a system dynamics model for a single-stage multi-product kanban production system
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A System Dynamics Model for aSingle-Stage Multi-Product Kanban Production System
L. GUERRA, T. MURINO, E. ROMANO
Department of Materials Engineering and Operations Management
University of Naples Federico II
P.le Tecchio 80125 Napoli
ITALY
[email protected]@unina.it [email protected]://www.impianti.unina.it
Abstract: The actual socio-economic dynamics and the aggressive competition on a global scale lead companies to frequent
revision of their organizational structure, strategic objectives and decision-making processes. Organizations need, therefore,
some methods that can provide for an innovative approach to their investigations to business problems. Even if the publishingstorm around JIT may have subsided to a certain degree in recent years and many analytical methods have been published for
its analysis, most of the academic papers concerning pull production suggest Discrete Event Simulation (DES) for systemsmanagement. Only little attention has been paid to System Dynamics (SD) applications. In this paper a SD model for a
Single-Stage Multi-Product Kanban system will be proposed and tested under different demand patterns.
Key-Words: System Dynamics, Pull Production, Kanban, Simulation
1 Introduction
The actual socio-economic dynamics, the aggressive
competition on a global scale, more educated and
demanding customers and a rapid pace of change in process
technology, lead companies to frequent revision of their
organizational structure, strategic objectives and decision-
making processes [1, 15]. This essentially means thatcompanies have to show great ability in adapting to changes
imposed by their own target market [16, 17].
Organizations need, therefore, some methods that can
provide for an innovative approach to their investigations to
business problems in order to [2]:
identify the main cause-effect relations whichcharacterize the environment in which they operate;
find new approaches allowing for better control onproduction systems and more effective use of the
enterprise resources.
In this regard, System Dynamics (SD) provides a useful
interpretation of business contexts, analyzing how policiesand decisions affects the structure of companies and the
dynamics of the available resources [13].
Even if the publishing storm around JIT may have subsided
to a certain degree in recent years [11] and many analytical
methods have been published for its analysis [10, 3], the
kanban system is still a subject of active research and its
potential for significant improvements of operations is
documented by several studies [12, 5].
Particularly, in this paper a SD model for a Single-Stage
Multi-Product Kanban system will be proposed and tested
under different demand patterns.
2 Problem Formulation
As is well known, in pull systems the customer acts as the
only trigger for movement. Demand is transferred down
through the stages of production from the order placed by
customers, achieving a continuous flow at the production
system. However, where this is not possible, according with
lean production principles, a kanbanpull supermarket willdecouple processes, avoiding stocks increase: the supplier
workstation will produce output only on the instructions of
the customer workstation (kanban production), providing
for what have been consumed.
Generally speaking, each item picked-up from the store
determines a replenishment signal: a production card is
collected in a special board that displays items consumption
and then used to start production according to the
sequencing rules of the upstream section (Fig. 1).
Fig. 1 - Kanban supermarket management system
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Thus the upstream production will be pulled by the items
requested in the supermarket, where the continuous flow is
broken, and the lot production process is implemented,
aiming at minimizing setup and change over time.
It is noticeable that determining the exact quantity of each
product code to be stored in the supermarket is essential forthe efficiency of the system. Particularly, they must be
considered:
daily output of each product line; number of items stored in each bin; daily milkrun frequency (replenishment rate); safety stocks or buffers.
In this paper the effects of the dynamic behavior of a
Single-Stage Multi-Product Kanban system on the suitable
size of its supermarket will be analyzed. The system
consists of one production unit in which three different
products are made, one supermarket and one kanban boardto collect and manage work orders according to a pull logic.
3 Literature Review
System Dynamics is an approach that combines theory,
methods and philosophy for complex systems study.
Particularly, concepts drawn from the field of feedback
control are used to analyze policies, decision-making
processes and time delays effects on system behavior [4].
