RELATIONSHIPS BETWEEN BATCH SIZES, SEQUENCING
AND LEAD-TIMES
Vladimír Modrák
Faculty of Manufacturing Technology, Technical University of Košice, Bayerova 1, Prešov, Slovakia
Ján Modrák
T-Systems Slovakia s.r.o.. Košťova 1, Košice, Slovakia
Keywords: Simulation, Manufacturing lead time, Sequencing, Batch production.
Abstract: This paper treats the optimization of production batches by computer simulation in a manufacturing
company producing electric and pneumatic actuators. In its introduction part the article deals about a wider
context of batch production optimization. Subsequently, the paper presents a procedure for creation of a
simulation model in SIMPLE ++ software environment. Based on simulation of a manufacturing process,
selected dependences of lead manufacturing time on changes of production sizes was studied. As a result of
optimization has been determined optimal minimal value of production sizes, by which minimal lead-time
can be achieved.
1 INTRODUCTION
Manufacturing lead time reduction is one of the
most critical issues in gaining a competitive
advantage in the marketplace. Manufacturing lead
time (MLT) can be defined as the time span from
material availability at the first processing operation
to completion at the last operation. Obviously, there
are abundant reasons to reduce lead times in most
organizations. Obviously, reducing MLT doesn't
mean speeding up operation times, but all efforts
should be focused on shortening changeover times,
eliminating needless operations and reduction of
production and logistical bottlenecks. Especially,
batch sizes effect on MLT through changeover
times. When using larger batches, then changeover
times compared with the manufacturing times will
be insignificant. Contrariwise, if applying smaller
batches, then longer changeover times would reduce
the capacity of the factory greatly. Research in this
paper is oriented on the optimization of production
batches by computer simulation in a manufacturing
company, in which mentioned issues present a
topical problem. The paper is structured as follows.
After a short section on related work, the theoretical
background is outlined. Then, testing of relations
between batch sizes, sequencing and lead times is
treated. Finally, discussion on obtained results is
presented.
2 RELATED WORK
Importance of manufacturing lead times in generally
depends on production policies. Manufacturing
policy in this relation is associated with one of the
two strategies: Make-to-Order (MTO) or Make-to-
Stock (MTS). In a case of MTO, some products are
commonly under extreme pressure, which creates a
situation where certain products need to get priority
over other products (Akkerman and van Donk,
2007). However, this prioritization doesn’t solve
problem with excessive throughput times in the
plants. Thus, the same authors used the average lead
time to investigate the effects of different product
mixes. Fahimnia et al. (2009) analyzed obstacles in
reducing manufacturing lead times and observed that
relatively long MLT is the major cause of inefficient
manufacturing, since it generates large amount of
wastes and creates considerable environmental
encumbrance. In a context of integrated supply
chain, duration of lead time of original equipment
manufacturers causes a different retailer’s profit.
380
Modrák V. and Modrák J. (2009).
RELATIONSHIPS BETWEEN BATCH SIZES, SEQUENCING AND LEAD-TIMES.
In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Intelligent Control Systems and Optimization,
pages 380-383
DOI: 10.5220/0002209603800383
Copyright
c
SciTePress
Based on this assumption Mukhopadhyay (2008)
studied optimal policies of retailers in different cases
depending on the contract type with original
equipment manufacturers. Guiffrida and Nagi (2006)
focused their research on strategies for improving
delivery performance in a serial supply chain based
on evaluation of delivery performance. By them,
‘delivery performance is classified as a strategic
level supply chain performance measure’.
Instructive consequences formulated Wacker (1996):
‘If customer lead time is longer than manufacturing
lead time, firms deliver from their production system
and if customer lead time is shorter than
manufacturing lead time, firms store finished goods
inventory and incur holding costs’. A number of
other authors studied the relationship between batch
sizes and length of lead time. For instance, Kuik and
Tielemans investigated the relationship between
batch sizes and lead-time variability, or Millar and
Yang
(1996) analyzed relations between batch
sizing and lead-time performance through the use of
a queuing network model. Summarily stated, there
are many options to achieve lead-time reduction.
3 THEORETICAL POSITION
In calculating the manufacturing lead time, the
structure of the activities in production is one of
decisive issue. Groower (1987) proposed to divide
main production activities in two main categories,
operation and no operation elements, excluding
setup procedures that are generally required to
prepare each production machine for the particular
product. Thus, MLT is calculated as the sum of
setup time, processing time, and non-operation time
(Groover, 1987):
)(
1
noioi
n
i
sui
TQTTMLT
m
++=
=
(1)
where i indicates the operation sequence in the
processing and i = 1,2,…,n
m
.; T
su
represents setup
time for each process; T
o
is operation (processing)
time per item per process; Q demonstrates batch size
and finally T
no
denotes non-operational time
including mostly waiting times for each process.
Equation 1 is considered only for one batch
scheduling problem. For actual factory data, with its
inherent variations in parameter values, equation 1
can be transformed to the multiplication process:
)(
noosum
TQTTnMLT ++=
(2)
where Q and n
m
are represented by straight
arithmetic averages and variables T
su
, T
o
, T
no
are
calculated as weighted-average values.
Then, the formula for calculation of average
MLT, can be expressed as
where n
Q
equals the number of batches, Q
j
represents the batch quantity of batch j among n
Q
batches, n
mj indicates the number operations in the
process routing for batch j. In the weighted-average
expressions individual symbols mean: T
suj - the
average setup time for batch j, T
noj - average non-
operation time for batch j and Toj - average operation
time for batch j.
