THE 1900 INTERNATIONAL GUNFERENGE UF THE SYSTEM DINAMICS SOCIETY, SEVILLA, OCTOBER, 1986.
A SYSTEM DYNAMICS PERSPECTIVE ON JIT-KANBAN
by Ramon O'Callaghan
(doctoral candidate)
Anderson 25
Harvard Business School
Boston, Mass. 02163
Paper presented at the
1986 International Conference of the System Dynamics Society
960 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
A SYSTEM DYNAMICS PERSPECTIVE ON JIT-KANBAN
by Ramon O'Callaghan
Abstract
Just-In-Time (JIT) production is the notion of producing the
necessary products in the necessary quantities in the necessary
time in every process of a factory and also among companies. It
is not uncommon to find JIT used synonymously with "Kanban," which
is the name for a specific inventory replenishment system
developed by Toyota to accomplish JIT production. The Kanban
system employs cards (kanbans) to signal both the need to deliver
more parts and the need to produce more parts. A unique feature
that distinguishes the kanban-based JIT system is its unique
“pull” nature.
The paper begins with a review of JIT production and the Kanban
system. Then, using the structuring principles of System
Dynamics, a simulation model of a kanban-based JIT production
system is developed. The formulation effort begins with the
"simple structure" of one production stage. By connecting a few
of these "basic structures" and adding a market interface module,
a complete multi-stage manufacturing system is developed later.
To test the internal consistency of the model, several simulation
experiments are conducted. The unifying theme in these
experiments is the issue of flexibility: How well does the system
adapt to changes. The simulations are thus designed to show, for
different management policies, the behavior of the system in
response to unexpected circumstances. The following cases are
considered: normal response, changing the number of kanbans, a
breakdown, small and large demand increases, bottlenecks, and
capacity planning. Finally, the results of these simulations are
used to point out some of the managerial trade-offs involved in
JIT production.
Although the major contribution is the conceptualization and
formulation of the system dynamics model, the paper lays the
groundwork for subsequent normative research in the field of
operations management.
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 961
BACKGROUND ON JUST-IN-TIME PRODUCTION AND THE KANBAN SYSTEM
Just-in-Time~ production is the notion of producing the necessary
products in the necessary quantities in the necessary time in
every process of a factory and also among companies.
In ordinary production control systems, various production
schedules are issued to all the processes. Parts and assemblies
are produced according to these schedules, employing the method of
the preceding process supplying materials and parts to its
following process (see figure 1). This is known as a PUSH system.
This method makes it difficult to promptly adapt to changes caused
by demand fluctuations. For adapting to these fluctuations, the
company must change each production schedule for each process
simultaneously, and this approach makes it difficult to change the
schedules frequently. As a result the company must hold inventory
among processes to absorb troubles and demand changes.
By contrast, Just-in-Time (JIT) is a PULL system, in the sense
that the subsequent process withdraws parts from the preceding
process. Only the final assembly line knows accurately the
necessary timing and quantity of parts required. The final
assembly line goes to the preceding process to obtain. the
necessary quantity at the necessary time for assembly ( fig. 2).
Thus, the preceding process produces the parts withdrawn by the
subsequent process. The procedure is repeated further down the
line. The beauty of this method is that no production schedules
need to be issued simultaneously to all processes (at least in the
short run). Additionally, inventory levels are indeed quite low
because nothing is produced that has not been requested (by the
subsequent process) for immediate use. (Hall, 1983).
The Kanban system
"Kanban" (pronounced kahn-bahn), literally translated, means
"visible record" or "visible plate." More generally, kanban is
taken to mean "card,"
The Kanban system can be viewed as an information system that
controls Just-in-Time production.
The Kanban System employs cards ("kanbans") to signal the need to
deliver more parts, and the need to produce more parts. Kanbans
are attached to units or containers holding a given number of
units. When a unit (or container) is used up, its associated
kanban is detached. Then, the detached kanban becomes an order
962 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
A PUSH SYSTEM: MRP
DEMAND
FINAL
SUB.
CO PARTS => |asseMaLy] P| ASSENSLY a) SHIPPING Lp}
* ‘TRANSMISSION OF INFORMATION
* FORWARD : BY AVAILABILITY OF INVENTORIES.
* NO BACKWARD INFORMATION
+ SIMULTANEOUS INFO. FROM M.P.S.
Figure - 1
(1 1900 INFERIVANUNAL GUNTENCNGE UP INE SYSTEM UINAMILS SULIELY, SEVILLA, OCTOBER, 1986. 965
A PULL SYSTEM: JIT - KANBAN
sue. a0
Oo rs Pe .sSeNaLy | sseusLy POY SHIPPING fea
* TRANSMISSION OF INFORMATION
* FORWARD : BY AVAILABILITY OF INVENTORIES.
“BACKWARD: BY KANBAN (PRODUGTION ORDERS)
Figure - 2
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THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
requesting a new unit.
Two kinds of Kanbans are used: 1) WITHDRAWAL Kanban that specifies
the kind and quantity of product to be withdrawn from the
subsequent process, and 2) PRODUCTION Kanban that specifies the
kind and quantity of product to be produced. See appendix A. The
withdrawal Kanban is used as an INTER-PROCESS signal: to move
physical units from one process to another process that takes
place at a different location; whereas the production Kanban is an
INTRA-PROCESS signal: to issue production orders in a particular
process.
As result of this dual chain of kanbans, the rate of production of
the succeeding process is transmitted to the preceding process and
every process receives the necessary units at the necessary time
in the necessary quantities. The Just-in-Time ideal is realized
at each process.
CONDITIONS FOR THE KANBAN SYSTEM
Smoothing of production:
\
A
The JIT ideal is to make one piece just in time for the next
operation. The kanban system is the information system that
carries out this ideal by ensuring that the preceding processes
continuously produce their product in the quantities withdrawn by
the subsequent processes. Since the subsequent processes will
require a single unit or a small lot size, the preceding processes
must make frequent setups according to the frequent requisitions
by the subsequent processes. The Japanese use engineering to cut
machine set-up times so that it is economical to run very small
batches.
Traditionally, the Economic Order Quantity (E0Q) concept has been
used as the “optimal” lot size. The EOQ is a compromise between
inventory carrying costs and set-up costs. But, as the Japanese
experience demonstrates, these are only the obvious costs. ‘The
Japanese have found that producing and carrying smaller lots
results in many benefits other than savings on inventory carrying
costs. The main benefits are in quality, worker motivation and
productivity (Schonberger, 1982).
For a small-lot withdrawal and a small-lot production, the
smoothing of production (leveled daily production) is a necessary
pre-requisite. The Kanban system itself is merely a dispatching
means for actual production actions during each day at each
process. Before entering the phase of dispatching the jobs by
Kanban, overall planning throughout the plan must be made in
advance. Toyota, for example, informs each process and each
AIIVEIME VYNEERENVE UF INE OTOIEM UINAMIVS OUUIETY. SEVILLA, UUIUBEN, 1900, YOO
supplier each month of a predetermined monthly production quantity
for the next month’s production so each process and each supplier
can prepare in advance its cycle time, necessary workforce,
necessary number of materials, etc. (Monden, 1983). Based on
such overall plans, all processes in the plant can start
Just-in-Time production (according to the new schedule) the first
day of the month. .
