Modelleren en simuleren van supply chains door middel...

Faculteit Ingenieurswetenschappen

Vakgroep Technische Bedrijfsvoering

Voorzitter: Prof. dr. ir. H. Van Landeghem

Academiejaar 2006–2007

Modelleren en simuleren van supply chains

door middel van Petri Netten

Thomas Decan

Promotor: Prof. dr. ir. H. Van Landeghem

Begeleider: dr. C. Bobeanu

Scriptie voorgedragen tot het behalen van de graad van

Burgerlijk Ingenieur Werktuigkunde Elektrotechniek

optie: Bedrijfskunde

Voorwoord

Na wat denk- en zoekwerk had ik voor mezelf uitgemaakt in mijn scriptie een theoretisch onderwerp

te willen behandelen. In de suggesties van Prof. dr. ir. H. Van Landeghem kon ik het onderwerp

”Modelleren en simuleren van supply chains door middel van Petri Netten” vinden. Onmiddellijk

trok deze titel mijn aandacht. ”Modelleren” was voor mij onontgonnen terrein en het leek mij dan

ook interessant dit nieuwe gebied beter te leren kennen en uit te diepen.

Prof. dr. ir. H. Van Landeghem aanvaardde dat ik het onderwerp zou behandelen. Mijn oprechte

dank gaat dan ook naar hem uit voor de kans die ik aldus kreeg.

Dr. C. Bobeanu heeft mij heel wat vakliteratuur aangereikt. Zij heeft helpen zoeken naar bepaalde

oplossingen en zij verbeterde in detail mijn eindwerk. Tevens was zij steeds bereid materile hulp

te bieden bij het opstarten van simulaties. Kortom, zij was mijn dagelijkse toeverlaat, waarvoor

ik haar zeer hartelijk dank.

De Heer Kurt De Cock, computerbeheerder, heeft gedurende het hele traject, de veelvuldige

softwareproblemen opgelost. Veel van zijn kostbare tijd heeft hij geschonken om mij vooruit te

helpen. Ik ben hem daar uiterst dankbaar voor.

Een bijzonder woord van dank gaat naar mijn vriendin Isabel Decramer, die veel begrip aan de

dag legde gedurende deze thesistijd.

Niet in het minst dank ik mijn ouders, die mij hielpen bij heel wat praktische zaken tijdens de

volledige onderzoeks- en schrijfperiode.

Alle hiervoor genoemde personen betekenden, elk op hun manier, een ongelofelijke steun voor mij.

Thomas Decan, juni 2007

De auteur en promotor geven de toelating deze scriptie voor consultatie beschikbaar te stellen.

Elk ander gebruik valt onder de beperkingen van het auteursrecht, in het bijzonder met betrekking

tot de verplichting uitdrukkelijk de bron te vermelden bij het aanhalen van resultaten uit deze

scriptie.

The author and promoter give the permission to use this thesis for consultation. Every other use

is subject to the copyright laws, more specifically the source must be extensively specified when

using from this thesis.

Gent, Juni 2007

De promotor De begeleider De auteur

Prof. dr. ir. H. Van Landeghem dr. Carmen Bobeanu Thomas Decan

Modelleren en simuleren van supply

chains door middel van Petri Netten

door

Thomas Decan

Scriptie ingediend tot het behalen van de academische graad van

Burgerlijk Ingenieur Werktuigkunde - Elektrotechniek:

optie bedrijfskunde

Academiejaar 2006–2007

Promotor: Prof. dr. ir. H. Van Landeghem

Scriptiebegeleider: dr. C. Bobeanu

Faculteit Ingenieurswetenschappen

Universiteit Gent

Vakgroep Industrial Management

Voorzitter: Prof. dr. ir. H. Van Landeghem

Samenvatting

In deze thesis is een analyse gemaakt van het modelleren en simuleren van supply chains doormiddel van Petri Netten (PN). Het voorgestelde PN-model werd gebouwd en gesimuleerd in de toolGreatSPN. Het model is opgebouwd uit twee basis componenten: de leverancier en een mechanismevoor het verweken van de orders en het aansturen van de leveranciers. Deze modules laten toe omsnel diverse supply chains te modeleren. Voor- en nadelen van het simuleren van supply chains inPN wordenopgesomd, alsook de voor- en nadelen van de tool GreatSPN. Resultaten van simulatiesworden gepresenteerd en vergeleken met resultaten verkregen uit een simulatie in een spreadsheet(Vila, 2004).

