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

 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):

)(

noioi

sui

TQTTMLT

++=

∑

(1)

where i indicates the operation sequence in the

processing and i = 1,2,…,n

.; T

represents setup

time for each process; T

is operation (processing)

time per item per process; Q demonstrates batch size

and finally T

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

are represented by straight

arithmetic averages and variables T

, T

are

calculated as weighted-average values.

Then, the formula for calculation of average

MLT, can be expressed as

where n

equals the number of batches, Q

represents the batch quantity of batch j among n

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

⎪

⎭

⎪

⎬

⎫

⎪

⎩

⎪

⎨

⎧

⎟

⎠

⎞

⎜

⎝

⎛

∑

∑∑∑

∑

∑∑

===

QQQ

nojmj

ojjmj

sujmj

nQn

TQn

111

(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

sui

TTQTTTT

MLT

+++++++=

∑

−

sun

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

) was indicated. For the calculation of

MLT

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

(see in figure

1b) and that all machines and equipment are

available for processing parts in time t

. 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

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

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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