Production Systems Engineering for

Factory Floor Management

Lecture 4: BOTTLENECK IDENTIFICATION

AND ELIMINATION

Semyon M. Meerkov, University of Michigan

Jingshan Li, University of Wisconsin – Madison

Liang Zhang, University of Wisconsin – Milwaukee

Copyright J. Li, S.M. Meerkov and L. Zhang 2012

Outline

4.1. Introduction

4.2. What is the bottleneck machine?

4.3. What is the bottleneck buffer?

4.4. Identification of BN-m and BN-b in serial lines

4.5. Identification of BN-m and BN-b in assembly systems

4.6. Potency of buffering

4.7. Designing continuous improvement projects

4.8. Measurement-based management

4.9. Case studies

4.10. Summary

4.11. Lab: PSE Toolbox function for BN-m and BN-b identification

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Due to breakdowns and other perturbations, it is not

uncommon that machining lines operate at 60%-70% of their

capacity.

In assembly systems, these numbers are 80%-90%.

Therefore, continuous improvement is of central importance.

4.1. Introduction

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In practice, continuous improvement projects (i.e., improving

machines and buffers or purchasing new ones) are often

designed without a rigorous justification. As a result, many

continuous improvement projects do not measure up to

expectations.

The goal of this lecture is to present quantitative engineering

methods for designing continuous improvement projects with

rigorously predicted results.

The approach developed here is based on identification and

elimination of bottleneck machines and bottleneck buffers.

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4.2. What is the Bottleneck Machine?

Often, the worst machine is isolation is viewed as the bottleneck

machine.

This understanding is wrong because it is local in nature and

does not look at the system as a whole.

We define the bottleneck as the machine that affects the overall

system performance in the strongest manner.

To quantify this understanding, we introduce the following

definition:

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Definition:

mi, i ϵ {1,…, M}, is the bottleneck machine (BN-m) in a

Bernoulli line if

mi, i ϵ {1,…, M}, is the c-bottleneck (c-BN) in a

line with continuous time models of machine reliability if

for all ;i j

PR PRj i

p p

for all .i j

TP TPj i

c c

i

i

j

j

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(c) Machine with the smallest capacity is not the c-bottleneck

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cannot be measured on the factory floor

during normal system operation.

Also, they cannot be evaluated analytically.

So, how the BN-m can be identified?

or i i

PR TP

p c

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4.3. What is the Bottleneck Buffer?

Definition: bi, i ϵ {1,…, M – 1}, is the bottleneck buffer (BN-b)

if

The smallest buffer is not necessarily BN-b:

How the BN-b can be identified?

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4.4. Identification of BN-m and BN-b in Serial Lines

It turns out that BN-m (or c-BN) and BN-b can be identified using

blockages and starvations of the machines.

Specifically, consider a production line and determine (either by

measurements on the factory floor or by calculations) the probabilities

(or frequencies) of blockage and starvation of each machine.

Place BLi and STi under each machine as follows:

STi 0 0.01 0.39 0.37 0.27

BLi 0.41 0.20 0.27 0.01 0

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Assign arrows from one machine to another according to the

following rule: If BLi>STi+1, assign the arrow pointing from mi to

mi+1. If BLi<STi+1, assign the arrow pointing from mi+1 to mi.

STi 0 0.01 0.39 0.37 0.27

BLi 0.41 0.20 0.27 0.01 0

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Bottleneck Indicator:

The machine with no emanating arrows is the BN-m (or c-BN).

If there are multiple machines with no emanating arrows, the one with

the largest severity is the Primary BN-m (Pc-BN), where the severity

of each local bottleneck is defined as follows:

BN-b is one of the buffer surrounding the BN-m (or c-BN); it is before

BN-m if STi > BLi; it is after BN-m if STi < BLi.

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4.5. Identification of BN-m and BN-b in Assembly Systems

The definitions for BN-m and BN-b remain the same.

The arrow assignment rule also remains the same, with the only

difference that the merge operation may be starved by multiple

component lines.

Given this arrow assignment, the Bottleneck Indicator remains the

same as in serial lines.

