The Effect of Shop Floor Continuous Improvement Programs
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Transcript of The Effect of Shop Floor Continuous Improvement Programs
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ORIGINAL ARTICLE
The effect of shop floor continuous improvement programs
on the lot sizecycle time relationship in a multi-product
single-machine environment
Moacir Godinho Filho & Reha Uzsoy
Received: 27 August 2008 /Accepted: 2 June 2010# Springer-Verlag London Limited 2010
Abstract While continuous improvement on the shop floor is
a major component of many popular management movementssuch as lean manufacturing and Six Sigma, there are few
quantitative studies of the cumulative effects of such
improvement programs over time. On the other hand, lot
sizing has long been recognized as an important problem in
manufacturing management. In this paper, we use a system
dynamics model based on the Factory Physics relationships
proposed by Hopp and Spearman [1] to examine the effect of
different continuous improvement programs on the relation-
ship between lot sizes and cycle times. We compare two
different types of improvement programs: large improve-
ments in a single parameter, such as might be obtained by a
focused project, or small improvements in many parameters
simultaneously. Our results show that the relationship
between lot sizes, cycle times, and shop floor parameters is
complex and nonlinear. The cycle time benefits of improve-
ments in shop floor parameters are significantly enhanced by
the reduced lot sizes they enable; on the other hand, a poor
choice of lot sizes can negate the benefits of a continuous
improvement program. Although the largest cycle time
reduction is achieved by a large reduction in setup time,
small, simultaneous improvements in several parameters can
achieve much of the same benefit. The cycle time benefits of
multiple simultaneous improvements are mutually reinforc-ing, creating a positive feedback between shop floor
improvements and reduced lot sizes. Our model yields
insight into why the Toyota Production System has been
able to obtain such excellent results over time, and suggests a
number of interesting future directions.
Keywords Lot size . Cycle time .
Continuous improvement. System dynamics .
Factory physics .
Multi-product single-machine environment
1 Introduction
According to Buffa [2], manufacturing decisions, such as lot
sizing, can have major strategic implications for the firm. An
extensive literature on lot sizing problems exists [3, 4], most
of which seeks to find an optimal lot size (called Economic
Order Quantity (EOQ) or Economic Production Quantity)
that achieves the optimal tradeoff between fixed costs of
ordering and inventory holding costs. Reviews of the lot
sizing literature are available in [3, 4]. Despite its benefits,
the EOQ model has been criticized in the literature, for
failing to consider several key issues such as uncertainty in
demand and resources with limited capacity [5].
According to Kuik and Tielemans [6], criticism of cost
accounting methods for production planning led to a
growing interest in physical measures of manufacturing
performance. One such measure is manufacturing cycle
time (also known as lead time or flow time), defined as the
mean time required for a part to complete all its processing.
Time-based competition [7], initially proposed by Stalk [8],
focuses on cycle time reduction as a primary manufacturing
M. Godinho Filho (*
)Departamento de Engenharia de Produo,
Universidade Federal de So Carlos,
Via Washington Luiz, km 235, Caixa Postal 676, So Carlos,
SP 13.565-905, Brazil
e-mail: [email protected]
R. Uzsoy
Edward P. Fitts Department of Industrial and Systems
Engineering, North Carolina State University,
Campus Box 7906,
Raleigh, NC 27695-7906, USA
e-mail: [email protected]
Int J Adv Manuf Technol
DOI 10.1007/s00170-010-2770-8
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goal. Despite this interest in cycle time reduction, de
Treville et al. [9] point out that the literature on cycle time
reduction has been largely anecdotal and exploratory.
Some exceptions are the Factory Physics work of Hopp and
Spearman [1, 10], and the Quick Response Manufacturing
approach of Suri [11] that use queuing theory to develop a
set of relationships between throughput, cycle time and
critical shop floor parameters, aiming to increase themanagers understanding of manufacturing dynamics. One
such is the relationship between lot size and average cycle
time, which is studied in this paper. Karmarkar et al. [12]
first introduced the convex relationship between lot size
and average cycle time. This relationship is derived from
queuing theory, specifically the Kingman approximation of
the expected cycle time in system for the G/G/1 queue [1],
and is illustrated in Fig. 1. Lambrecht and Vandaele [13]
describe this relationship: Large lot sizes will cause long
cycle times (the batching effect); as the lot size gets smaller
the cycle time will decrease but once a minimal lot size is
reached a further reduction of the lot size will cause hightraffic intensities resulting in longer cycle times (the
saturation effect).