The logic is extremely pragmatic and its based on System
Thinking where different building blocks (elementary
circuits) are put together to generate representations of more
complex systems [13].Six basic steps can be identified and summarized as follows
(Fig. 2):
1. Identification and description of the system to beanalyzed;
2. Analytical description of the system in terms of keyvariables and equations to be considered. The
dynamic formulation of the hypotheses aims at
explaining the basic structure of causalities among
the investigated variables (System Dynamics Tools);
3. Developing of a formal simulation model and itsimplementation;
4. Alternative policies analysis and modeldeepening/review;
5. Results discussion and implementation planning;6. Business structure/policies review.
It must be specified that these steps may be modified as
appropriate and that one can go back to a previous step so to
improve the understanding of the system.
Most of the academic papers concerning pull production
suggest Discrete Event Simulation (DES) for systems
management and control [7, 14] and only little attention has
been paid to SD application in this field.
In [9] SD principles are used to build a simulation model of
a Multi-Stage Kanban system. To check model consistency,
several simulation have been carried out. The real aim of
the simulations was experimenting system flexibility in
terms of capacity to adapt to sudden changes. Simulations
were also useful to analyze different management policies
and system behaviors in case of unpredictable situations. In
particular, the response of the production system to specific,little variations was examined (such as small changes in
demand). Even if the model is rather straightforward, the
main objective was to show SD effectiveness in JIT Kanban
system modeling.
Fig. 2 - System dynamics steps: from problem symptoms to
improvement [4]
In [6] an Electronic Commerce (EC) JIT system has been
modeled using SD. The EC represents an emerging concept
which includes the processes of buying/selling/exchanging
products (or services) and information via computernetworks. A kanban pull model was developed to analyze
several management policies and the JIT relationships
among customers, competitors and suppliers. The latter
have proven to be harder to interpreter because of the
existence of many interdependent factors. It was found that
in order to avoid disruptions in production, communication
among stakeholders and a reliable supplier network are
crucial.
4 Model structure
A deep insight into the considered system and the
hypothesis on which the model is based can be found in [8].
Powersim Studio(vs. 2005) was adopted to formalize the
model.
Three Stocks(level variables) were used to represent:
the supermarket; the green-white zone of the kanban board; the red zone of the kanban board;
while Flowswere used to represent:
the production rate; the demand rate;
the inflow rate of kanbans into the green (red) zone;
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the outflow rate of kanbans from the green (red)zone.
Particularly, a specific product is assembled (determining an
outflow from the supermarket) only when it is requestedfrom the customer. In turn, the picking from the
supermarket determines production orders that will
replenish the store (Fig. 3 - The Supermarket logicFig. 3).
Fig. 3 - The Supermarket logical model
The size of the green-white kanban zone and the red zone
one are upper bounded by two auxiliary variables which, in
turn, work like inputs for the supermarket. This is because
before processing any request form the customer somesafety stocks are needed for each specific product.
Therefore, the initial size of the supermarket was set for
each product ias:
Supermarket InitSizei= Threshold Limiti+ Red Zone SizeiThis initial stock level in the supermarket, however, does
not exceed the maximum size of each column in the kanban
board.
As previously mentioned, when items are picked from the
supermarket to perform the assembly, a certain number of
production kanbans will enter the green zone of the kanban
board (or at worst the red zone).The green-white zone of the kanban board is depicted in
Fig. 4.
Fig. 4 - Green-white zone logical sub-model
It should be noted that the green-white zone and the red one
were separately modeled in order to identify involved
variables and to better understand their patterns of
operation.
Anyway, the green-white zone size (Green-White ZoneStock) increases at Kanban In rate, which represents
production requests, and decreases at Kanban Out rate,
which represents assembly requests. Really, theres a
kanban inflow in the green-white zone only if (Fig. 5):
Diff 1 = Green-White Zone Threshold Limit > 0
that is only if theres still some space in the kanban board
column associated with the considered product. The
auxiliary variable:
GAP = Threshold Limit Green Zone Queue
determines what kind of product will have higher priorityhold as proportional to the probability of entering the red
zone.
Fig. 5 - Green priority assessment
The red zone of the kanban board is depicted in Fig. 6.
