Approximate performance analysis of CONWIP disciplines in unreliable non homogeneous transfer lines

For a given choice of the maximum allowable total storage parameter, the performance of constant work-in-process (CONWIP) disciplines in unreliable transfer lines subjected to a constant rate of demand for parts, is characterized via a tractable approximate mathematical model. For a (n−1) machines CONWIP loop, the model consists of n multi-state machine single buffer building blocks, separately solvable once a total of (n−1)2 unknown constants shared by the building blocks are initialized. The multi-state machine is common to all building blocks, and its n discrete states approximate the joint operating state of the machines within the CONWIP loop; each of the first (n−1) blocks maps into a single internal buffer dynamics, while the nth building block characterizes total work-in-process (wip) dynamics. The blocks correspond to linear n component state equations with boundary conditions. The unknown (shared) constants in the block dynamics are initialized and calculated by means of successive iterations. The performance estimates of interest—mean total wip, and probability of parts availability at the end buffer in the loop—are obtained from the model and validated against the results of Monte Carlo simulations.