Color matching

"Therefore, I was trying to understand where does the color changes throughout this process ( is it scanner , image storing or printing problem)?"...

When you have a printed sample and you scan it, the resulting scan depends on the capture RGB.  Often you'd take the scan into Photoshop and, based on the result vs. the original vs. an initial print, you'd adjust the image to closer values to the original.  Scanners come with a software scan application that allow you to use a particular RGB to tag your scan.  Mine is set to Adobe RGB because I work predominantly in print, graphic arts not photographic.

In your case, I would recommend you scan using different profiles.  Open each scan and print them without any adjustments.  The prints will tell you which one to use in capturing the type of original you are working with.  You have not specified what scanner, what printer, etc., so the missing information leaves us a bit handicapped in recommending any particular course of action.

It requires a bit of experimentation on your part.  But, when you look at an image on your monitor, it is considered transmissive light ( sort of like looking at a color transparency on a light box with very little ambient light ).  You will see color that, in most cases, cannot be replicated in a print which is considered a reflective light source.  That in itself explains why some color on the monitor does not look the same in a print.  You did not mention the type of printer used, the type of paper used, and the application's color settings.

"Also, I understand that a digital image is stored in RGB format, whereas print consists of CMYK colors. Nevertheless, I was wondering is it possible to make some scanner, monitor and printer calibration or do something else to print in the original color?"

Not always.  Some images can be stored as CMYK with an embedded profile.  But, you are asking some very comprehensive questions that cannot be easily explained here.  For instance, I just printed a card in which I had to match a sample of Red that was probably printed with an offset press using a spot color.  The only way I could come anywhere near that Red was to export my file out of Illustrator as an RGB tif @150ppi. No RGB color tag applied.  Then, I opened the tif in Photoshop and assigned it a "Pro Photo RGB" profile and printed the RGB file on glossy paper.  When I place the original card next to my print I can see a very close but not exact match.  I could do this because I am using a closed loop work space.  And I am using an 11 cartridge inkjet proofer to print on glossy paper.  In short, there is no way I am ever going to match that original card that has been printed using spot color.  But, I can come close.

I suggest you give us some more specific information like the paper used, and the printer used.  Then, maybe you can follow what I did or we can help you with a work around.