Store - Order Problem
Your problem is essentially the same as set cover, a classical NP-complete problem.

In set cover, we are given sets $S_1,\ldots,S_n$ together covering a universe $U$, and the problem is to find the smallest subset that still covers $U$. The only difference between this and your problem is that you want to cover some $V \subseteq U$. You can get the classic formulation by intersecting all sets with $V$.