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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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ISSN: 1790-5117 176 ISBN: 978-960-474-193-9

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