Monotone bounds on the productivity of fixed-cycle production lines

This research analyzes a class of fixed-cycle production lines. The main concern is the productivity of the lines. Productivity is defined to be the average number of items produced per unit time in the long run. Closed form solutions are derived for the productivity of a two-machine line with dependent machines. These solutions are used to obtain bounds on the productivity of longer lines. The transition matrix associated with an N-machine line is shown to be stochastically monotone yielding monotone increasing lower bounds and monotone decreasing upper bounds which converge to the productivity of the line. These results are then extended to include lines with Markov machines. With the transition matrix in this case having a conditional monotone property, the monotonicity of the bounds is maintained.