23. Retrieved 2022-09-23.
  45. ↑ Du, Jun-Liang; Liu, Si-Feng; Javed, Saad Ahmed; Goh, Mark; Chen, Zhen-Song (2023). "Enhancing Quality Function Deployment Through the Integration of Rough Set and Ordinal Priority Approach: A Case Study in Electric Vehicle Manufacturing". IEEE Transactions on Engineering Management: 1–12. doi:10.1109/TEM.2023.3282228. ISSN   1558-0040.
  46. ↑ Irvanizam, Irvanizam; Zulfan, Zulfan; Nasir, Puti F.; Marzuki, Marzuki; Rusdiana, Siti; Salwa, Nany (2022). "An Extended MULTIMOORA Based on Trapezoidal Fuzzy Neutrosophic Sets and Objective Weighting Method in Group Decision-Making". IEEE Access. 10: 47476–47498. doi: 10.1109/access.2022.3170565 . ISSN   2169-3536. S2CID   248698791. Archived from the original on 2022-09-23. Retrieved 2022-09-19.
  47. ↑ Mahmoudi, Amin; Abbasi, Mehdi; Yuan, Jingfeng; Li, Lingzhi (7 September 2022). "Large-scale group decision-making (LSGDM) for performance measurement of healthcare construction projects: Ordinal Priority Approach". Applied Intelligence. 52 (12): 13781–13802. doi:10.1007/s10489-022-04094-y. PMC   9449288 . PMID   36091930.
  48. ↑ "Web-based solver". ordinalpriorityapproach.com. Retrieved 2022-10-15.
  49. ↑ Mahmoudi, Amin (2021-01-21), Excel-based solver, doi:10.5281/zenodo.4453887 , retrieved 2022-10-15
  50. ↑ Lingo-based solver, github.com, 2022-07-07, retrieved 2022-10-15
  51. ↑ "Matlab-based solver". www.mathworks.com. Retrieved 2022-10-15.
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