Who was the first to define Flow Shop / Job Shop problem?
Coffman and Demming's famous Operating Systems Theory, 1973, section on Job Shop and Flow Shop problems (pp. 123-128) cites Conway, Maxwell, and Miller, 1967 as &quot;a comprehensive treatment&quot; of Job Shop scheduling.  In the next paragraph, they introduce Flow Shop scheduling as a specialization of Job Shop, and cite

Johnson, S.M.; &quot;Optimal two- and three-stage production schedules with set-up times included.&quot;  Naval Research Logistics Quarterly, 1(1):61-68, 1954.

Naval Research Logistics Quarterly seems to be a Wiley pay-walled journal, but my library has a subscription to it.  Johnson's paper begins:

Let us consider a typical multistage problem formulated in the following terms by R. Bellman:
&quot;There are n items which must go through one production stage or machine and then a second one.  There is only one machine for each stage.  At most one item can be on a machine at a given time.
&quot;Consider $2n$ constants $A_i, B_i, i = 1, 2, \cdots, n$.  These are positive but otherwise arbitrary.  Let $A_i$ be the setup time plus work time of the $i$th item on the first machine, and $B_i$ the corresponding time on the second machine.  We seek the optimal schedule of items in order to minimize the total elapsed time.&quot;

He doesn't give the full reference to Bellman. Johnson's paper extends the definition in the obvious way to 3 machines.