Approximate analysis of production systems

Abstract

In this paper complex production systems are studied where a single product is manufactured and where each production unit stores its output in at most one buffer and receives its input from at most one buffer. The production units and the buffers may be connected nearly arbitrarily. The buffers are supposed to be of finite capacity and the goods flow is continuous. For such networks it is possible to estimate the throughput by applying repeated aggregation over the production units. The approximation appears to be best when the network shows some resemblance with a flow line.

Assembly/Disassembly Systems: An Efficient Decomposition Algorithm for Tree-Structured Networks

“…In the innermost, p..(i.m) or pAi,m) is chosen to satisfy conservation of flow (11) (among all the two-machine lines except the last line encountered), or flow rate-idle time (13), or it is determined by boundary conditions (35). The evaluation sequence is followed in this process.…”

“…Most of these authors considered only infinite-buffer systems, and most contemplated the application of their work to computer systems and not to manufacturing systems. More general structures were treated by Baccelli, Massey, and Towsley [5], de Koster [13], [14], Liu and Buzacott [28], Adan and…”

“…The algorithm alternatively follows the evaluation sequence forward and reversed. In the forward direction, it calculates exactly half of the r; and 'd parameters using (14) and (15) and half of the p; and Pd parameters using (13). The quantities that it calculates are those of the first machine encountered of each two-machine line following the sequence forward.…”

A Petri net model for the operational design and analysis of segmented flow topology (SFT) AGV systems

“…To overcome this di culty approximation procedures aggregating the routeing probabilities and the processing times are applied. Sometimes the systems are described as open queueing models (De Koster 1988) while in many instances the standard product-form closed queueing network (CQN) is used for such purposes. Tanchoco et al 1987 applied CQN to determine a lower bound on the required number of transportation vehicles.…”

Performance Evaluation Models for Single-Item Periodic Pull Production Systems

“…The entries of the resulting one-step transition probability matrix M are as follows:N m[Ef(k -1), Ef(k)] = , ((P(k -l))P[D5(k -1) = dS?IIN+ 1(k -1)] HI P[Pj(k -1) = pYIOJ{k -1)] (9) M = {P(k -1) = [Pl(k -05 ...,5 PN(k -1)5 Ds(k -1)]: O< P jk-1) Oj(k-1), 1 < Nj N,O < Ds(k-1)I+ < in+ (k-1)}(10) :(P(k -1)) = if P(k 1) causes a transition from Ef(k -1) to Ef(k) -) =0 otherwise (1. In this formulation, the limiting distribution of the states of the system X could be found (if it exists) by solving the stationary equations of the Markov chain under consideration with the following boundary condition imposed: RM= n and n:eT = 1(12) where e is a row vector with all elements equal to one, and X is the unique solution of the aboveequations. A discussion on the variety of methods to compute the stationary probabilities of large Markov chains can be found in Philippe et al27 and Baruh and Altiok28.…”