As per,

PMBOK Page no. 83 "Direct and Manage Project Execution"

Bullet No. 10 (i.e. line no 13, exculding paragraph header, in the page 83)

 - Manage Sellers and Suppliers

PMBOK Page no. 335 "Administer procurements"

First line of the Section (i.e. line no 6, exculding paragraph header, in the page 335)

 - Administer procurements is the process of managing procurement relationships....etc. etc.

So vendor management occurs in two process groups.

Lets assume the question describes that we are resolving a delivery issue or a schedule issue, then as per PMBOK both the processes are equally plausible? How do you determine which one of the process we are in precisely.