Loading in 2 Seconds...
Loading in 2 Seconds...
Modeling and Analysis of High Volume Manufacturing Systems. Discrete vs. Continuous Flow and Repetitive Manufacturing Systems (Figures borrowed from Heizer and Render). Operation Process Chart Example for discrete part manufacturing (borrowed from Francis et. al.).
Assembly Line 1: Product Family 1
Fabrication (or Backend Operations)
Assembly Line 2: Product Family 2
& mixThe product-process matrix
High volume, high
Few major products,
Remark:The above performance measures essentially provide a link between the directly quantifiable and manageable aspects and attributes of the considered operational environments and the primary strategic concerns of the company, especially those of responsiveness and cost efficiency.
Station 3KANBAN-based production lines
MmThe G/G/1 model
any additional non-processing time
te = E[T] = to / A or equivalently re = 1/te = A (1/to) = A ro
Which is very high!
(the same as before)
Which is low!
E[S] = tS / NS ; Var[S] = (S2 / NS) + tS2((NS-1) / NS2);
te = E[T] = to+tS / NS ; ;
Flexibility can reduce variability.
Shorter, more frequent setups induce less variability.
MTTR ~ expon.
MTTR ~ expon.
Ca2=1.0Example: Employing the presented results for line diagnostics
Desired throughput is TH = 2.4 jobs / hr but practical experience has shown that it is not attainable by this line. We need to understand why this is not possible.
i.e., the long outages of M1, combined with the inadequate capacity of the interconnecting buffer, starve the bottleneck!
This option is dominated by the previous one since it presents a higher CT and
also a higher deployment cost. However, final selection(s) must be assessed and validated through simulation.
Mean Value Analysis - the key underlying ideas:
A CONWIP-based flow line with single-machine stations and its WIP level set to W, can be modeled by a closed queueing network (CQN) with general processing distributions, W jobs in it, and the following structure:
II. In a CQN with W jobs and exponential processing times, the expected number of jobs observed at the various stations by a job arriving at some station Sj, is equal to the expected number of jobs observed at any random time at the same stations when the system is operated with W-1 jobs in it.
III. Assuming that this effect applies in an approximate sense for more general distributions of the processing times, we proceed to develop an algorithm that will compute the performance measures of interest iteratively, for various W levels, starting with W=0.
n = number of stations
te(j) = mean effective processing time at station j
ce2(j) = SCV for effective processing time at station j
TH(W) = the line throughput when operated with WIP level W
CT(W) = expected job cycle time through the line
CTj(W) = expected job cycle time at station j when the WIP level is W
WIPj(W) = expected WIP level at station j when the WIP level is W
uj(W) = utilization of the server at station j when the WIP level is W
CTj(W) = E[remaining processing time for the job at the server of Sj] +
(E[number of jobs at station Sj]-E[number of jobs in service])te(j) +
E[remaining processing time for the job at the server of Sj] =
Prob(Server of Sj busy)E[remaining process time | busy] =
uj(W-1)E[remaining process time | busy]
(b) E[number of jobs at station Sj] WIPj(W-1)
E[number of jobs in service] uj(W-1)
(d) uj(W-1) = TH(W-1) te(j)
Combining the results of the previous slide:
Obviously, for W=0, CT(0) =TH(0) = WIPj(0) = 0
Furthermore, application of the above formulae for W=1 gives:
(from Little’s law)
CT=To=5Example: Attaining the throughput upper bound with balanced, deterministically paced line
T = 0
T = 6
T = 12
T = 18
T = 24
TH = W / (W To) = 3 / 24= 1 / 8
Ideal Operational Point
Remarks: As expected, TH(1) = rb/Wo =1/To and TH() = rb. A performance that is worse than that of the “benchmark” case is a strong indication of mismanagement / bad practice.
WEffective Mechanisms for Improving the System Performance
The problem: Given a line operating at a desired throughput rate, TH, what are some possible mechanisms to reduce the expected cycle time through the line, CT (and through Little’s law, the line WIP, W) ?
The key idea: We need to “pull” the curve describing the line performance in the W-TH(W) space to the left.
(i) Increase rb(by adding capacity or making more effective use of the existing capacity at the line bottleneck(s))
(ii) Add capacity to some non-bottleneck station(s) (this addition essentially enables the better catering to the bottleneck needs, but it can help only to a limited extent)
(iii) Reduce the inherent variability at the different stations; the corresponding reduction of the station CVs will “pull” the performance curve in the W-TH(W) space closer to the curve characterizing the upper bound.
(iv) Increase the line flexibility, which essentially enables the better utilization of the bottleneck capacity (and takes us back to item (i) above).