Production planning for smooth production:
The objective of production planning in JIT is to prepare to
execute a level schedule. A level schedule is one that has as
even a distribution as possible of material requirements as well
as labor requirements.
Prior to JIT production, most companies operated on either a
monthly ordering system, or on the basis of MRP. With monthly
ordering, parts schedules are based on forecasts, many of them
independently made for each part number. With MRP they are most
generally made by back scheduling due dates for parts based on an
explosion of requirements from the Master Production Schedule. If
production is repetitive, these schedules are normally converted
into daily schedules for the plant floor. (fig. 1). (Morecroft,
1983).
With JIT production, planning the final assembly schedule is
critical. The final assembly schedule is the key that triggers
the whole system. JIT production requires development of the
ability to synchronize everything from the final assembly
schedule. All other schedules are only in preparation for this.
Except for final assembly, actual production is executed in
response to a pull signal, not a schedule.
The pre-planning of final assembly schedules may start a few
months before the final assembly schedules (actual runs) are given
daily to the lines. Planning is approximate in the early stages.
A “master production schedule" (MPS) is developed as a summary in
daily buckets of "expected" final assembly schedules. The
preplanning (the MPS) is done based on a forecast, and the closer
the plan comes to the time of execution, the more it is revised,
based on a combination of forecast and actual demand. The final
assembly schedules which will really drive the pull system are the
last revisions, and these may be developed as little as one day
before they are run.
The initial stage of final assembly scheduling is to fix the line
rates. If final assembly lines are to be balanced and fabrication
balanced to run with them, initially fixing the overall line rate
is important to allow everyone to plan ahead for the most
significant changes in equipment configuration and manning. If
966
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
equipment is flexiole and workers are cross-trained to work at
several different positions with skill, the possibility of a plant
rebalancing itself to operate at a different rate is increased,
but that change cannot be made frequently. What is most often
done in Japan is to adjust the length of the planned work day,
usually by overtime.
In summary, these are the main points in planning production for a
JIT system:
1 - The overall rate of production and an approximate model mix
are fixed so that everyone can prepare in advance.
2 - Within the confines of the overall fixed rate, total output
and model mix can be adjusted, within limits, from that which was
first planned.
"Freezing" the production schedule:
The length of time required for production planning depends on how
much time is required physically and organizationally for
preparation. During this planning period, the current production
schedules are held “frozen” (i.e. they are not changed). The
amount of time over which the overall production rate is “frozen”
ranges from 5 to 25 working days. The fabrication schedules are
developed by exploding the master production schedule using the
bills of materials. .Since the production schedule is "frozen,"
what results is a set of fabrication schedules: one for each
identical day in the planning interval (a 15 day period, for
example). Again, the purpose of these schedules is to allow
fabrication, subassembly, and supplier supervisors to have advance
warning about the scope of the schedules to be run. This allows
pre-planning of the workplace, manning, and tooling organization
required to balance the operations, move the material, and perform
preventive maintenance. The idea is that advanced planning for
JIT should provide for capacity in excess of what is required well
in advance. This idea is captured in figure 3.
Note however, that the planned fabrication schedule only ADVISES
departments of the impact of the PLANNED final assembly schedule
on each product. ACTUAL fabrication takes place only IN RESPONSE
to the PULL system coming from final assembly.
Coping with demand changes:
In general, the number of Kanbans is kept constant. Therefore,
when daily demand increases, the lead time must be reduced. This
requires reducing the time of standard operations by changing the
allocation of workers in the line. However, a workshop incapable
RHIVINAR UYWFERENVE UF IME STOLEN UVINAMILS SUGIEIY. SEVILLA, OCTOBER, 1986.
THE "MARRIAGE" OF MRP AND JIT (YAMAHA'S. SYNCHRO )
Ce Pants plasseuory| p> |asseucn p>) SHIPPING |
V4 FR
‘CAPACITY ‘CAPACITY ‘CAPACITY
PLANNING PLANNING PLANNING.
DEMAND
Figure - 3
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THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
of such improvements will suffer line-stops or force the use of
overtime. Shops may increase the number of Kanbans to adapt to
demand increase.
To illustrate this adaptability (known as "volume flexibility"),
it is worth examining what happens in-companies not using Kanban.
These companies lack the means to deal smoothly with sudden,
unexpected demand changes. The ordinary control system centrally
revises the current production schedules, determines the new
production schedules and issues them simultaneously to all
production processes. Typically, this is a task that requires
seven to ten days. As a result, the various processes are faced,
from time to time, with abrupt changes in production requirements.
Instead, companies using the Kanban system do not issue detailed
production schedules simultaneously to the preceding processes
during a month; each process can only know what to produce when
the production-ordering Kanban is detached from the container at
its store. It is only the final assembly line that receives a
schedule for a day's production. The way the Kanban system
achieves volume flexibility is by means of "fine-tuned
production". That is: the system is able to produce a few more
units than the number predetermined by schedule without actually
vevising the schedule. Such fine-tuning of production by Kanban
can only adapt to small fluctuations in demand. According to
Toyota, demand variations of 10% can be handled without revising
the schedule and without changing the number of Kanban (that is
without increasing the inventory levels).
However, in case of larger seasonal changes in demand, or in the
case of an increase or decrease of the actual monthly demand over
the predetermined load or the preceding month’s load, all the
production lines must be rearranged. The cycle time of each
workstation and the number of workers in each process must be
changed. Otherwise, the number of Kanbans must be increased or
decreased (allowing more or less inventory in the system).
A SYSTEM DYNAMICS MODEL OF JIT-KANBAN
The model presented in this paper is a multi-stage manufacturing
system, It consists of a transfer line including the following
processes: 1) parts procurement, 2) sub-assembly, 3) final
assembly, and 4) shipments.
This structure is shown in figure 2.
The development of such a relatively large model begins with the
understanding and formulation of its integral components. We will
IE 100 INTEMIVATIUNAL UUNFERENUE UF IME SYSTEM VINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 969.
The
start with the formulation of one "basic structure." The model of
the “basic structure" will be that of an individual stage
(production process) within the chain of processes that
constitutes the entire manufacturing system. Later, we will
develop the complete multi-stage. model by chaining several of
these "basic structures"
“basic structure"
In the "basic structure," a workstation stands in between two
inventories: the inbound stock and the outbound stock. The
inbound stock consists of parts or assemblies that are inputs to
the production process. The outbound stock results from the
accumulation of the assemblies or products that are manufactured
by the workstation (its output). Thus, the production process at
a given workstation depletes its inbound inventory and increases
its outbound inventory. As we have seen, the production Kanbans
regulate this process.
When consequent workstations are located apart from each other,
the output of one station has to be physically transported to its
succeeding station (where it becomes the input to the next
production process). This transportation process takes time and
holds some inventory ("in-transit" inventory). In this
transportation process, "In-transit" inventory results from the
“transportation lead ti (delay due to the time to move a unit),
and a “withdrawal" kanban is used to trigger the moving of units.