Several other papers have used queuing models and
simulation to study the relationship between lot size
decisions and cycle time. Karmarkar et al. [14] present
heuristics for minimizing average queue time. Rao [15]
discusses alternative queuing models in relation to lot sizes
and cycle time. Lambrecht and Vandaele [12] develop
approximations for the expectation and variance of the
cycle time under the assumption of individual arrival and
departure processes. Kenyon et al. [16] use simulation to
evaluate the impact of lot sizing decisions on cycle time in
a semiconductor company. Vaughan [17] uses queuing
relationships to model the effects of lot size on cycle time.
Other papers relating lot size and cycle times are [1820].
Although these studies provide a basis for understanding
the relationship between lot sizes and cycle times, there is
no literature showing the impact of continuous improve-
ment (CI) efforts on this relationship. This is despite the
repeated observation that reduction of lot sizes and cycle
times is a critical component of lean manufacturing and the
Toyota Production System [21]. In this context, this paper
compares the effect of six shop floor continuous improve-
ment programs on the lot size-cycle time relationship in a
multi-product, single-machine environment using a combi-
nation of system dynamics and factory physics approaches.
The next section gives a short review of the relevant
literature on CI and the two modeling approaches used inthis paper (system dynamics and factory physics); Section 3
presents the model developed and the experimental design
and Section 4 the results of the experiments. We conclude
the paper in Section 5 with a summary and some future
directions.
2 Literature review
2.1 Continuous improvement
Caffyn [22] defines continuous improvement as a massinvolvement in making relatively small changes which are
directed towards organizational goals on an ongoing basis.
Continuous improvement has been recognized for many years
as a major source of competitive advantage, and is inherent in
many recent management movements such as the Theory of
Constraints [23], Six Sigma [24] and the Toyota Production
System [21]. Inability to effectively implement continuous
improvement programs is seen by many scholars and
practitioners as one of the reasons why Western firms have
not fully benefited from Japanese management concepts
[25]. Savolainen [26] points out that CI is a complex process
that cannot be achieved overnight, but involves considerable
learning and fine tuning of the mechanisms used. The core
principles of CI are, according to Imai [27]:
1. process orientation
2. small step improvement of work standards
3. people orientation.
Leede and Looise [28] suggest that the main issue
regarding CI is the problem of combining extensive
employee involvement with market orientation and present
the mini-company concept, which they claim incorporates
these elements. However, there appears to be a lack of
quantitative studies examining how different CI approaches
affect manufacturing performance over time.
In this paper, we deal with CI in six different shop floor
parameters: (1) arrival variability, (2) process variability
(natural process time variability, repair time variability and
set up time variability), (3) quality (mean defect rate), (4)
mean time to failure, (5) mean repair time, and (6) mean set-up
time. Basically, these improvements deal with improvement in
different parameters: mean times and rates and their variabil-
ity, measured in terms of coefficient of variation (cv).
0
500
1000
1500
2000
2500
3000
0 100 200 300 400 500 600 700
Lot size (pieces)
CycleTime(hours)
Fig. 1 Relationship between lot size and cycle time
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Hopp and Spearman [1] indicate that increasing variability
always degrades the performance of a production system in
terms of cycle time, work in process inventory (WIP) level or
throughput. So, if a company cannot reduce variability, it will
pay in one or more of the following ways: reduced throughput,
increased cycle times, higher inventory levels and long lead
times [1]. Schoemig [29] presents a simulation study illustrat-
ing the corrupting influence of variability caused by machineand tool unavailability on manufacturing performance.
Although the negative effects of variability are well
known, there is little research examining the dynamic
behavior of these effects over time, especially when linked
to other shop-floor parameters. Newman et al. [30] claim
that reducing variability and increasing flexibility enable
capacity, inventory and time to be reduced, increasing
companys performance; Mapes et al. [31], by means of a
study in 963 manufacturing plants in UK, determine that
the high performance companies utilize processes and
procedures that have low levels of variability and uncer-
tainty. Despite this conclusion, these authors state that theirpaper considers the performance of the plants at a particular
point of time, and suggest studies of the relation between
variability reduction and performance in a dynamic envi-
ronment in the face of ongoing reductions in variability,
which is exactly the issue addressed in this paper.
The literature suggests a number of methods that can help
reduce the arrival and the process variability. For reducing
arrival variability, Hopp and Spearman [1] suggest: (1)
decreasing process variability at upstream stations, (2) better
scheduling and shop floor control to smooth material flow, (3)
eliminating batch releases, and (4) installing a pull production
control system such as Constant Work in Process or Kanban
[21]. For a review about kanban variations see Lage Jr and
Godinho Filho [32]. They formalize the relationship between
different shop floor parameters in the form of a diagnostic tree
[33]. Process variability is routinely addressed in practice
using techniques such as Six Sigma, operator training,
standardized work practices and automation. Other methods
to improve manufacturing parameters include the Single
Minute Exchange of Die system [34] to reduce the mean set
up time; Total Productive Maintenance [35] to achieve
improvements in mean repair time and mean time to failure;
and finally, quality control methods like Statistical Process
Control, Six Sigma and Total Quality Management to reduce
mean defect rate, Lean Manufacturing [36], Quick Response
Manufacturing [11], among others.
