Two Approximations as a Basis for the Optimization of Production in Unreliable Markovian Long Transfer Lines

Abstract

Optimizing buffer sizes in manufacturing transfer lines has been a long standing problem. By providing some amount of decoupling between various production stages, parts buffering can significantly help increasing manufacturing productivity in the face of potential individual machine failures and part processing time variability. However, buffering comes at a cost, both in terms of occupied space and frozen capital within the plant. Transfer line decomposition methodologies have aimed, among other goals, at simplifying the analysis of this question. Two approximations, the machine decoupling approximation and the socalled demand averaging principle, are presented. They lead to a characterization of the transfer line, when controlled via a class of KANBAN like production policies, as a collection of isolated failure prone machines with random failures described by recursively coupled statistical parameters. Subsequently, the well developed single machine theory can be used as a building block in the analysis and optimization of the line. The approximations are tested via regenerative Monte Carlo simulation, and illustrative dynamic programming based transfer line optimization results are reported.