Cooperative flow dynamics in production lines with buffer level dependent production rates

Abstract

We study, in the fluid flow framework, the cooperative dynamics of a buffered production line in which the production rate of each work-cell does depend on the content of its adjacent buffers. Such state dependent fluid queueing networks are typical for people based manufacturing systems where human operators adapt their working rates to the observed environment. We unveil a close analogy between the flows delivered by such manufacturing lines and cars in highway traffic where the driving speed is naturally adapted to the actual headway. This close analogy is thoroughly explored. In particular, by investigating the dynamic response of small perturbations around free flow stationary regimes, we can draw a "phase diagram". This diagram exhibits two different flow patterns, namely the free and jamming production regimes. The transitions between these regimes are tuned by the production control parameters (i.e. the buffer capacities, the reaction sensitivity, the control sampling time, . . . ). We finally extract a dimensionless dynamic parameter directly relevant for design purposes.

A tuning strategy to avoid blocking and starving in a buffered production line

“…1 This response is widely used in the field of control theory (Nise, 1995). It was recently reported that a buffered production line has the same dynamics as the OV traffic model (Radons and Neugebauer, 2003;Filliger and Hongler, 2005). Blocking and starving in the production line correspond to the stopand-go phenomenon of the OV model.…”

“…1, based on a previous study (Filliger and Hongler, 2005). This line consists of N work cells, where each cell has one machine and one buffer.…”

“…Previous studies (Filliger and Hongler, 2005;Nagatani and Helbing, 2004) assumed work cells to be identical. Thus, the sufficient condition for smooth production flow (i.e., no-jam flow) was somewhat conservative.…”

“…The production line has one piecewise linear function and is a simplification of a model proposed in (Filliger and Hongler, 2005). The main purpose of the present paper is to provide a strategy to avoid blocking and starving in the production line.…”

“…This analogy is useful for studying the production line dynamics. On the basis of the no-jam condition of a traffic model (Konishi et al, 1999a), Filliger and Hongler derived a sufficient condition under which blocking and starving never occurs in the production line (Filliger and Hongler, 2005), and Nagatani and Helbing provided a stability condition of linear supply chains and compared five strategies for stabilizing supply chains (Nagatani and Helbing, 2004).…”