A note on optimal order of M machines in tandem with blocking

The author considers a flowshop of machines with no intermediated storage between two successive machines. The problem is to find the permutation of machines which will maximize the throughput. Based on the method of branching, it is shown that for the case of four machines the optimal order is to arrange the two slowest machines in the first and last positions and the two fastest machines in the middle positions and the fastest one next to the slowest one, provided the processing times on the machines are comparable in the sense of stochastic ordering