We consider the optimal control of two parallel servers in
a two-stage tandem queuing system with two flexible servers.
New jobs arrive at station 1, after which a series of two
operations must be performed before they leave the system. Holding
costs are incurred at rate h1 per unit time
for each job at station 1 and at rate h2 per
unit time for each job at station 2.
The system is considered under two scenarios; the collaborative
case and the noncollaborative case. In the prior, the servers
can collaborate to work on the same job, whereas in the latter,
each server can work on a unique job although they can work
on separate jobs at the same station. We provide simple conditions
under which it is optimal to allocate both servers to station
1 or 2 in the collaborative case. In the noncollaborative case,
we show that the same condition as in the collaborative case
guarantees the existence of an optimal policy that is exhaustive
at station 1. However, the condition for exhaustive service
at station 2 to be optimal does not carry over. This case is
examined via a numerical study.