Trefwoorden

Supply Chain, Modelleren, Petri Netten, Discrete Event Systems, Simuleren

Modelling and Simulating Supply

Chains by Petri Nets

by

Thomas Decan

Mastersthesis submitted to gain the academic degree of

Master of Electromechanical Engineering

Main Subject: Industrial Engineering

Academic year 2006–2007

Promoter: Prof. dr. ir. H. Van Landeghem

Supervisor: dr. C. Bobeanu

Faculty of Engineering

Ghent University

Department Industrial Management

Head of the Department: Prof. dr. ir. H. Van Landeghem

Abstract

In this mastersthesis an analysis is made of the modelling and simulating Supply Chains in themodeling language Petri Nets. The proposed model was built and simulated with the tool Great-SPN. The model is composed from two modules: a supplier and a mechanism to process theorders and the deliveries between suppliers. The connection of several of these modules resulted ina complete supply chain with multiple competitors at every level. Results of several expermentson this model are provided. Also some problems when simulating supply chains by Petri Nets inthe tool GreatSPN are denoted.

Keywords

Supply Chain, Modelling, Simulating, Petri Nets, Discrete Event Systems

Modelling and Simulating Supply Chains with PetriNets

Thomas Decan

Supervisor(s): Hendrik Van Landeghem, Carmen Bobeanu

Abstract—This thesis proposes a simulation model of Supply Chains (SC)in the modeling language Petri Nets. Two modules were developped: a sup-plier and an order and delivery mechanism. The connection of several ofthese modules resulted in a complete supply chain with multiple competi-tors at every level. Results of several experments on this model are pro-vided. Also some problems when simulating supply chains by Petri Nets inthe tool GreatSPN are denoted.

Keywords—Supply Chain, Modeling, Petri Nets, Discrete Event Systems

I. INTRODUCTION

SIMULATING can be used as a support tool for optimizingsupply chains at tactical level. Supply Chains are often mod-

eled with textual languages. In the proceeding research a com-puter model of a supply chain is proposed. This model was madein the modeling language Petri Nets (PN) and several scenario’swere under investigation. Petri Nets are a mathematical and agraphical environment and are fundamentally different than tex-tual modeling languages. This approach with PN could result inother insights then those gained by textual languages.

II. SUPPLY CHAINS

A supply chain is a coordinated system of companies whichpurpose it is to bring products or services to their final cus-tomers. The performance of a supply chain is defined by sev-eral parameters: There is cost, lead-time, reliability, robustness,capacity, spoilage,. . . Optimizing all those performance indica-tors and making good trade-offs is the difficulty of supply chainmanagement.

In practice every supply chain for every product is different.Willing to present a model and its experimental results, a certainsupply chain is selected. The selected supply chain is describedby [6] and already simulated in a spreadsheet by [7]. The advan-tage of simulating a well-known suplly chain is that comparisonaftherwards is possible. The modelled supply chain conforms tothe next requirements:• The first 3 levels of suppliers have several competitors at sev-eral locations• The 4th level of suppliers has one competitor who deliversdirectly to the customer• Orders are transmitted between levels only once per week• The suppliers of the first three levels can all break down andhave their own MTBF an MTTR• Spoilage: When a product is produced or has arrived at oneof the first three levels, there is a possibility that the product iswasted• Only complete orders are sent to their customers• Orders can be processed directly or they can be backlogged

III. PETRI NETS

Petri nets (PNs) are a mathematical language which is definedby CA Petri in 1962. The dynamic behavior of systems canbe modeled in PNs. Petri Nets were designed as a languagewhere it is possible for some events to occur concurrently. Fromthe definition of Petri Nets, Petri Nets can be visualized as anordered bipartite graph without isolated nodes; this results in agraphical representation [4].

