Dear Eng. Hamida,

Since one objective is more important than other, you may use weighted sum of the two objectives and assign a wight of one as a multiple of the other.

Otherwise, you can select one method from the following:

-Aggregated Indices Randomization Method (AIRM)

-Analytic hierarchy process (AHP)

-Analytic network process (ANP)

-Best worst method (BWM)

-Characteristic Objects METhod (COMET)

-Choosing By Advantages (CBA)

Regards,

Mahmoud

Thanks, Dr/Mahmoud

i thought about weighted some by i have troubled in understanding how to calculate factors and if i solve in how many points to optain pareto optimal solutions

if you could help, I appreciate this

thanks again

Could you send me your problem?

My problem simply is to

Min z1=manufactruing costs and Max z2=overall quality index

I want to assign higher importance to the quality index

hi Hamida

you must send your objective function to minimize and to maximize in details with their different parameters and if you have constraints also on these parameters i mean complet objective functions

you can also try compromise programming approach

In the general case, the decisions maker iteratively modifies the weights observing the behavior of the optimization criteria and incrementing that criterion that in his opinion must to be decresed (while minimizing). By the way, the obtained points of the efficient solutions are being found (or Pareto from). In the case of two single objectives this is very easy to make. The problem emerges when there an important number of criteria exists.

In your particular case, you can optimize the quality índicator and to restrict the cost to it desirable value.

Dear Hamdia

It looks that you have two conflicting objectives since minimizing manufacturing costs ( Z1) and maximizing quality normally (Z2) are opposite.

However,  I am confused because you are talking about optimization using MCDM techniques, when NONE OF THEM can guaranty optimality, but compromise..

If you use Goal Programming most probably you will find a Pareto efficient solution, not a compromise or satisfying one

Thanks for all

but i think that i am not sure that i understand what you  mean as it is the first time to work on bi-objective.

I ask(as in main quesstion) for any useful material about transfering bi-objective to single and what is pareto solution or pareto optimal

Thanks again For All

It is right, it is required to look for a compromise solution. In general, as optimization under multiple criteria is understood the science of finding a commitment solution (efficient, non dominated). It could even be required to find a population of solutions close to the best commitment corresponding to the used model. The solutions population could be subjected to simulation by a more complex model or to constitute proposals for the more span system, among those this last one must select that solution that satisfies in the best way it objective.

Weighted factor score is usually fine, but determining the  weights needs some attention. Weights alone are not sufficient, as the weights need to be multiplied by the score on each of the criteria to determine the overall impact. 

For both objectives (manufacturing costs and quality) you will have a scale to measure them - obviously for costs it is dollars, for quality it will be some index.

My suggestion: determine how much additional money you are willing to pay for an increase of one unit of quality. Then use that to determine the weights.

The above is sufficient is you value an increase in quality from index 1 to index 2 as equal to an increase of 9-10. If not, your preferences are not linear and you need to use a method that deals with non-linear preferences.

Hamdia

If you are concerned with weights determination, you can use entropic weights which are not subjective , because are produced by the data itself, and in addition easy to compute in Excel. In the other hand, these weights, as opposite as weights found by any other procedure, truly represent the capacity of a criterion to evaluate alternatives, which is not the case in subjective weights which only indicate importance between criteria.

If you need assistance for entropic weights determination, let me know it.

Assigning weights to objectives based on the intuitive notion of their importance is known in the MCDM literature: "the most coomon critical mistake"!

Jan Telgen has already provided some essential insights about this mistake.

You should study MCDA methods in order to assign them,

Article Common Mistakes in Making Value Trade-Offs

Hamdia,

I think you are looking for a bi-level formulations and pareto optimal solutions. you would be interested in Jagannatha Rao's work at university of houston www.me.uh.edu/faculty/rao 

Farrokh Mistree and others are also stalwarts in this field.

Good Luck,

Chakradhar

Hamdia,

I think you can use Swing weights for this purpose. See Kirkwood "Strategic Decision Making: Multiobjective Decision Analysis with Spreadsheets"

Dear,

For providing weights to factors you can implement AHP or MDL approach , Following paper may be helpful for you:

Implementation of fuzzy TOPSIS methodology in selection of procedural approach for facility layout planning

Parveen Sharma