what, this one?

Soprano with Piano Obligato & orchestra.

the atual orchestration, you have to look up yourself.

Simple, it's orchestration. If the arrangement is for smaller groups or solo instruments with or without piano, it might be called instrumentation.

Orchestration is best described as composing or otherwise arranging music for an orchestra to play. It is also used when one manipulates arrangements to make something happen.

# Co-ordinate. # Arrange for orchestra.

http://en.wikipedia.org/wiki/West_side_story scroll down to "Orchestration"