Table 1 shows examples of methodologies/tools used to
improve the shop floor parameters studied in this paper.
2.2 System dynamics
System dynamics (SD) were developed by Jay Forrester in
1956 at the Massachussets Institute of Technology [37]. In
complex systems such as manufacturing systems objects
interact and a change in one variable affects other variables
dynamically, which feeds back the original variable, and so
on [38]. An excellent introduction to system dynamics
modeling is given by Sterman [39].
The structure and the relationship between variables in
an SD model are represented by means of causal loop
diagrams or stock and flow diagrams [39]. In this paper, we
use the causal loop diagram, which has four main elements:
(a) Stocks that characterize the state of the system and
generate the information upon which decisions and
actions are based [39]. The stock level is given by thedifference between cumulative inflow and outflow.
(b) Flows that lead to the increase or decrease of stocks.
These represent the dynamic behavior of the system
over time and may depend on the stock levels.
(c) Auxiliary variables that may be functions of stocks, as
well as constants or exogenous inputs [39].
(d) Links that represent information exchange between
stocks, flows and auxiliary variables.
System dynamics models have been used to address
problems in a wide variety of areas [40, 41]. However,
there is a lack of SD applications to manufacturing systems,
despite evidence that this technique is suitable for industrial
modeling. Baines and Harrison [42] point out that the
computer simulation of manufacturing systems is common-
ly carried out using Discrete Event Simulation, and suggest
that manufacturing system modeling represents a missed
opportunity for SD. This is also the opinion of Lin et al.
[43], who propose a framework to help industrial managers
apply SD to manufacturing system modeling. This is one of
our motivations for the work in this paper. Recent advances
in interactive modeling, tools for representation of feedback
Table 1 Examples of methodologies/tools used for shop floor
improvement
Shop floor variable Examples of methodologies/tools
used to improve such variables
(1) arrival variability (cv) decreasing process variability at
upstream stations; using a better
scheduling and shop floor control
to smooth material flow; eliminatingbatch releases, and; installing a pull
production control system
(2) process variability (cv) Six sigma, operators training,
standardizing work practices
and automation
(3) mean defect rate SPC, Six Sigma and TQM
(4) mean time to failure TPM
(5) mean repair time TPM
(6) mean set up time SMED
TQM Total Quality Management
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structure, and simulation software make SD models much
more accessible to practitioners than they have been in the
past [39].
2.3 Factory physics
The Factory physics approach was created by Hopp and
Spearman [1, 10]. This approach is based on a set ofmathematical principles derived from queuing theory. It
has, according to Hopp and Spearman [10], three proper-
ties: it is quantitative, simple and intuitive; so it provides
managers with valuable insights. The basic approach
consists of a set of equations that relate the long-run steady
state means and variances of critical performance measures
such as cycle time and WIP levels to the mean and variance
of system parameters such as time between failures, setup
times and processing times.
As noted by Standridge [44], factory physics provides a
systematic description of the underlying behavior of a
production system. This description can provide supportssimulation studies in the following ways:
1. It helps in deciding what performance measures to
collect and what alternatives to evaluate as well as in
interpreting simulation results.
2. It helps identify the properties of systems that may be
important to include in models.
3. It provides an analytic foundation that helps in under-
standing the behavior of systems and gives insight into the
types of issues addressed in simulation studies.
4. Verification and validation evidence can be collected
based on the underlying relationships.Some recent papers that use the factory physics approach
are [4549].
3 Modeling and analysis
The use of the factory physics concepts in a system dynamics
model may, at first glance, appear to be somewhat contradic-
tory. The factory physics approach as presented in Chapters
8 and 9 of Hopp and Spearman is based on long-run steady
state analysis of the production system, generally derived
using the methods of queuing analysis. System dynamics, on
the other hand, usually emphasizes the dynamic behavior of
complex systems that are not in steady state. However, for our
objective in this paper, the factory physics equations provide a
systematic mathematical model linking the mean and variance
of key system parameters such as setup and repair times to key
performance measure such as cycle time and utilization. In
order to use these equations as the basis for a system dynamics
model, we assume that the time increments that form the basis
of the system dynamics model are quite long, corresponding
to periods of the order of several months. This is a reasonable
assumption in our context, since it generally takes some time
to identify opportunities for improvements, implement the
necessary changes and obtain the results. We thus assume that
within each time period, the queue representing the manufac-
turing system will be in steady state, allowing us to use the
factory physics equations to describe the behavior of the
system. The assumption of long time periods also allows us toneglect the transient behavior at the boundaries between time
periods.