This is analogous to the production process where "In-process"
inventory results from the "production lead time" (delay due to
the time to complete a unit), and a "production" kanban is used
for triggering production. The analogy is so strong that most
modelers of kanban systems do not make any distinction and
consider transportation as another process that is interleaved in
the manufacturing chain. (Kimura and Terada, 1981).
Given that the transportation process does not add anything
conceptually new to the "basic structure", it ‘will be assumed that
the workstations in our model are so close to each other that no
physical transportation is required (the effect of transportation
is neglected, and the "withdrawal kanbans" are not used). Our
discussion will thus revolve around the "production" kanbans only.
.Each time a unit is withdrawn from inventory, its kanban is
detached and placed in the collection box (See Appendix A).
Periodically (every few hours) the detached kanbans that have
accumulated in the box are taken to the dispatching post, where
they become production orders. The time interval at which the
kanbans are taken from the collection box and moved to dispatching
is fixed. This interval is called the “Kanban cycle." The
kanbans in the collection box become production orders when they
970
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
are dispatched in the next time interval (kanban cycle).
It is important to realize that the "kanban cycle" determines how
fast the system will react to changes in production rate. Using
the system dynamics terminology, the "kanban cycle" is a “time
constant." In the real world this parameter will be determined by
different factors. ‘In the case of suppliers, it is established by
a contract whereby the supplier agrees to deliver once or twice a
day, fot example. In the case of a production process, it will be
determined by the flexibility to transfer workers to the
workstation when required, by the policies on the use of overtime,
and especially, by the production lot size (which in turn will be
determined by the set-up times).
From the previous section that has introduced JIT-kanban, we can
summarize the essential points determining the structure and
operation of the Kanban system:
Production is not instantaneous: it takes time to produce a unit.
That means there will be a production "lead time", and,
consequently, some “work-in-process" inventory at each
manufacturing stage.
The number of Kanbans determines the maximum inventory. In fact,
any Kanban has to be either attached to a container (in
Work-in-process. inventory, or: in output inventory), or in the
Kanban receiving box, or in the dispatching post.
The kanbans in the receiving box (that have been detached by the
succeeding process each time a container has been used), will
eventually get to dispatching. So, all the detached kanbans that
have not yet joined the production process, constitute a, BACKLOG
of PRODUCTION ORDERS. The size of this backlog is determined by
the kanban eycle (in equilibrium the number of kanbans in this
backlog is the number of kanbans detached during a kanban cycle,
that is = normal production rate x kanban cycle ). See figure 4.
* This backlog of production orders determines the DESIRED
production rate (in units/day). I say "desired" because the
ACTUAL production rate will also depend on other factors like:
availability of inventory from the preceding stage, availability
of enough workers, or constraints on overtime.
- The total number of Kanbans is given (a system’s parameter) and
equals the sum of the number of "“work-in-process" containers plus
all containers in "output" inventory (units completed) plus
backlog of production orders.
IME 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
THE KANBAN SYSTEM
INVENTORY
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PRODUCTION
PROCESS
INVENTORY
af
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PRODUCTION
ORDERING
KANBAN POST
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Figure - 4
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KANBAN
971
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THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986,
Formulation of the "basic structure"
With the preceding points in mind, let’s now move to the stock and
flow diagram which is shown in the figure 5.
The figure shows the backlog of kanbans that have been detached
(prod. orders, P02). The inflow rate of this production orders
backlog is controlled by the rate at which units are withdrawn
from inventory (12), which is the production rate of the
succeeding stage (PR3). The outflow rate is controlled by the
actual production rate of the current stage (PR2).
All production kanbans accumulated in the production orders
backlog (P02) are supposed to be dispatched during the time
interval of the Kanban cycle (TI2). Thus, the desired production
rate (DPR2) is determined by the production orders backlog (P02)
and the Kanban cycle (TI2).
But actual product rate is not always the "desired" production
rate. There are some constraints that prevent production rate
(PR2) from being the "desired" production rate (DPR2) at all
times. Figure 5 also shows those constraints:
1) availability of inventory from the preceding stage (I1): we
cannot produce if do not have enough inventory at the input.
Instead of using a step function (that would abruptly change from
zero to one, or one to zero) to model the effect of the
availability of inventory from the preceding stage, I have
preferred to use a continuous function (SW2), A reason for doing
so is to avoid the technical problems associated with a
discontinuity. Another reason is that the inventory in our model
may in fact represent the aggregate inventories of different
parts, assemblies or products (and not one single product). The
global effect can thus be seen as being more gradual.
2) production capacity ("Maximum production rate" MPR2) (i.e.
number of workers, or maximum overtime allowed, etc.. A way to
formally model capacity is in terms of the number of workers
assigned to the station, their productivity (output/hour), and the
maximum overtime allowed. For the sake of generality, however,
production capacity in our model will be expressed in the form of
“maximum production rate." That is: without especifying the
source that limits capacity.
Finally, there is the product completion rate (PCR2) which is the
production rate delayed by the production lead time LT2 (the time
to produce a unit) and the work-in-process inventory (WIP2).
A slight variation of the "basic structure" of the kanban system
is presented in figure 6. Here, the backlog of kanbans
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 973
KANBAN SYSTEM: BASIC STRUCTURE
ce LEAD
mpROcEss TIME
ur
INVENT.
3 wip pp} VENT. SZ
ft > pel 12 >
PROD.
Proouct
COMPLETION RATE
PR3
PROD.
oADERS GB
Por
PROD.
K
sac #e
were TIME INTERVAL.
FOR KANBANS
(KANBAN CYCLE)
Figure - 5
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THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
representing production orders has been replaced by an information
structure whose central point is the auxiliary variable P02
(production orders). In this new structure, the production rate
is expressed as a function of the total number of kanbans (maximum
inventory allowed), and the existing inventories (work-in-process
and finished units). This means using equation (I) instead of
equation (II) (appendix B).
Recall that, at all times, a kanban is either in the backlog of
production orders, or in the work in-process (WIP) inventory, or
in the inventory of finished units. The sum of kanbans in
inventory, kanbans in WIP, and kanbans in backlog is constant.
This sum is the total number of kanbans for the production process
in question. Since the total number of kanbans is kept constant
in practice, we can always express the kanbans in the backlog as a
function of the kanbans in WIP, and inventory.
Prod. orders = Total # of kanbans - # of kanbans attached to WIP
- # of kanbans attached to finished units inventory
As commented earlier, the number of kanbans determines the maximum
inventory in- the system. This is illustrated with a simple
example. Let's imagine that the succeeding stage does not
withdraw any unit from inventory. Then no new kanbans will go
into the production orders backlog. WIP will eventually be
completed and accumulated into the inventory of finished units.
Then, the few orders still in backlog will go to WIP, and finally
into inventory of finished units. In the final state, backlog
will be zero, WIP will also be zero, there will be no production
and all kanbans will be in the inventory of completed units.
Summarizing, the essence of the kanban system can be explained by
this basic structure which is no more than a "GOAL SEEKING"
FEEDBACK LOOP, with ‘the GOAL being the MAXIMUM INVENTORY ALLOWED
in the system (which is entirely determined by the number of
kanbans) .
