A proof of production line reversibility

Abstract

A production line is a series arrangement of k work stations. Each production item passes through all of the stations in sequence. The service time for a single item at station j is assumed to be a random variable. In this mode of operation any station will at any time be either busy, or idle, or blocked. A measure of the productivity of such a line is its mean production rate r. It has been conjectured that the production rate remains invariant under reversal of the production line. Line reversal means that every item passes through the stations in the reverse order, that is, beginning with station k and ending with station 1. A summary of a general proof of the reversibility property is given.