Our basic approach then is to model the performance of
the system over an extended time horizon of several years
using time increments of the order of several months.
Continuous improvement policies are modeled as a reduc-
tion in the mean or variance of the parameters studied
(arrival variability, process variability, quality, time to
failure, repair time, and setup time) obtained in each period.
In each period, the new parameter values are calculated
based on the improvements implemented in the previous
period, and the factory physics equations are used topropagate the effects of these improvements to system
performance measures. We assume a completely determin-
istic model of the effects of continuous improvement on
average cycle time, following the suggestion of Sterman
[36] that a deterministic approach is generally sufficient to
capture the principal relationships of interest. Note that the
effects of randomness in the operation of the system itself
are captured by the variances used in the factory physics
equations, and our primary performance measure is the
expected cycle time of the system in each period.
Surprisingly, given the extensive discussion of continuous
improvement and cycle time reduction in the literature and
industry, there seems to be very little industrial data available
on the rates of improvement realized over time in different
industries, which makes it difficult to calibrate models of this
type. Hence, we demonstrate the behavior of our model
through a simplified example of our own construction.
3.1 The model
We consider a manufacturing system modeled as a single
server with arbitrary interarrival and processing time distribu-
tions, which we shall represent as a G/G/1 queue. The
notations and relations used in the model are as follows:
t0=>mean natural processing time (the time required to
process a job without any detractors other than the
variability natural to the production process);
0=>standard deviation of the natural processing time;
te=>mean effective time to process one good part
(which is the natural processing time modified by the
impacts of disruptions such as setups and machine
failures);
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ce=>coefficient of variation of the effective time to
process one good part;
L=>average lot size;
ta=>mean interarrival time between lots;
ca=>coefficient of variation of the mean interarrival
time between lots;
l=>arrival rate of lots (the inverse of time between
arrivals, giving l=1/ta);D=>mean annual demand
H=>total number of hours worked in a year.
As the system must be in steady state to avoid
unbounded accumulation of jobs in the queue, the mean
arrival rate to the system must equal the mean demand rate,
implying ta=LH/D.
The mean time to process a lot of L parts is then given
by Lte, and the mean utilization of the server by:
uLte
ta
Dte
H1
The other primary performance measure of interest in
this study is the mean cycle time. For the G/G/1 queue, no
exact analytical expression exists, but the following
approximation has been found to work well and is
recommended by Hopp and Spearman [1]:
CTc2a c
2e
2
u
1 u
Lte Lte 2
where LTe is the mean time to process one lot.
The average work in process is given by the well known
Littles Law [1]:
WIP l CT L 3
The effective time to make one piece is constructed from
the natural processing time by adding in first the effects of
preemptive disruptions, in our case machine failures, then
the effects of non-preemptive outages, in our case setups;
and finally the effect of defective items. Both the means and
the variances of the effective processing times must be
calculated, as reflected in the model. Thus we first calculate
the mean and variance of the intermediate effective process-
ing time with machine failures, which we shall denote as tfe .
Following Hopp and Spearmans treatment, we shall assume
that the time between failures is exponentially distributedwith mean mf, and that the time to repair has mean mr and
variance s2r. Then the mean availability of the server is
given by A mf= mf mr
, yielding tfe t0=A, and
sfe
2
s20
A2
m2r s2r
1 A t0
Amr4
We now incorporate the effects of setups, assuming, as in
Hopp and Spearman [1], that a setup is equally likely after
any part is processed, with expected number of parts
between setups equal to the specified lot size L. The mean
setup time is denoted by ts, and its variance by s2
s. We thus
obtain the mean of the effective processing time with both
non-preemptive and preemptive outages (denoted by teo)as
toe tfe ts=L. Its variance is given by:
soe
2 sfe
2
s2
s
L
L 1
L2
t2s 5
Finally, incorporating the effect of defective items, we
have the overall mean of the effective processing time te,
given by te toe= 1 p , where p denotes the proportion of
defective items. The overall variance of the effective
processing time is given by:
s2e
soe
21 p
p toe 2
1 p 26
Figure 2 shows all of these relationships in a stock and
flow diagram.
Since our objective is to examine the effects ofcontinuous improvement in six parameters on the cycle
time of the system over time, we need a mechanism to
model continuous improvements. We use an exponential
model of improvement, where the value of a parameterA at
time t is given by:
At A0 G et=t 7
where, A0 denotes the initial value of the parameter, and G
the minimum level to which it can be reduced. The
parameter represents the average amount of time it takes
for the improvement to be realized, representing in our case
the difficulty of improving the parameter in question.Figure 3 shows the SD structures used to model improve-
ment on mean setup time. This structure is linked to the
variable setup time with improvement in Fig. 2. Similar
structures are used to model the improvements in the other
parameters studied (arrival variability, process variability,
setup time variability, repair time variability, and natural
process time variability), quality, mean time to failure, and
repair time. These structures are linked to the following
variables, respectively: arrival coefficient of variation with
improvement, variance of setup time with improvement,
variance of repair time with improvement, variance of
natural process time with improvement, defect rate with
improvement, mean time to failure with improvement, and
repair time with improvement.