It is worth mentioning at this point the subtlety of the kanbans:
their double mission. Individually taken, each kanban is a
signaling device that triggers production (a kanban becomes a
production order). But taken together, all kanbans constitute the
goal of the basic feedback loop: the maximum inventory allowed.
This will be illustrated later with some simulation experiments.
It is important to realize that the two missions are simultaneous.
If there is a small number of kanbans (a tight inventory policy)
there is little flexibility for reacting to desired changes in
production rate (in case of an increase of demand for example,
there may not be enough kanbans to generate the number of
production orders per kanban cycle required to get a higher
production rate). If you want more flexibility you need more
kanbans to have the necessary slack in terms of production orders.
INE 1900 INIEMNATIUNAL GUNFERENGE UF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 975
KANBAN SYSTEM: BASIC STRUCTURE
i LEAD
wenocess / TIME
LT2
i 7
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"1 2
PROD.
ORDERS
PROD.
CAPACITY
MPR2
TOTAL NUMBER
OF KANBANS
TR
TIME INTERVAL,
FOR KANBANS
(KANBAN CYCLE)
Figure - 6
976 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
But then, of course, you have to allow higher levels of inventory.
This flexibility-versus-inventory trade-off stems from the very
essence of the kanban system.
A Dynamo version of the “basic structure"
Pee LAPHP PRADA O ANH HE EH
ap
As an example of a possible implementation, the Dynamo equations
of one such “basic structure" are included here.
A word about the notation. In this model, Stage 1 represents the
preceding process (parts), stage 2 represents the current process
(sub-assembly), and stage 3 represents the succeeding process
(final assembly). The subscripts (1,2, or 3) in the equations
indicate the stage each variable refers to.
STAGE (2) : Sub-Assembly
Stocks
12.K=12.J+(DT) (PCR2.JK-PR3.JK) Inventory of finished units
12=NK2*CC2- (ND*LT2) - (ND*TI2)
WIP2.K=WIP2.J+(DT)(PR2.JK-PCR2.JK) Work-in-Process inventory
WIP2=ND*LT2
flows
POR? .KL=DELAY3(PR2.JK,LT2) Product completion delay
LT2=.5 DAYS due to production lead time.
PR2.KL=CLIP(MPR2.K,DPR2.K,DPR2.K,MPR2.K)*SW2.K
MPR2.KeL.1*PP.K max, prod. (capacity) = 10% above prod. plan
$W2.K=TABLE(TSW2,CI1.K,0,10,1) effect of inventory of preced. stage
TSW2=0/.85/.95/1/1/1/1/1/1/1/1
CIL.KeI1.K/CCL
CC1=10 UNITS/CONTAINER
Information feedback and policies
PO2.K=NK2.K*CC2-12.K-WIP2.K prod. orders (as a function of
Number of Kanbans, WIP, and Inventory)
DPR2.K=PO2.K/TI2
TI2=0.5 DAY
where PR = production rate
PCR = product completion rate
I = inventory
(ME 1900 INTERWALIUNAL VUNFERENGE UF IME SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 977
NK == number of Kanbans
cC = container capacity
LT = lead time (production)
TI = time interval (Kanban cycle)
WIP = work-in-process inventory
ND = normal demand
MPR = maximum production rate
DPR = desired production rate
SW = effect of inventory availability (from preceding stage)
PP = production plan
PO = production orders
Although the model documentation is meant to be self-explanatory,
the following points are worth further comments.
In equilibrium, production rate (PR) and product completion rate
(PCR) are constant and equal to “normal demad" (ND). WIP
inventory is also constant, and it is equal to the amount of units
kept in process during the production lead time (=ND*LT2). The
backlog of production orders is also constant, and it equals the
usage (ND) during the kanban cycle (number of kanbans detached per
cycle) (=ND*TI2). The level of finished-units inventory is
determined by the total number of kanbans minus the number of
kanbans attached to WIP, minus the number of kanbans in the
backlog of production orders. Therefore, the initial value of
finished-units inventory is unequivocally determined by the
expression:
N 12 = NK2*CC2 - (ND*LT2) - (ND*TI2)
Production rate (PR2) is perhaps the most complex equation. A
special Dynamo function, CLIP, is used to mean the following: if
"Desired production rate" (DPR2) is lower than the "Maximum
production rate" (MPR2), then let "Production rate" be the
"Desired production rate." Otherwise, let "Production rate" be
the "Maximum production rate." This how the effect of a capacity
constraint is introduced. But, there is another effect to be
taken into account: the availability of inventory from the
preceding stage (SW2). This effect is introduced as a
multiplicative effect on production rate. The auxiliary variable
$W2 acts as a switch: when the preceding stage has enough
inventory (Il) its value is one. When the level of inventory
approaches zero, SW2 gets values lower than one, and eventually
becomes zero. This has been implemented by means of a table
function.
Finally, the number of product orders to be dispatched (P02) is
978
The
‘THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
determined by the number of kanbans that are not attached to
physical units (or containers). This variable might be expressed
as a backlog: a level whose inflow would be the usage of finished
units by the succeding stage, and whose outflow would be
production rate at the current stage. However, this is not how it
is has been expressed in our model. PO2 has been written,
instead, as the difference between the "maximum inventory allowed"
(as given by the total number of kanbans, NKK2*CC2) and the
existing inventories (sum of WIP and finished units).
PO2.K = NK2.K*CC2 - I2.K - WIP2.K
This has the advantage of reflecting the goal-seeking nature of
the information feedback loop: the short-fall between actual
inventory and "maximum inventory allowed" signals the need for
more production. Also, having the total number of kanbans (NK2)
included explicitly in the expression for P02 is quite useful,
because it allows us to treat this parameter (NK2.K) as another
variable (whose value may be changed in the course of a simulation
run). This will be helpful later when we will conduct several
experiments with the model.
complete multi-stage model:
A multi-stage model is developed by connecting a series of “basic
structures" like the one described above. Our model of a complete
manufacturing system is a simple three stage transfer line that
includes parts, sub-assembly, final assembly. The model also
incorporates a market-interface module to take care of shipments
and customer orders backlog. Figure 7 shows one such stage at the
end of the manufacturing line.
The structure contains a typical customer order backlog that
determines "desired" shipping rate given a "normal delivery delay"
(the days of backlog is assumed to be a company’s policy).
Shipping a unit depletes both the "backlog" of customer orders and
the inventory of "finished products." At the same time, taking a
unit out of the finished goods inventory leads to the issuance of
a production order through the kanban that has been detached.
This is how the PULL system is triggered.
"Demand" is the external stimulus that triggers the PULL system.
An increase in "demand," leads to an increase in the final
production rate. This is the causal sequence:
Demand ---> + Backlog ---> + DSR ---> + SR ---> - F. Products
F. Products ---> - Prod, orders ---> + DASR ---> + F. Assmbly rate
INE 1¥60 INTEKNAIIUNAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986, 979
SHIPMENTS AND BACKLOG
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THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
where "+" stands for increase, and "-" stands for decrease.
