Inventory based allocation policies for flexible servers in serial systems

Motivated by an industry example, we study a two-station serial system in which we allocate flexible servers in order to maximize throughput. We investigate two cases which are different in the way that servers work together when at the same station; namely collaboratively or non-collaboratively. For the collaborative case we prove the optimal policy to be such that the servers work together at a single station at any point in time. In addition to the policy being state-dependent, it also follows a switching-curve structure. In the non-collaborative case, on the other hand, it may be optimal to allocate servers to different stations. Some numerical examples and results regarding policy assignments, switching curves, and system throughput are presented.