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4.6. Potency of Buffering

Definition: The buffering of a production system is:

weakly potent if the BN-m is the worst machine in the

system (i.e., the machine with the smallest throughput in

isolation); otherwise, it is not potent;

potent if it is weakly potent and its production rate is

sufficiently close to the BN-m efficiency (e.g., within 5% of

the BN machine efficiency);

strongly potent if it is potent and the total buffer capacity is

the smallest possible to ensure the desired throughput).

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To determine if the buffering is weakly potent, the methods

introduced in this lecture may be used.

To determine if it is potent, the methods introduced in Lecture

3 may be used.

To determine if it is strongly potent, the methods introduced in

Lecture 5 may be used.

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Along with its practical utility, the notion of buffering potency is important conceptually.

Indeed, typically, production supervisors concentrate their attention on the machines – their reliability, efficiency, capacity, etc.

Attention to buffering is often missing, although the buffers are also important for system operation.

The notion of buffering potency provides a language necessary to focus attention on the buffers.

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4.7. Designing Continuous Improvement Projects

4.8. Measurement-Based Management

The process of continuous improvement requires a

mathematical model of the system at hand.

This may be difficult to obtain (especially for large systems).

Therefore, a simpler method, referred to as MBM, is proposed.

It consists of the steps described next.

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Examples of the first step can be given as follows:

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The second step can be carried out based on measuring the

blockages and starvations and using the expressions:

Thus, to carry out MBM, the manager must receive daily, or

weekly information of the time of blockages and starvation of

various units.

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The third step is carried using the arrow-based method of BN

identification:

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The last step is up to the manager and his/her staff – to

determine which actions should be taken to eliminate the BN.

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4.9. Case Studies 4.9.1. Automotive ignition coil processing system

Bottleneck identification:

Improving m9-10 by 10% and b9-10 by 1 leads to TP = 505 parts/hour

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Bottlenecks of the improved system:

Increasing b5 by 1 leads to TP = 511 parts/hour – an acceptable

performance.

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Bottleneck identification:

The main reason for m3 to be the bottleneck is starvation by

empty carriers. Assuming the empty carriers are always

available, we obtain

4.9.2. Automotive paint shop production system

Bottlenecks of the improved system:

Increasing efficiency of m3 by 4% leads to

and machine m4 becomes the new bottleneck.

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4.9.3. Automotive ignition module assembly system

Conclusion: MHS is not potent.

Increasing capacity of all buffers:

Increasing capacity of buffer conveyor: over 9% TP

improvement.

Eliminating starvations of Op.1 and Op.9 and blockage of Op.18:

Last two actions have been implemented.

4.10. Summary

In the same manner a medical doctor cannot treat patients

without taking their vital signs, production systems cannot be

managed without appropriate measurements.

This lecture shows that the most important “vital signs” of a

production system are blockages and starvations.

Based on this information, managers can exercise MBM – a

rigorous way for achieving good performance of production

systems.

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4.11. Lab: PSE Toolbox Function for BN-m and

BN-b Identification

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BN-m and BN-b in serial lines with Bernoulli machines

Input:

M, number of machines

p, reliability of each machine

N, capacity of each buffer

Output:

BN-m and BN-b

Production rate (PR)

Work-in-process (WIP)

Probability of starvation (ST)

Probability of blockage (BL)

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BN-m and BN-b in serial lines with exponential machines Input:

M, number of machines

, failure rate of each machine

, repair rate of each machine

c, speed of each machine

N, capacity of each in-process buffer

Output: Throughput (TP)

Work-in-process (WIP)

Probabilities of starvation (ST) and blockage (BL)

Machine efficiency (e)

BN-m and BN-b.

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BN-m and BN-b in serial lines with general model of machine reliability

Input: M, number of machines

Tup, average uptime of each machine

Tdown, average downtime of each machine

Output: Probabilities of starvation (ST) and blockage (BL)

BN-m and BN-b.

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BN in assembly systems with Bernoulli machines

Input:

M0, M1, M2, number of machines in assembly line, component line 1 and component line 2, respectively

p0, p1, p2, Bernoulli reliability of each machine

N0, N1, N2, capacity of each buffer

Output:

Production rate (PR)

Probability of starvation (ST)

Probability of blockage (BL)

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