Finally, note that shipping rate may also be affected by the
availability of finished products inventory in a way similar to
how production rates are affected by the availability of inventory
in the preceding stages affects.
The figure also shows the master production schedule developed as
a function of the backlog (desired ship rate, in fact) and a
forecast of demand. This production schedule will be used for
developing the monthly "frozen schedule" which will then be used
to plan capacity in the different stages (a resource allocation
process), Later, with the simulation results, we will have an
opportunity to expand on the issue of capacity planning.
A dynamo version of the complete multi-stage model is shown in the
appendix.
SIMULATION EXPERIMENTS
The objective of this section is to test the internal consistency
of the model by looking at its behavior under different
circumstances. In order to do that, a series of different
experiments are run on the model. This helps us understand the
dynamics of a kanban-based manufacturing system and illustrate
ways in which the model can be used for further research.
Each experiment involves one or more simulation runs. The results
of each simulation are presented as a set of three graphs, each
plotting different variables over time. Each set will be referred
to as one single figure. These are the graphs and the variables
plotted in each figure:
* Production Rates
- PR3: Final Assembly rate (stage 3)
- PR2: Sub-assembly rate (stage 2)
- PRL: Parts arrival rate (stage 1)
- D: Demand (shown only as a reference)
* Inventories
- INV3: Finished products (stage 3)
- INV2: Sub-assemblies (stage 2)
IE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 981
- INV1: Parts (stage 1)
* Backlog and Shipments
- D: Demand
- B: Customer orders backlog (stage 4)
- SR: Shipping rate (stage 4)
Note that the first 3 stages of the manufacturing chain (1 to 3)
are concerned with procurement and production processes. The
variables characterizing their behavior are: production rates and
level of inventories. The results regarding these variables are
found in the first two graphs. The stage at the end of the chain
(stage 4) is not concerned with manufacturing activities. Stage 4
is the market interface: it receives, accumulates and dispatches
customer orders by shipping units from the inventory of finished
products. The results that have to do with this stage are found
in the third graph ("Shipment and Backlog").
The series ofX\experiments follows.
Normal response
The first simulation shows the behavior of the system in response
to a oné-time step increase in demand. The increase in demand is
not too big, and falls within the range of changes that the system
can handle (there is enough production capacity and enough kanbans
for the new production rate).
The results are presented in fig. 8. Note the pull nature of the
system. The increase in demand triggers a chain reaction with
some delay between stages: ship rate goes up, then final assembly
rate follows, then sub-assembly rate, and finally parts arrival
rate. As production rates increase, inventory levels decrease.
They do so in the same sequence (from end to beginning of the
chain): first, finished products; then, sub-assemblies; and
finally, parts. The main reason why inventories (of completed
units) diminish is because more units are now held as
"work-in-process" inventory due to the increase in production
rate, and also, because the backlog of production ordering kanbans
needs to be larger to signal a higher production rate. (Remember:
the sum of WIP inventory, completed units inventory and backlog of
production orders is fixed).
Changing the number of kanbans
This experiment is aimed at understanding what happens when the
982 — THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
Fig. 8 - Normal response
PRODUCTION RATES
INVENTORIES
BACKLOG AND SHIPMENTS
‘HE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
983
Fig. 9 - Increase in number of kanban
PRODUCTION RATES
pee ats
PR oP.
INVENTORIES
984
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
number of kanbans is changed suddenly while other things remain
equal. In this simulation run, we are not changing demand. This
simulation illustrates some of the subtleties of the kanban system
that we saw before.
Figure 9 shows the result of increasing the number of kanbans in
stage 3 (final assembly) by 20% in day 1. We see that the
immediate result is an abrupt peak in production rate due to the
fact that new kanbans enter the system as production ordering
kanbans (thus increasing the level of production orders backlog).
Note again how the pull system works: it transmits the production
peak to the preceding stages of the chain (sub-assembly, and
parts).
This sudden increase in production rate is artificial. Since
demand stays the same, we know that in the long run production
rates will resume their normal value (= demand). What happens is
clearly illustrated by the graphs plotting inventories. The
introduction of more kanbans in stage 3 (final assembly) has
raised the level of "inventory allowed". Due to the goal seeking
nature of the main feedback loop (of the "basic structure") the
system reacts so as to build up more inventory in stage 3
(finished products inventory). This is why in the new equilibrium
this inventory has a higher level than before. During the
transient period, the inventories of the preceding stages are
temporarily depleted (levels go below their normal value) due to
the higher-than-normal rate of production of the succeeding stages
(the succeeding stages are withdrawing more units than normal).
Breakdowns
Simulating a machine breakdown is an interesting way to test a
pull system.
In a "pure" push system, the stages preceding the "broken-down"
station continue their production according to their schedule even
after the breakdown has occurred. The result is that inventory
accumulates at the input of the "broken-down" station.
In a pull system, the preceding stage does not produce anything
that has not been requested (recently) by the succeeding stage.
Therefore, in the event of a breakdown, the flow of production
ordering kanbans to the preceding stages ceases. This stops
production in the preceding stages.
Figure 10 shows a one-day breakdown in final assembly (the system
was previously in equilibrium). We observe how the production
rates of the preceding stages do go down after some delay (due to
the duration of the kanban cycle). After station 3 has been
repaired, its production rate goes up as much as it can go
BNE W900 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
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THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986,
(remember that it is limited by the capacity constraint: "maximum
production rate"). The Yeason for doing so is the big
accumulation of customer orders (backlog) that has taken place
during the period in which stage 3 was out of order (and therefore
the corresponding pressure for delivering finished products).
After a few days producing at the "maximum prod. rate" to clear
the abnormally high level of customer orders in backlog,
production rates resume their normal level (= normal demand) in
day 13 and beyond.
It is interesting to see what happens to inventories. Finished
products inventory goes to zero once the few units in inventory
have been shipped. The preceding stages are not notified
instantaneously about the breakdown. Due to the delay of the
kanban cycle, they are still producing what’ they were asked for in
the periods before the breakdown. If the situation persisted,
these inventories would reach the "maximum inventory allowed"
level (determined by the total number of kanbans as we have seen
before). But this situation is, of course, temporary. As soon as
production activities resume (once stage 3 has been repaired),
inventories are being used up again by the succeeding stages in
order to produce at what it is now the "maximum production rate".
At this point, inventory levels fall below the normal level,
because the current production rates are higher than normal.
Later, in the steady state all inventories regain their normal,
equilibrium level.
The "shipments and backlog" graph shows what happens at the market
interface stage. After the breakdown, and once the available
inventory of finished products has been exhausted, shipping rate
falls to zero. In the meantime, customer orders keep arriving.
But, since we are not able to dispatch them, the backlog grows and
grows rapidly. After the break-down has been fixed, the natural
tendency of the system is to ship as much as possible. This
pressure is captured by the variable "desired ship rate" (not
shown in this graph). However, there is a constraint on shipments
(a "maximum ship rate") which in our model plays a role similar to
the capacity constraint in production. In the long run, backlog
is reduced to its normal level (1.3 days), and shipping rate
matches demand.