Fig. 6 - Red zone logical sub-model
The sub-model operates as the one discussed above and the
priority assessment model showed in Fig. 5 applies in the
same way too: the Red Zone GAP variable defines the
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Red Priority variable that in turn determines which of the
three products has the higher production priority.Finally the Priority variable, combining Green Priority
and Red Priority variables, determines which kanban has
to be processed.
In this way production can replenish the supermarket once
production capacity is assessed (Fig. 7).
Fig. 7 - Pull production flow
5 Results and discussion
Simulations were carried out to test the model in two
scenarios characterized by different demand trends.Furthermore, it will be assumed:
Threshold Limit= [6; 7; 9]; Red Zone Size= [3; 5; 7].
These hypothesis result in the initialization of theSupermarketon [9; 12; 16].
5.1 Case 1 Results under constant demand
Considered demand patterns are shown in Fig. 8. It must be
noticed that it was assumed:
DemandP1=DemandP2= 5 pcs/day
Fig. 8 - Demand patterns
The Green-White Zonesize of each item initially increases
according to demand patterns and required production times(Fig. 9)
Fig. 9 - Green-White Zone Size
However, when the Threshold Limit is reached a further
request of the item determines the entry of the same one inthe red zone and, hence, an increase of the Red Zone size
(Fig. 10).
Fig. 10 - Red Zone Size
This size begins decreasing as soon as the system starts
producing the items corresponding to the red kanbans,
consistently with their priorities.At the same time, while Supermarket size exhibit a
maximum 43% decrease for Product 1, theres a maximum25% decrease for Product 2and a maximum 33% decrease(22% increase) for Product 3 (Errore. L'origine riferimento
non stata trovata.). Supermarket size varies until a
dynamic equilibrium is reached between production flowand assembly flow.
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Fig. 11 - Supermarket Size
5.2 Case 2 Results under variable demand
Considered demand patterns are shown in Fig. 12.
Fig. 12 - Demand patterns
With regard to the Green-White Zonesize, the initial trendsare quite similar to those showed in the previous case, sincedemand is steady up to period 4 (Fig. 13). When demand
goes down, the zone size (whichever the product) decreasestoo and levels off when demand is zero.
Fig. 13 - Green-White Zone Size
Similarly, theRed Zonesize for Product 3 initially increases
but quickly falls as no more requests have to be met (Fig.14). As it concerns Product 1 and Product 2, assumeddemand trends (and priorities achieved) are not enough for
Red Zonesize to increase.This last consideration affects Supermarketsize too: theresno further slope growth in Product 1and Product 2 trends
(from period 4 to period 5). However, whichever theproduct, Supermarket size quickly increases after period 4until it reaches stable values when items demand falls to
zero.
Fig. 14 - Red Zone Size
Fig. 15 - Supermarket Size
6 Conclusions and future developmentsThe aggressive competition on a global scale lead
companies to frequent revision of their organizationalstructure, strategic objectives and decision-making
processes. Investigating these changes, learning how theelements and structure of a business process can bring aboutsuch changes and how the performance of the processchanges over time is nowadays critical for companies to
survive.The methods of Systems Thinkingprovide firms with tools
for better understanding management problems, supporting,
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at the same time, a pro-active behavior, allowing a quick
and effective adaptation to changes.In this paper System Dynamicshas been adopted to analyze
the dynamic behavior of a Pull Kanban production system.
Particularly, the kanban board has been modeled
considering two stock variables, one for the green-white
zone and another one for the red zone, while kanban flowsare used to determine the supermarket size.Simulations were run under two different demand patterns.
The dynamic evolution of the interest variables is quite
consistent with what was expected in theory. This proves
the reliability of the relations adopted in the model.
However, modelrobustness might be further tested as:
different production times; different level of service and safety stock policies; Multi-Stage Multi-Product Kanban production
systems;
could be considered.In any case, the model could be useful when taking strategic
decisions in unpredictable market conditions due to the
increasing frequency of new products introduction, changes
in parts for existing products or fluctuations in productdemand and mix.
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