AN EXTREMAL PRODUCTION-LINE PROBLEM.

Let G_i, ,G_r be groups of n₁, , n_r workers on a production line, all members of G₁ performing identical operations in the time t₂, on entities drawn (repeatedly) from a pool P. When the production line starts all members of G₁ are put to work at the time T₁, and some time thereafter all members of G₂ are put to work at the time T₂, etc. We assume that n₁/t₁ = =n_r/t_r  R Let d_j = g c d (n_j-1, n_j) We prove the theorem Let T_j-1=0 Then T_j = (n_j-1+n_j-d_j)/R is the earliest time at which G_j can be put to work so that supply for G_j is at any time greater than or equal to demand (j=2, ,r). [ABSTRACT FROM AUTHOR]