Bottlenecks
There are several situations in which we may encounter a
bottleneck. The case in which a bottleneck in one stage prevents
the system from adequately responding to an increase in demand is
particularly interesting.
Two kinds of bottlenecks are possible in one stage of a JIT-kanban
system. One is obvious, the other. one is not so obvious.
Tr, (9OU INTERIVATIUIVAL UVUNPERCNUE UF IME STSIEM VINAMICS SUCIETY. SEVILLA, OCTOBER, 1986.
987
The obvious bottleneck is the classical capacity constraint of a
particular stage: when its value happens to be lower than the
capacity of the other stages causing the line to be unbalanced.
The not-so-obvious bottleneck is due to a constraint in the number
of kanbans at a given production stage.
Let's analyze the former case first.
Bottleneck caused by capacity constraint:
This type of bottleneck is simulated in stage number 1 of our
médel (Parts). That is: "maximum production rate” (MPR) in stage
1 is only 10% above the normal production rate (= normal demand),
whilst MPR is 20% above normal. The step increase in demand is
208.
Figure 11 shows the results of the simulation run. The bottleneck
is clearly seen in the graph of production rates. We observe the
tendency of production rates to go up in a "chain" response to the
increase in demand (in the typical "pull" fashion). The problem
arises when parts arrival rate (PR1) reaches its constraint level
("maximum level = 10% above normal demand). Beyond this point,
stage 1 (Parts) does not produce enough to meet the needs of stage
2 (Sub-assembly), and its lack of inventory forces the rate of
stage 2 to drop. Similar considerations apply to the effect
of
stage 2 on stage 3 with some delay. So, in the long run all
production rates (and eventually the shipping rate) converge
to
the value of the production rate of the stage experiencing the
bottleneck.
Note the effect on the market interface (stage 4). For a while,
ship rate is able to meet demand. But later, when the effect
of
the bottleneck has been transmitted to the end of the chain,
shipping rate drops and backlog grows hopelessly.
Bottleneck caused by Kanban constraint:
This is the "not-so-obvious" kind of bottleneck. As mentioned in
the preceding section, the number of kanbans does not
only
establish the "maximum inventory allowed" but does in fact
determine the slack (flexibility) to place more production orders
when required (by an increased in demand, for example). We may
have a system with enough production capacity, but a tight
inventory policy (small number of kanbans) at the same time.
In
such a situation, production rate is not limited by capacity.
Instead, the lack of kanbans prevents the system from placing more
production orders. Production rate is thus limited by the number
of kanbans as well.
988 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
Fig. 11 - Bottleneck due to capacity constraint
PRODUCTION RATES
INVENTORIES
BACKLOG AND SHIPMENTS
IME 1900 INTENIVALIUNAL VUNFERENUE UF IME SYSIEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. YS9
Fig. 12 - Bottleneck due to kanban constraint
PRODUCTION RATES
INVENTORIES
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BACKLOG AND SHIPMENTS
990
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
This kind of botvleneck is simulated in our model, again, in stage
1. The results >of the simulation are shown in figure 12. We can
see that the behavior of the systes: row is similar to the case of
a bottleneck caused by a capacity constraint. The causes are,
however, quite different.
REFINING THE MODEL TO INCLUDE CAPACITY PLANNING
Until now, we have been assuming that the capacity is fixed. The
next set of simulations consider the case in which-eapacity is in
fact changed each time a new master -production schedule jis
developed. As seen in the introductory section on JIT, each month
(or every few weeks) a "frozen production schedule" is developed.
This schedule is supposed to be the fixed: the "leveled"
production rate that will prevail during the month. Some
deviations can be permitted later. In practice, the purpose of
this pre-established schedule is to allow fabrication,
sub-assembly, and supplier supervisors to have advance warning
about the scope of the schedule to be run. This allows planning
of the workplace: manning, tooling, materials, and preventive
maintenance. .
This kind of planning has finally been included in our model.
There are two main modules (information structures) to consider:
1) the development of a “master production schedule" (based on a
forecast of demand and the customer orders backlog), and
2) the assignment of more capacity to the different stations (both
in terms of "maximum production rate", and total number of kanbans
in the production process).
Figure 7 shows these two blocks.
It is important to realize that we are now departing from what it
is the basic kanban system. Things can get very complex as we
attempt to link the logic of a push system (like MRP) for
planning, with the effectiveness of a JIT system for executing
production. New factors now enter the picture. The flexibility
of the system to respond to changes in demand may be affected by
system parameters like:
length of the planning period (amount of time over which the
overall production rate is "frozen")
which in turn depends on how much time is required physically and
organizationally for preparation and allocation of resources.
IH 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 991
* the constraint on capacity change from one planning period to the
next. How much can we change in one period? What flexibility do
we have in capacity change?
* forecasting : Is forecast just the smoothing of past demand? or,
is it based on other exogenous factors that anticipate long term
trends?
* the way in which the master production schedule is developed: is
it based on the forecast? or, is it based on the backlog of
accumulated customer orders? or, both?
The link of MRP and JIT is an entire subject per se. Here, we do
not pretend to explore all of the above points. The objective is
to show that the model can certainly be used to get some insights
into some of these issues.
So, we will be tackling just one issue of the above list: the
effect of the "master production schedule" on the flexibility of
the entire system to respond to increases in demand (beyond the
range of what the "basic" kanban system is able to handle).
Simulations experiments with capacity planning:
The simulation starts with a one-time step increase in demand
which is higher than the existing "maximum production rate". As
we have seen in the study of the bottleneck, backlog keeps growing
in the steady state because there is not enough production
capacity to meet demand. In the next planning period, new
capacity will be added. The question is how much? What should be
the next "leveled" production schedule?
If we look at the backlog the pressure is tremendous. If we set
the next "leveled" schedule to the current “desired rate", we may
end up with excess capacity once the backlog has been reduced. On
the other hand, if we look at the forecast (which is basically a
smoothing of past demand) it will tell us that demand seems to be
increasing and will report just a fraction of the actual step
increase (because it will still be averaging over time). If we
set the "leveled" schedule at the value given by the forecast we
will be below the real need.
A linear combination of both has been chosen to develop the
“frozen" schedule for the next planning period. That is:
Production plan = X * Forecast + (1-X) * Desired Ship Rate
992
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
Note that when X = 1 , the production schedule is determined
exclusively by the forecast. When X = 0 , the production schedule
is entirely determined by "desired ship rate".
Figures 13 and 13 show the result of simulations using different
values for X.
We can see that XK = 1 leads to a very reactive response. The
production plan ("leveled" schedule) that results at each planning
period always falls short of real needs. As a consequence, we
have to use overtime almost at all times. It is interesting to
see how, in fig. 18, production rates are above the production
plan (the square symbol line) staying at their “maximum production
rate" (a 5% above the production plan).
The situation is different when we consider the case of X = 0.8
What happens here is an "overshoot:" the production schedule jumps
to the level of 155 units/day which is above the long term
equilibrium of 120 units/date (= new demand). This level
represents 55% increase in capacity. We may well question whether
this would be feasible in real world (this goes back to one of the
points in the above list: the constraints on capacity change).
