Branch and bound algorithm for ordering of tandem constant-service stations

We study tandem ordering of constant-service stations with unlimited buffers and arbitrary arrival process where service at each station adds a certain value to the job. The goal is to order the stations such that the total expected value of the jobs in the system or, equivalently, the work-in-process inventory cost is minimized. Assuming that the added value-service length ratio increases with the service length, we provide a branch and bound method that finds an optimal order.