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Weighted Product Method in Multi Criteria Decision Making
Introduction
Within the domain of decision−making, there are often multiple criteria that have to be considered at the same time. Whether it's selecting an unused item to dispatch, choosing a venture procedure, or making an individual choice, assessing and positioning choices based on different components can be a complex assignment. Multi−Criteria Decision Making (MCDM) strategies offer an organized approach to handling such issues. One such strategy is the Weighted Product Method (WPM), which gives an orderly way of consolidating preferences and weighting criteria to reach at the last choice. In this article, we'll dig into the complexities of the Weighted Product Method, exploring its key components, preferences, impediments, and real−world applications.
Understanding the Weighted Product Method (WPM)
The Weighted Product Method could be a multi−criteria decision−making procedure that facilitates the comparison and positioning of options based on numerous criteria. It takes a step-by-step process, empowering decision−makers to relegate weights to each measure and after that apply these weights to assess the options.
Step 1: Criteria Identification and Choice
The primary step within the WPM is to recognize and select the pertinent criteria that will be utilized to survey the choices. These criteria should be quantifiable, commonly selected, and collectively thorough. For case, when evaluating potential job offers, criteria such as compensation, area, company culture, and career development openings might be considered.
Step 2: Normalization of Criteria
Once the criteria are built up, it is basic to normalize them to guarantee that they are on the same scale. This step is significant since distinctive criteria might have distinctive estimation units or ranges. Normalization involves changing each basis into a dimensionless value, typically between and 1, where represents the worst value, and 1 speaks to the best value. A few normalization procedures can be utilized, such as min−max normalization, z−score normalization, or linear normalization.
Step 3: Weight Assignment
After normalization, decision−makers relegate weights to each basis based on their relative significance or inclination. These weights speak to the significance of each basis within the decision−making preparation. The entirety of the weights ought to rise to 1, indicating the relative importance of each model within the by and large assessment. The weights can be doled out subjectively by the decision−maker or determined through more formal forms like Analytic Hierarchy Process (AHP) or coordinate ratings.
Step 4: Weighted Product Calculation :
In this step, the weighted item for each alternative is computed by duplicating the normalized esteem of each model by its comparing weight. The item is calculated for each elective, and the choices are positioned based on their coming about weighted item values. The elective with the most noteworthy weighted product value is considered the foremost favorable choice.
Example
#import the required library
import numpy as np
#create the matrix
decision_matrix = np.array([
[5, 7, 9],
[6, 8, 4],
[9, 7, 6],
[4, 6, 8]
])
weights = np.array([0.4, 0.3, 0.3])
normalized_matrix = decision_matrix / decision_matrix.sum(axis=0)
weighted_matrix = normalized_matrix * weights
weighted_product = np.prod(weighted_matrix, axis=1)
normalized_weighted_product = weighted_product / weighted_product.sum()
rankings = np.argsort(normalized_weighted_product)[::-1]
for rank, alternative in enumerate(rankings, start=1):
print(f"Rank {rank}: Alternative {alternative}")
Output
Rank 1: Alternative 2 Rank 2: Alternative 0 Rank 3: Alternative 3 Rank 4: Alternative 1
Advantages of the Weighted Product Method
Simplicity and Ease of Execution: The Weighted Product Method is generally direct to get it and actualize, making it open to decision−makers with shifting levels of skill in choice hypothesis.
Adaptability: WPM permits decision-makers to relegate weights subjectively based on their inclinations or utilize more organized strategies for weight assurance, such as AHP. This adaptability makes the strategy versatile to a wide run of decision−making scenarios.
Straightforwardness: The WPM gives a straightforward preparation for decision−making, permitting partners to get the basic components and the relative significance doled out to each basis. This straightforwardness can improve belief and acknowledgment of the ultimate choice.
Computational Effectiveness: Compared to a few other MCDM strategies, the WPM is computationally productive. It includes basic numerical calculations and does not require broad computational assets, making it appropriate for quick decision−making processes.
Limitations of the Weighted Product Method
Subjectivity in Weight Task: The assignment of weights may be a subjective preparation and depends on the decision−maker's judgment. Distinctive decision−makers may relegate distinctive weights to the same criteria, possibly driving to varieties within the last choice.
Lack of Consensus: In circumstances where there are numerous decision−makers included, coming to an agreement on the weights can be challenging. Dissimilar conclusions and inclinations may make differences, preventing the adequacy of the WPM.
Affectability to Criteria Normalization: The WPM intensely depends on the normalization of criteria. In case the normalization handle is imperfect or biased, it can impact the ultimate rankings and compromise the judgment of the decision−making prepare.
Real−World Applications
The Weighted Item Strategy has found various applications in different spaces, counting:
Venture Selection: When organizations have multiple project recommendations, the WPM can be utilized to assess and rank them based on predefined criteria such as productivity, achievability, and arrangement with organizational targets.
Supplier Choice: When selecting providers, decision−makers can utilize the WPM to evaluate diverse providers based on variables such as price, quality, reliability, and conveyance time.
Product Plan: In item improvement, the WPM can be utilized to assess and prioritize plan options based on criteria such as usefulness, taken a toll, aesthetics, and user−friendliness.
College Admissions: Colleges can receive the WPM to evaluate and rank candidates based on different criteria like scholarly execution, extracurricular exercises, proposal letters, and individual explanations.
Conclusion
The Weighted Product Method may be a flexible and natural approach to multi−criteria choice making. By allotting weights to criteria and calculating the weighted product, decision−makers can efficiently assess and rank choices in a straightforward and proficient way. Whereas the WPM offers a few focal points such as effortlessness and adaptability, it is basic to consider its impediments, such as subjectivity in weight task. By understanding its intricacies and applying it judiciously, the Weighted Product Method can be a profitable device for decision−makers over different businesses and spaces.
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