Note also in ‘the same figure, that some overtime takes place at
the beginning of the planning period (days 14-20), but then
production rates begin to fall below the "leveled" production
schedule. Production rates would get down to the new demand (120
units/day), if the "leveled" schedule remained at the high level
of 155 units/day. In the next planning period (day 24), the new
"leveled" production schedule is finally set to 120 units/day. At
that point, and despite the reduction of production capacity, we
observe considerable undertime. What is the reason for this
apparent contradiction?
The reason has to do with the subtleties of the kanban system:
when the new production schedule is developed and issued to all
stages, the capacity planning module does not only change the
capacity constraint of each stage but also the number of kanbans.
In our case, production capacity and number of kanbans are reduced
in day 24. The withdrawal of kanbans from the system at that
point gets translated into an immediate goal: reduction of
inventory! The "maximum inventory allowed" is now much less than
what we had in the previous period (days 14-23). Therefore
production rates are slowed down until this "all-of-a-sudden"
excess inventories is cleared.
The difference between the two ways of developing the production
schedule is dramatic when we compare the backlogs in figure 13 and
figure 14.
For X = 1 (a reactive production schedule), backlog goes up to 320
orders and it takes 45 days to recover. Instead, for X = 0.8 (a
‘THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
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THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 995
more aggressive, more "nervous" way to develop the production
schedule), backlog peaks at 290 orders and it takes only 22 days.
From a service point of view the "aggressive way" may be more
interesting than the "reactive". But, has the company enough
flexibility to change capacity so much, so often? what are the
costs?
The answers to these questions are beyond what this model can
provide.
Our model has shown, however, that the flexibility of a company
adopting JIT-kanban will not depend so much on the kanban system
as it does on other factors, such as the ability to change
capacity, and the ability to plan production. Only when demand
fluctuations are small does the basic kanban system seem to be an
effective way to respond to demand uncertainties.
CONCLUSION
A system dynamics model of a kanban-based just-in-time (JIT)
production system has been developed. The production process is a
simple three stage transfer line. The modeling emphasis has been
on classical production scheduling and production smoothing. The
model has been used to examine the response of the production
system to small shocks, such as small changes in demand, when the
system is run on "automatic" mode, i.e. management is allowed to
make only very routine responses (such as overtime). The shocks
are simulated with different levels of kanbans in the system, The
second use of the model has begun to explore larger shocks, when
management is allowed to change capacity.
Deliberately, this paper has been quite technique oriented, rather
than problem oriented. Its objective was to show that a JIT-
kanban system could be built using the structuring principles of
system dynamics modeling. Hence, the paper has devoted a long
extension to check the internal consistency of the model by
exposing it to a series of experiments.
The model has limitations that could be overcome in future
versions. For example, the transfer line is very simple: one
product, one linear sequence of material flow. Given that set-up
times have been used to motivate some of the formulas, it seems
that a multi product model would be more appropriate. This is
true. Mixed production should definitely be the enhancement to
include in the next version of the model. Then, issues like
product mix flexibility (and not just volume flexibilit) could be
996
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
explored.
Finally, from a Production and Operations Management perspective,
the contribution of the model (as presented in this paper) is more
latent than real. However, the paper lays the groundwork for more
normative research.
By concentrating on management decisions and policies, research
based on this model could be useful to practitioners. For a given
manufacturing system, what are the objectives that JIT-Kanban
tries to accomplish? What are its problems? What are the levers
available to managers of the transfer line? How should they be
used? How does the system dynamics model give them insight into
what to do?
In summary, subsequent research ought to focus on the “burning”
issues in the management of JIT/kanban systems, and use the model
to shed some light on them.
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 997
APPENDIX-A: OPERATION OF THE KANBAN SYSTEM
This-is how the Kanbans are used:
1 - Production Kanban:
The parts processed at a certain stage are put in a container. A
Kanban is attached or hung on the container and then stored at the
location designated by the Kanban (1) (see figure 15).
When a succeeding process withdraws this part or material, a
worker lifts off the Kanban and puts it into a Kanban box (2).
Kanbans are collected from the box at regular intervals and hung
on hooks on a schedule board. The sequence of various Kanbans on
the board shows-workers the dispatching order of jobs in the
process (3).
A worker produces various items, in accordance with the sequence
of the various Kanbans on the board, as indicated by the Kanban,
at the rate which is set in advance. The Kanban itself moves in
the process with the first unit of the batch (4).
The procedure (1) through (4) is repeated and the production is
continued effectively.
Note that it is probable in procedure (2) that if the succeeding
process never withdraws material from the preceding process then
the Kanban is neither collected from the Kanban box nor is it hung
on a hook of the schedule board. Consequently the item is never
processed at this shop.
2 - Withdrawal Kanban:
The withdrawal Kanban is used for moving materials from the output
of one process to the input of another (distant) process. The
withdrawal Kanban is handled in a way similar to the production
Kanban, with the difference that the process is transportation
instéad of manufacturing (see figure 16).
We should keep in mind that it is also the rule that withdrawals
are equal to what the Kanban indicates and nothing will be
withdrawn unless a Kanban is in the box.
In figure 16, broken lines imply a production Kanban and its
movement in the preceding shop. When material or parts are
withdrawn from storage, a production Kanban on the container is
exchanged with a withdrawal Kanban. The production Kanban removed
will be transferred to a production Kanban (collection) box.
998 — THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
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'HE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 999
APPENDIX - B
DETERMINATION OF THE NUMBER OF PRODUCTION KANBANS:
In a "constant cycle" inventory control system, the re-order date
is fixed and the quantity ordered depends on the usage since the
previous order was placed and on the outlook during the lead time.
The following formula is used to calculate the maximum inventory:
Maximum Inventory =
= daily demand x ( order cycle + lead time ) + safety stock
where the order cycle is the time interval between an order time
and the next order time and the lead time is simply the time
interval between placing an order and receiving delivery.
Theoretically, the order cycle is determined by the formula:
order cycle = ( economic lot size ) / daily demand
In practice however, the order cycle is often determined by
external constraints such as steps in the monthly production
scheduling or a contract between the supplier and the
manufacturer.
The following formula is used for computing the total number of
Kanbans:
Maximum Inventory
Total number of Kanban = ----------------------- -
Container Capacity
[ daily demand x (order cycle + lead time + safety period ) ]
container capacity
DETERMINATION OF THE ORDER QUANTITY:
The order quantity in a "constant cycle" inventory control system
1.000 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
is given by the formula:
(eq. 1) Order Quantity = (maximum inventory - existing inventory)
- (orders placed but not yet received)
With a Kanban system, this order quantity is automatically
specified by the number of Kanbans detached by the time of regular
Kanban collection since the previous collection. That is:
(eq. IT) Order Quantity =
= ( number of Kanban detached by the time of regular Kanban
collection since the previous collection ) x container capacity
The reason that validates this expression for order quantity is due
to this relationship:
(Number of Kanbans detached since the previous collection of
Kanbans) =
= (Total number of Kanbans) - (number of Kanbans attached to the
existing inventory at the subsequent store) - (Number of Kanban
still kept in the preceding process)
The kanbans move in a circular fashion. A production kanban can
only be in three places: either 1) attached to work-in-process
inventory at the current storé, or 2) attached to the inventory of
finished units at the subsequent store, or 3) detached and put
into a kanban collection box where they become production orders.