3.2 Parameters of the model
We will vary individual parameters in different experiments
to examine their effect on the relationship between lot sizes
and cycle times. The basic time period in the system
dynamics model is assumed to be 3 months or 12 weeks.
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This is a reasonable time increment for the purposes of this
paper, since it is likely to require several months to develop
and implement the improvements needed to make a
significant reduction in repair or setup times. We simulate
the operation of the system over a period of 10 years, or 40
quarters. Since our objective is to study the effects of
continuous improvement in system parameters, the annual
demand is held constant at D=11,520 parts/year. We
assume an initial lot size of 200 parts, and that the plant
operates a total of H=1,920 h/year. The interarrival times
are assumed to be exponentially distributed (ca=1), as is the
natural processing time per part, with t0=6 min and c0=1.
At the start of the simulation, the mean time between
failures mf=9,600 min, the mean time to repair is mr=
480 min, and the mean setup time is ts=180 min. The
parameter of the improvement process was chosen to
provide a half life for the exponential decay of 1 year. The
initial proportion of defective items p=5%.
We vary the lot size in order to examine the effect of lot
sizes on cycle time. This is done for all improvement
policies tested: (1) no improvement, (2) 50% improvement
in arrival variability, (3) 50% improvement in each of the
parameters affecting process variability (natural process
variability, repair time variability and setup time variabil-
ity), (4) 50% reduction in defect rate, (5) 50% increase in
mean time between failures, (6) 50% improvement in mean
repair time, (7) 50% improvement on setup time, (8) 5%
improvement in all variables, (9) 10% improvement in all
variables, (10) 15% improvement in all variables, and (11)
20% improvement in all variables.
4 Results
Figure 4 shows the effect on expected cycle time of all 50%
improvements over the time period (cases (1) to (7)) for a
lot size of 200 parts. Similar figures can be drawn for the
Set up Time with
improvement
Improvement
on set up time
Error on set up time
improvement
GOAL REGARDING SETUP TIME
IMPROVEMENT
Improvement rate onset up time
ADJUSTMENT TIME FORSET UP TIME
IMPROVEMENT
-
+
B2
VARIANCE OF
SET UP TIME
Fig. 3 SD Structure of improvement in setup time
arrival rate throughput
Utilization
Set up Time with
improvement Arrival coefficient ofvariation withimprovement
Coefficient of variation for
effective processing time
Lot Size
NATURAL
PROCESS TIME
TIME WORKED
DURING THE YEARANNUAL
DEMAND
Number of pieces on
queue
Queue Time
Cycle Time
Variance of of effective processingtime with nonpreemptive and
preemptive outages
Mean repair time with
improvement
Availability
Mean of effective processingtime with nonpreemptive and
preemptive outages
Variance of set up time
with improvement
Variance of effective processingwith preemptive outage
(machine failures)Variance of natural
process time withimprovement
Total WIP
Variance of repair time
with improvement
Defect Rate withimprovement
Mean time to failure
with improvement
production rate
Overall mean ofeffective processing
time
Overall variance of
effective processing time
Fig. 2 Main body of the SD model
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other lot size values tested (600, 400, 170, 150, 130, 100, 80,
70, 60, 40, 30). From these results, lot size-cycle time curves
are drawn for each improvement policy after these curves
become stable. The resulting lot size-cycle time curves for the
large improvement program are discussed in Section 4.1. The
same procedure is performed for the small improvement
program and reported in Section 4.2.
4.1 Effect of large improvements in just one variable on lot
size x cycle time relationship
Figures 5, 6, 7, 8, 9, and 10 present the effects of each of
the six 50% improvement programs (cases (2) to (7)) on the
lot size-cycle time relationship, while Fig. 11 presents all
the effects in a single graph for comparison. Table 2
presents the values used to build Figures 5, 6, 7, 8, 9, 10,
and 11. In these figures, it can be seen that:
50% improvement in arrival cv has only slight effect on
cycle time reduction for given lot size. This effect is
even shorter when lot sizes are decreased. This may be
because of the fact we are considering a single
workstation.
As expected, a 50% improvement in defect rate, repair
time, time to failure, setup time, and process variability
shift the lot size-cycle time curve down and to the left,
reducing the lot size required to achieve a given cycle
time.