Equation 3 is usable in
a case when elements of
non operation times are predicable. In case when
applying a parallel batch processing approach, then
previous equation needs to be modified. A parallel
batch scheduling assume that batches are processed
on machines in smaller lots, while for a serial batch
processing is typical that all components are
completed at a workstation before they move to the
next one. If the batches are divided into N equal-size
sub-batches, the idle time becomes (Kodeekha and
Somlo, 2008). Accordingly, for a given problem we
divided non-operational time to two groups: the
down time waiting for parts – T
nop and waiting time
of parts in queue - Tnoq. Differences between these
two methods are shown in figure 1.
Figure 1: Time components of serial batch scheduling (a),
parallel batch scheduling (b).
As is shown in figure 1b, item's manufacturing
lead time of parallel batch processing legitimately
consists of four components: setup time, processing
time for given units in the batch, queuing time
+
+=
=
=
===
=
==
Q
QQQ
Q
QQ
n
j
mj
n
j
nojmj
Qm
n
j
ojjmj
Q
n
j
j
n
j
mj
n
j
sujmj
Q
n
j
mj
n
Tn
nQn
TQn
n
Q
n
Tn
n
n
M
LT
1
111
1
11
.
.
..
(3)
RELATIONSHIPS BETWEEN BATCH SIZES, SEQUENCING AND LEAD-TIMES
381
resulting from limited capacity, and down time
resulting from component unavailability. Equating
an item's MLT to its average manufacturing lead
time may not be the best alternative because such
lead times ignore the impact of lead-time variability
(Mohan and Ritzman, 1998). Following the previous
assumptions, then MLT for individual batches that
are processed copying approach in figure 1b, can be
computed by the formula:
nopinononnoqinopioi
n
i
sui
IB
TTQTTTT
N
Q
T
MLT
+++++++=
=
=
sun
1
1
T )(
(4)
where n represents the number of operations (or
machines) of individual batches and N indicates
number of sub-batches obtained from batch
fragmentation.
4 TESTING OF RELATIONS
Testing of relations betweens between batch sizes,
batch sequencing and lead times was conducted
through computer simulation using SIMPLE++
(SiMulation in Production, Logistics and
Engineering) software. A simulation model was
developed to calculate individual lead times under
different batch sizes and batch sequencing.
Simulation model was specifically created for
testing real manufacturing environment in a
company producing electric and pneumatic
actuators. In a manufacturing company, where
testing was applied, 90 different products were taken
under consideration. Those products are processed
on modern machine tools and another machines and
equipment in a batch manner with applying
sequencing based on prioritization schemes. Batches
during our experiment varied from 60 to 250 parts.
Simulation model composition, respecting the main
optimization criterion to minimize individual
manufacturing lead times, started with definition of
two groups of objects required for material flow
modeling. Defined were sets of 90 parts and 68
machines with single processing and multi
processing ability. Subsequently, the general and
detailed model of production flows at disposal to
each product was designed.
Thereafter, loading of actual time values for each
product in table forms with optional attributes was
performed. Subsequent defined optional attribute of
parts was size of batch.
From the predefined methods, as examples, the
following can be mentioned:
- data input method, by which values of times
related to individual part are assigned to the
pertinent machine.
- output method that is functional for the purposes
to allocate part routings to machine cells in
compliance with a operation sequence prescription.
Mentioned relations through simulation experiments
in the following order were tested. Firstly, it was
detected, how a change from a serial batch
processing to a parallel batch processing can
influence the manufacturing lead time duration. To
test it, all batches were gradually divided into N
equal-size sub-batches where for batch #1 is N=1,
batch #2 is N=2, batch #3 is N=3, batch #4 is N=4,
batch #5 is N=5 and for batch #6 is N=6. In this
experiment whole manufacturing lead time of all
batches (MLT
W
) was indicated. For the calculation of
MLT
W
it was applied equation 4 that is sufficient to
cover the whole manufacturing lead time under
condition that waiting time of parts in queue T
noq is
being calculated for all batches from t
0
(see in figure
1b) and that all machines and equipment are
available for processing parts in time t
0
. Then the
whole manufacturing lead time can be calculated by
the following expression:
IBW
MLTMLT max=
(5)
Secondly, computer experiment was focused on
learning influence of batch sequencing on whole
manufacturing lead time. For this purpose, batches
in above-mentioned six experiments were sequenced
in two manners. In a first mode bathes were
sequenced according to planned schedule. In the
second mode bathes were allocated to processing
machinery and equipment in a random manner.
The results from these two experiments are
presented simultaneously in figure 2.
Figure 2: Whole lead times for different batches.
ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics
382
Another experiment was focused on comparison of
MLT of selected individual batches due to the fact
that changes in MLT
w
between the manners of batch
sequencing in the second experiment were not
exposed. Therefore, individual first 5 parts for the
next experiment were selected. Afterwards, batches
of selected parts were gradually divided into batch
#1 with N=1, batch #2 wit N=2, batch #3 with N=3
and batch #4 with N=4. Individual manufacturing
lead times for given batches were calculated
according to the equation 4. Evenly, as in second
experiment, batches were sequenced in the same two
manners. The results of these two experiments are
shown in figures 3 and 4.
Figure 3: Individual lead times for different batches
sequenced in random manner.
Figure 4: Individual lead times for different batches
sequenced according to the schedule.
5 CLOSING REMARKS
Obtained results presented in figure 2 showed that
size of batches in performed experiments influenced
whole lead times. Moreover, local optimum solution
of the problem between batch 2 and batch 4 can be
identified. However, differences in MLT
w
between
batch sequencing manners in the second experiment
practically were not ascertained. From the next two
experiments it is possible to articulate that changes
in MLT
that was calculated for individual batches
were influenced by different sequencing manners.
Experimental results, which are demonstrated in
figures 3 and 4, also showed that size of batches is
influencing individual manufacturing lead times.
Accordingly, in a given case there is no sense to
modify sequences of batches, vice versa, it is
reasonable to transform batches to the optimal sizes.
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