There are 4 options with the different distance and carbon footprint value (as per in attachment). What is the method that can be used to choose the best minimum value for both distance and carbon footprint from those 4 options.
Individually the minimum distance is Option 4, but the minimum carbon footprint is Option 3. How can the option be selected by considering both distance and carbon footprint in that data set?
Hi,
Interesting question,
So, in the 1st column you have minimum value at the 4th row, and in the 2nd column you minmum value at the 3rd row, and you are asking how to choose the most optimum option by combining both values of each option.
I suggest that you first normalize the 1st column (A) and 2nd column (B). Then, you add column 1 and column 2 of each option. By doing this, you should get 4 values ( i.e. 1 value per row). Hence, the minimum value should be the most optimum value.
If any one who reads the answer can relate this method to any reference in literature, this would be great.
Dear Al Amin bin Mohamed Sultan,
This problem represents a Multi-Criteria-Decision-Making (MCDM) situation in which there are several alternatives (options) with different values in some criterion.
There are plenty of methods for MCDM. They are classified in two groups based on the dependency between the criterion. For example, AHP, TOPSIS, VIKOR, weighted-sum, etc. are among the methods in which the criterion are independent. On the contrary, ANP is an appropriate method for problems with dependent criterion.
For your simple problem, I would suggest to use weighted-sum method. In this method, you define a weight for each criteria. This weight shows how much important is that criteria in your opinion. If you are not sure about the correct weight, you can simply give similar importance to both of them.
Since the Distance and Carbon Foot Print have different scales, you should normalize them before proceeding. For doing so, every score of alternatives in each criteria should be divide into the sum of values on that criteria.
In the next step, every normalized score is multiplied by its corresponding weight. Sum of the products for each option is the final score of that option. Since both the criterion have negative aspect, the minimum final score shows the best option.
I have made the above calculations on your data with identical weights. You will find the results in attachment.
Here is the final ranking:
Option 3 > Option 1 > Option 2 > Option 4
Please note that the Carbon Foot Print in Option 4 is much greater than the other Options.
You can change the weights to see what will happen.
Hope the above explanations are sufficient.
Should you need any reference for MCDM methods, do not hesitate to ask me.
Kind regards,
Omid
Thanks a lot Mr Omid Amirtaheri. I have additional question about normalising the weightage which had been sent to your inbox. And yes, if you can suggest any reference that relates my case?
Try with the data Envelopment Analysis, which does not require normalizatioin of data and allows selecting a pareto-optimal solution under conflicting objectives. Thanks to the assurance regions you can also give more relevance to one of these criteria.However you would need more than 2 evaluating criteria.
Dear Martin Romauch & N. Epicoco,
Thanks for your comments. I would like to draw your attention to the difference between Multi-objective decision-making (MODM) and Multi-attribute decision-making (MADM).
Although both the above methods are classified as Multi-Critera decision making (MCDM) techniques, they have different applications in real world problems.
Please have a look at below link:
https://www.researchgate.net/post/MODM_vs_MADM_An_example_comparing_multi_attribute_and_multi_objective_decision_making
The methods based on Pareto approach are applied to the problems in which we have multiple conflicting objectives. In the problem described by Al Amin bin Mohamed Sultan, there is no evidence showing that Distance and Carbon Foot Print are conflicting objectives. Therefore, they should be considered as Criteria instead of Objective.
I hope the above comment is clear enough.
Kind regards,
Omid Amirtaheri
agree with suggestion by Martin and N.Epicoco.
Pareto optimality does not require conflicting objectives. Pareto optimality principle means that, any one of two or possibly more objective functions can be chosen as the unique target function, while all remaining are considered as constraints. In such a case Pareto optimal solution can be found by introducing Lagrangian multipliers for constraints.
Dear Al Amin bin Mohamed Sultan,
As requested, please find enclosed the formulation of weighted sum method,
Regards,
Omid Amirtaheri
Dear sir,
You can try multi-objective function methods which use pareto for finding optimum values.
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