The positive effect on cycle time of 50% improvement
in setup time, process variability and defect rate
Graph for Cycle Time600
500
400
300
2000 30 60 90 120
Time (months)
Improvement in Process variabilityImprovement in Arrival cv
Improvement in Time to failureImprovement in defect rateImprovement in repair time
No improvement
Improvement in set up time
Fig. 4 Cycle time performance of all 50% improvements over time for a lot size of 200 parts
0
500
1000
1500
2000
2500
3000
3500
4000
0 100 200 300 400 500 600 700
CycleTime(hours)
Lot Size (pieces)
no improvement
improvement in arrival cv
Fig. 5 The effect of 50% improvements in arrival cv on lot size-cycle
time curve
0
500
1000
1500
2000
25003000
3500
4000
0 100 200 300 400 500 600 700
Lot Size (pieces)
CycleTime(hou
rs)
no improvement
improvement in process
variability
Fig. 6 The effect of 50% improvements in process variability on lot
size-cycle time curve
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increases as lot sizes are reduced. This suggests a
strong interaction effect between lot sizes, cycle time,
and improvement in system parameters. In particular,
this indicates the presence of a virtuous cycle time:
improvements in setup time, defect rate, and process
variability allow the reduction of lot sizes, which
allows reduction of cycle times beyond the level that
would be achieved by improving the system but
keeping lot sizes constant. Thus, the small lot sizes
advocated by lean manufacturing are a result of
continuous improvement efforts; reduction of lot sizes
without any accompanying improvement in shop floor
capabilities will merely increase cycle time, as sug-
gested by Fig. 1. The cycle time reductions from 50%
improvement in repair time and time to failure increase
at extreme values of the lot sizes. This is to be
expected; the effect of these parameters is to make
more capacity available.
50% improvement in setup time achieves the best cycle
time reduction for small lot sizes. Improvement in
setup time is the only improvement that allows
production system to use really small lot sizes (e.g.,
30 or 40 parts);
On the other hand, the importance of lot sizes to
effective manufacturing performance is also evident from
the results. Table 2 shows that in the original system with
no improvements, a lot size of 150 parts leads to an
average cycle time of 530 min. Reducing the lot size to 80
leads to significantly higher cycle time even when all
improvements have taken place. Thus, a poor choice of lot
sizes can completely negate the benefits of a significant CI
program.
4.2 Effect of small improvements in several variables on lot
sizecycle time relationship
Figures 12, 13, 14, and 15 present comparisons between
50% improvement in set up time, no improvement and each
of the small improvement programs in all parameters
simultaneously (5%, 10%, 15%, or 20%). Figure 16
presents a comparison between the two large improvements
that achieves the best results in the last section (set up time
and process variability) and the small (5%, 10%, 15% or
20%) improvement in all parameters simultaneously. The
numerical values corresponding to this figure are shown in
Table 3. A 15% simultaneous improvement in all variables
outperforms all the large individual improvements, except
when very small lot sizes are used. Large improvements in
setup time achieve the best result in this case.
In Fig. 16, the curves for 50% improvement in setup
time and process variability represent situations where a
0
500
1000
1500
2000
2500
3000
3500
4000
0 100 200 300 400 500 600 700
Lot Size (pieces)
CycleTime(hours)
no improvement
improvement in
defect rate
Fig. 7 The effect of 50% improvements in defect rate on lot size
cycle time curve
0
500
1000
1500
2000
2500
3000
3500
4000
0 100 200 300 400 500 600 700
Lot Size (pieces)
CycleTime(hou
rs) no improvement
improvement in time tofailure
Fig. 8 The effect of 50% improvements in mean time between
failures on lot sizecycle time curve
0
500
1000
1500
2000
25003000
3500
4000
0 100 200 300 400 500 600 700
Lot Size (pieces)
CycleTime(hou
rs)
no improvement
improvement inset
up time
Fig. 10 The effect of 50% improvement in mean set up time on lot
sizecycle time curve
0
500
1000
1500
2000
2500
3000
3500
4000
0 100 200 300 400 500 600 700
Lot Size (pieces)
CycleTime(hours)
no improvement
improvement in
repair time
Fig. 9 The effect of 50% improvement in mean repair time on lot
sizecycle time curve
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major reduction in these parameters is obtained. An
improvement of this magnitude would very probably
require the adoption of new technology, or at least a
sustained, focused engineering effort. However, the curves
for 10% and 15% improvement in all parameters capture
almost the entire cycle time benefit of these programs,
except at small lot sizes. Even a 5% improvement in all
parameters yields a 50% improvement in average cycle
time at small lot sizes over the no improvement situation.
As suggested by the successful approach of Toyota,
investing in small, combined improvements in all shop
floor parameters yields better cycle time reduction than a
single large, high-investment improvement. Examination of
the Kingman equation relating cycle time to manufacturing
parameters suggests the reason for this. The benefit of
reduction in any given parameter may not be great in itself,
but the benefits tend to be multiplicative, and hencemutually reinforcing. In system dynamics terminology, this
suggests positive feedback between improvements in the
different parameters, which is good news for managers.