Since, the total number of kanbans is fixed, the number of kanbans
detached (which become production orders) can be expressed as the
above difference. So, there is no need to compute the order
quantity by using the formula above (eq.I). The order quantity is
automatically given by the kanbans detached by the subsequent
process (eq. II).
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 1.001
APPENDIX - C
A DYNAMO VERSION OF THE MULTI-STAGE MODEL
K14: 3 Stage JIT - Kanban system
by Ramon O'Callaghan, Nov. 1985
Demand
D.K=ND*(1+STEP(SD,TSD)) Demand
ND=100 UNITS/DAY Normal demand
SD=.20 Step increase
TSD=2 DAYS Time of step increase
Backlog (stock and flow)
B.K=B.J+(DT) (OR.JK-OFR.JK) Backlog
B=TI4%D
OR.KL=D.K . Customer order rate
OFR.KL=SR.JK Order fill rate
Production Planning (developing a frozen schedule)
PP.K=PP.J+(DT) (CPP.JK) Production plan
PP=DSR
CPP. KL=PULSE(1,TSD,PPT)*(NPP.K-PP.K)/DT Change in production plan
NPP. K=(X)#F.K+(1-X)*DSR.K
X=.8
F.K=SMOOTH(D.K, TAD) Forecast
TAD=5 DAYS
PPT=10 DAYS Planning period
NK1.K=((PP.K/CC1)*(LT1+TI1)*(1+ALPHA)) | Changing kanbans according
NK2.K=((PP.K/CC2)*(LT2+T12)*(1+ALPHA) ) to production plan
NK3 .K=((PP.K/CC3)* (LT3+T13)* (1+ALPHA) )
ALPHA=. 3 Safety coefficient
Shipping policies
SR.KL=CLIP(MSR.K,DSR.K,DSR.K,MSR.K)*SW4.K Ship rate
MSR.K=2*PP.K Max. ship rate
DSR.K=B.K/TI4 Desired ship rate
TI4=1.3 DAYS Normal delivery delay
SW4.K=TABLE(TSW4,CI3.K,0,10,1) Effect of inventory
HPAP PAX FOP PRPAAPAY RANKED DAM HHH QAAP HHH HHH HHH
TSW4=0/.8/.95/1/1/1/1/1/1/1/1 on ship rate
1,002 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986.
CI3 .K=13.K/CC3
CC3=10 UNITS/CONTAINER
3) Final Assembly (PR3, PCR3)
stocks
13.KeI3.J+(DT) (PCR3.JK-SR.JK) Inventory (completed units)
13=NK3%*CC3- (ND*LT3) - (ND*TI3)
WIP3.K=WIP3.J+(DT) (PR3.JK-PCR3.JK) Work-in-process inventory
WIP3=ND*LT3
flows
PCR3. KL=DELAY3 (PR3 JK, LT3) Product completion rate
LT3=.5 DAYS Production lead time
PR3.KL=CLIP(MPR3.K, DPR3.K, DPR3.K,MPR3.K) *SW3.K Prod. rate
MPR3.KeL.1*PP.K Max. prod. rate
S$W3 .KeTABLE(TSW3 ,CI2.K,0,10,1) Effect of inventory of
TSW3=0/.65/.9/1/1/1/1/1/1/1/1 preceding stage
C12.K=12.K/CC2
CC2=10 UNITS/CONTAINER
information feedback and policies
PO3 ,K=NK3.K*CC3-13.K-WIP3.K Production orders
DPR3 .K=P03.K/T13 Desired prod. rate
TI3=.5 DAY Kanban cycle
2) Sub-Assembly (PR2, PCR2)
12. K=12.J+(DT) (PCR2.JK-PR3.JK)
12=NK2*CC2- (ND*LT2) - (ND*T12)
WIP2.K=WIP2.J+(DT) (PR2.JK-PCR2.JK)
WIP2=ND*LT2
flows
PCR2 .KL=DELAY3(PR2.JK,LT2)
LT2=.5 DAYS
PR2.KL=CLIP(MPR2.K,DPR2.K,DPR2.K,MPR2.K)*SW2.K
MPR2.K=1.1*PP.K
SW2 .KeTABLE(TSW2,CI1.K,0,10,1)
TSW2=0/.65/.9/1/1/1/1/1/1/1/1
CI1.K=I1.K/CC1
CC1=10 UNITS/CONTAINER
information feedback and policies
LRRAP RPE RODEEEAO AOE HOP DR AX HOP HERP RADHe HH AM AMES EH HOD
IM 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986. 1.003
PO2 .K=NK2.K*CC2-12.K-WIP2.K
DPR2.K=P02.K/TI2
TI2=.5 DAY
1) Parts (PRI, PCR1)
1I1.K=I1.J+(DT) (PCR1L.JK-PR2.JK)
IL=NK1*CG1- (ND*LTL) - (ND*TI1)
WIP1.K-WIP1.J+(DT) (PRL. JK-PCR1.JK)
WIP1=ND*LT1
flows
PCR1.KL=DELAY3(PR1.JK,LT1)
LT1=.5 DAYS
PR1.KL=CLIP(MPR1.K,DPR1.K,DPR1.K,MPR1.K)
MPR1.K=1.1*PP.K
information feedback and policies
PO1.K=NK1.K*CC1-11.K-WIP1.K
DPR1.K=PO1.K/TI1
TI1l=.5 DAY
Control statements
SRE HOAP DEX DP DADHKH AO AOL H HAD D
SPEC LENGTH=50/DT=.05/PRTPER=1
PRINT D,SR,B,PP,PR1,PR2,PR3,11,12,13
RUN
1.004 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY, SEVILLA, OCTOBER, 1986.
BIBLIOGRAPHY AND REFERENCES
“Readings in Zero Inventories", Transcripts of papers presented at
the APICS 27th Annual International Conference, Las Vegas, Oct.
1984
"A Simulation Analysis of the Japanese Just-In-Time Technique
(with Kanbans) for a Multiline, Multistage Production System",
Decision Sciences, 1983.
Hall. “Zero Inventories," Homewood I11l.: Irwin, 1983
Kimura and H. Terada. “Design and Analysis of Pull System, A
method of Multi-Stage Production Control," International Journal
of Production Research, 1981, vol 19, no 3, p241
Monden. "The Toyota Production System," Atlanta Ga.: Industrial
Engineering and Management Press, 1983
Morecroft. "A Systems Perspective on Material Requirements
Planning," Decision Sciences, 1983, vol.14, p.1-18.
Schonberger. “Some Observations on the Advantages and
Implementation Issues of JIT production Systems," Schonberger,
Journal of Operations Management, Vol 3, No. 1, Nov. 1982, pl
Schonberger. “Japanese Manufacturing Techniques," New York: The
Free Press, 1982.
Sepehri. "How Kanban System is used in an American Toyota Motor
Facility," I.E. , February 1985, p50-56
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