Flexible Servers in Understaffed Tandem Lines

We study the dynamic assignment of cross-trained servers to stations in understaffed lines with finite buffers. Our objective is to maximize the production rate. We identify optimal server assignment policies for systems with three stations, two servers, different flexibility structures, and either deterministic service times and arbitrary buffers or exponential service times and small buffers. We use these policies to develop server assignment heuristics for Markovian systems with larger buffer sizes that appear to yield near-optimal throughput. In the deterministic setting, we prove that the best possible production rate with full server flexibility and infinite buffers can be attained with partial flexibility and zero buffers, and we identify the critical skills required to achieve this goal. We then present numerical results showing that these critical skills, employed with an effective server assignment policy, also yield near-optimal throughput in the Markovian setting, even for small buffer sizes. Thus our results suggest that partial flexibility is sufficient for near-optimal performance, and that flexibility structures that are effective for deterministic and infinite-buffered systems are also likely to perform well for finite-buffered stochastic systems.