However, the opposite is also trueif the values of several
parameters begin to deteriorate simultaneously, the detri-
mental effects will also be mutually reinforcing, leading to
precipitate degradation in cycle time.
5 Conclusions
In this paper, a combination of the SD and factory physicsapproaches is used to study the effect of continuous
improvement programs aimed at improving six key parame-
ters (arrival variability, process variability, quality (defect
rate), time to failure, repair time, and setup time) on lot size-
cycle time relationship in a multi-product, single-machine
environment. Two sets of experiments were performed: (a) a
large (50%) improvement in each parameter separately, as
might be obtained by a significant one-time investment; (b) a
small improvement in all parameters simultaneously.
There are two salient conclusions from this set of
simulation experiments. The first of these is the strong
interaction between improvements in different system param-
0
500
1000
1500
2000
2500
3000
3500
4000
0 100 200 300 400 500 600 700
No
improvement
Improvement
in set up
Improvement
in defect rate
Improvement
in arrival cv
Improvement
in repair time
Improvement
in time to
failureImprovement
in process
variability
Lot Size (pieces)
Cycle
Time(hours)
Fig. 11 Effect of 50% improvements on the lot size-cycle time curve
Table 2 Values of lot size-cycle time curve for all improvement programs
Lot size Cycle time
No improvement Improvement
in arrival cv
Improvement
in process cv
Improvement
in defect rate
Improvement in
time to failure
Improvement
in repair time
Improvement
in set up time
600 896.77 837.47 594.18 825.86 705.73 673.92 784.69
400 696.97 653.37 459.69 639.08 559.47 535.64 574.68
200 535.56 505.91 349.69 483.19 446.19 428.72 373.03
170 527.18 498.9 343.29 472.19 442.64 425.39 345.68
150 530.01 502.25 344.38 471.24 447.33 429.8 328.74
130 545.95 518.13 353.84 479.99 462.89 444.36 313.53
100 633.81 602.98 408.81 537.91 538.01 514.1 297.13
80 860.67 820.17 552.77 681.52 717.56 677.58 296.24
70 1,244.88 1,187.22 797.44 890.84 996.97 923.86 303.14
60 3,735.17 3,564.47 2,385.17 1,660.44 2,329.88 1,979.78 321.05
40 501.39
30 2,205.09
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eters and improved cycle time. While improvements in system
parameters provide cycle time benefits on their own, furtherbenefits can be realized by reducing lot sizes to the levels
permitted by the improvements. Similarly, when a firm sets its
lot size near the minimal value on the lot sizecycle time
curve, the need for improvement in machine availability
decreases. In other words, a good choice of lot size can offset
the disadvantages of unreliable equipment to some degree,
although clearly the firm should continue to improve its
equipment reliability. Similarly, when the lot sizes are small
and hence utilization is high, improved machine up time
creates additional capacity, reducing utilization and allowing
significant reduction in cycle time.
This close interaction between lot sizes and system
parameters has another implication. As seen in any of the
figures above, simply reducing the lot sizes without any
improvement in the system parameters may lead to a
catastrophic increase in cycle time. If the lot sizes were
extremely high to begin with, quite significant reductionsmay be possible with significant cycle time benefits,
essentially moving to the left along the linear portion of
the lot sizecycle time curve. Since very few manufacturing
facilities can predict the shape of the lot sizecycle time
curve with any degree of precision without a significant
data collection and analysis effort, this suggests that
management exercise considerable caution when reducing
lot sizes. A gradual reduction over time, making sure that
enough time has elapsed for the effects of each reduction to
be observed and understood, is probably the best strategy. It
is better to gradually reduce lot sizes than to reduce them to
such a degree that setups consume an undue amount of
capacity and compromise the performance of the system.
Our results in Table 2 show that a poor choice of lot sizes
can offset all the benefits of a major CI program.
