Mathematical Problems in Engineering
Volume 1 (1995), Issue 2, Pages 95-137

Mathematical theory of improvability for production systems

David Jacobs and Semyon M. Meerkov

Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor 48109-2122, MI, USA

Received 15 October 1994

Copyright © 1995 David Jacobs and Semyon M. Meerkov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A mathematical model for continuous improvement processes in production systems is formulated. Both constrained and unconstrained cases are addressed. A solution for the case of a serial production line with finite buffers and a Bernoulli model of machines reliability is given. In particular, it is shown that a production line is unimprovable under constraints if each buffer is on the average half full and each machine has equal probability of blockages and starvations. Based on this result, guidelines for continuous improvement processes are formulated.