I have scanned some materials at 600 dpi, ~ 9.36x12.67 inches and prepared in PostScript (PS) format.
Now when I try to transform PS to PDF with Ghostscript (GS),
You can set the used page size with -gNNNNxMMMM where NNMN is the width in pixels at 720 dpi (720 pixels == 1 inch), and MMMM is the height in pixels at 720 dpi.
Or you can set the custom size in PostScript points (72 points == 1 inch) with -dDEVICEWIDTHPOINTS=w -dDEVICEHEIGHTPOINTS=h.
If I'm not wrong, 9.36 inch ≈= 674 points and 12.67 inch ≈= 912 points.
You'll also have to apply -dPDFFitPage in order to fit your input onto the page.
So you could use either
gs \
-o output.pdf \
-sDEVICE=pdfwrite \
-dDEVICEWIDTHPOINTS=674 \
-dDEVICEHEIGHTPOINTS=912 \
-dPDFFitPage \
input.ps
or
gs \
-o output.pdf \
-sDEVICE=pdfwrite \
-r600 \
-g8112x7596 \
-dPDFFitPage \
input.ps