0
500
1000
1500
2000
2500
3000
3500
4000
0 200 400 600 800
CycleTim
e(hours)
Lot Size (pieces)
no improvement
10% improvement in all
variables
50% improvement in set up
time
Fig. 13 Comparison between 50% improvement in set up time, 10%
improvement in all variables and no improvement case
0
500
1000
1500
2000
2500
3000
3500
4000
0 100 200 300 400 500 600 700
CycleTim
e(hours)
Lot Size (pieces)
no improvement
20% improvement in allvariables
50% improvement in set up
time
Fig. 15 Comparison between 50% improvement in set up time, 20%
improvement in all variables and no improvement case
0
500
1000
1500
2000
2500
3000
3500
4000
0 200 400 600 800
CycleTime(hours)
Lot Size (pieces)
no improvement
15% improvement in allvariables
50% improvement in set uptime
Fig. 14 Comparison between 50% improvement in set up time, 15%
improvement in all variables and no improvement case
0
500
1000
1500
2000
2500
3000
3500
4000
0 200 400 600 800
Cycle
Time(hours)
Lot Size (pieces)
no improvement
5% improvement in allvariables
50% improvement in set up
time
Fig. 12 Comparison between 50% improvement in set up time, 5%
improvement in all variables and no improvement case
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The conclusion, again, is inescapable: improving the
parameters of the shop floor is beneficial in itself, but when
combined with the right choice of lot size the benefits are
significantly enhanced. This result supports the Quick
Response Manufacturing theory, which claims that in an
environment with considerable set up time, a lot size of one
piece, contrary to what is advocated by Lean Manufactur-
ing, actually contributes to increased cycle time. Put
another way, the lot size of one advocated in the Lean
Manufacturing literature requires signifciant improvements
in the parameters of the produciton system itself if it is to be
realized without compromising cycle time performance.
Our second salient finding is that a significant proportionof the benefits obtained by a major improvement in one
parameter, as might be achieve by investing in a new
technology, say, can be obtained by pursuing small
improvements in multiple system parameters simultaneous-
ly over time. As expected, setup time reduction allows the
system to operate with the smallest lot size (in our case for
30 or 40 parts). However, such a dramatic improvement
may be difficult to achieve without major capital expendi-
ture and interruptions to production. Our results suggest
that a substantial portion of the benefits of this type of
dramatic reduction in setup time can be improved by
relatively minor simultaneous improvements in otherparameters, which can be pursued in parallel with a longer
term setup reduction effort. Even a 5% improvement in all
parameters gives cycle time savings of almost 50% at low
lot sizes.
The results presented underscore the benefits of the
factory physics approach to understanding and diagnosing
manufacturing systems. As the factory physics equations
suggest, the behavior of these systems over time is quite
nonlinear; the effects of changes in parameters are
multiplied to yield nonlinear improvements or degradations
in cycle time. The presence of positive feedback between
improvements in system parameters, lot sizes, and cycle
time goes a long way towards explaining how Japanese
Table 3 Values of lot size-cycle time curve used to build Fig. 12
lot
size
Cycle time
No improvement 5% Improvement
in all variables
10% Improvement
in all variables
15% Improvement
in all variables
20% Improvement
in all variables
50% Improvement
in set up
50% improvement
in process cv
600 896.77 776.4 672.05 581.27 502.12 784.69 594.18
400 696.97 601.96 519.72 448.27 386.05 574.68 459.69
200 535.56 457.23 390.34 332.94 283.5 373.03 349.69170 527.18 447.46 379.95 322.43 273.22 345.68 343.29
150 530.01 446.13 377.56 318.77 268.82 328.74 344.38
130 545.95 456.19 381.95 320 267.95 313.53 353.84
100 633.81 513.44 418.69 342.83 281.3 297.13 408.81
80 860.67 654.91 508.69 400.53 318.16 296.24 552.77
70 1,244.88 863.25 629.57 473.5 363.17 303.14 797.44
60 3,735.17 1,656.39 985.35 657.72 466.07 321.05 2,385.17
40 501.39
30 2,205.09
0
500
1000
1500
2000
2500
3000
3500
4000
0 100 200 300 400 500 600 700
No improvement 5% improvement in allvariables
10% improvement in all
variables
15% improvement in all
variables
20% improvement in allvariables
50% Improvement in set up
50% improvement inprocess variability
Lot Size (pieces)
CycleTime(hours)
Fig. 16 Comparison between the large improvement in setup and
process variabilities and simultaneous small improvements in all
variables
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factories have been able to achieve the massive cycle time
and WIP reductions that many Western experts simply
could not believe were possible in the early 1980s.
Finally, the SD/Factory Physics combined model pro-
posed in this paper has been shown to be a valuable tool for
simulating the impact of alternative continuous improve-
ment programs on manufacturing performance measures
over time.A number of extensions of this approach suggest
themselves. An interesting direction is to provide insight
into the allocation of limited continuous improvement
resources in a complex systemshould all available
resources be directed towards improving one specific
resource, or should parallel efforts be maintained in several
different areas? Another interesting question is how the
benefits of different CI programs are affected by uncertainty
in ability to achieve improvements. One would conjecture
that a portfolio approach, where multiple improvements are
pursued simultaneously, would yield better average im-
provement over a given time interval than an effortdedicated at a single highly uncertain improvement.
Acknowledgments The research of Reha Uzsoy was partially
supported by the National Science Foundation under Grant No.DMI-
0559136. Moacir Godinho Filho would like to acknowledge FAPESP
Brazilian agency for funding this research.
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