IV. SIMULATION MODEL

An advantage of modeling in PN is the possibility to builtmodels by coupling modules [2]. Two modules were developed.One representing a supplier located between suppliers, see Fig-ure 1 (small modifications make it possible to transform this sup-plier for use at the end or at the beginning of a supply chain). Anexplication of the places of Figure 1 is shown in Tables I.

P10P

P11

P12

P8

PP9P

P3 P1

P7

P5

P2

P14

P13

P4

s

P6

P15P16 P17

t23t22

t21

t19

t10

t9

t8

t24

t25t26

t27 t28t29

t20

t18

t17

t16

t15

t13t12

t11

t3

t2

t1

t5

2π

t7

2π

t6

2π

t4

4π

t14

7π

_2 _2_3

_2 _2_3

_2 _2 _3

Fig. 1. Supplier Module

A second module is proposed representing an order and deliv-ery system that connects two suppliers, see Figure 2. The orderand delivery system has more than one function: It connects allthe suppliers with their their customers one level downstream, itensures that orders are sent to the right customer, it keeps dif-ferent orders separated, it delays the shipment proportional withdistances between the suppliers and it ensures that products areshipped to the customer only when the order is complete. Anexplication of the elements of the ordering and delivery systemis shown in Tables II.

Notation InterpretationP1 Incoming ordersP2 Outgoing ordersP3 Available productsP4 Stock of goodsP5 BackordersP6 Stock of assigned goodsP7 Outgoing goodsP8, P9 &P10

The implementation of the 40% source limit.

P11 State: Do not send ordersP12 State: Send OrdersP13 State: Shipping department is upP14 State: Shipping department is downP15, P16& P17

Token storage per 100

TABLE ITHE PLACES OF A SUPPLIER OF LEVEL 2 OR 3 FROM FIGURE 1

P9

P7

P5

P4 P3 P2 P1

P8

P6

t11

t10

t8

t7

t6

t3t5

2π

t4

3π

t2

3π

t9

4π

t1

4π

Fig. 2. Ordering and Delivery Mechanism Module

Not. InterpretationP1 Last order in rowP2 Place to keep the third and the second order sepa-

ratedP3 Second order in row waiting until the first order is

complete and releasedP4 Place to keep the first and the second order separatedP5 First order in rowP6 One token is stored here when an order arrives at an

empty queue to prevent the order from splitting at t3P7 Assigned products for the first order, waiting until

the order is complete (= until P6 is empty)P8 Goods on their way to the customerP9 Orders

TABLE IITHE PLACES OF A SIMPLE QUEUE FROM FIGURE 2

V. THE ACTUAL SIMULATIONS AND RESULTS

Four optimal scenario’s are calculated with the linear pro-gramming method (see [7] and [6]):

basic serial model: At every level only the cheapest supplierbasic model: Because the basic serial model proposes only onepath, the whole supply chain is extremely vulnerable for com-plete disruptions. In the basic model suppliers can order maxi-mum 40% to the same supplier.high reliability model: With a higher number of suppliers thereliability drops. Here a higher reliability is guaranteed by usinghigh reliable suppliers. Also with a 40% source limit.60% source limit model: To obtain a higher reliability with lesscostly suppliers, the total number of suppliers will be dropped.Control Layer Model: An extra layer is added to the basicmodel. It is not possible anymore for a customer to send ordersto a supplier with many backlogs.

VI. CONCLUSION

During the building of the model there were no obstaclesfound that PN couldn’t overcome. For this reason it is the au-thor’s belief that Petri Nets in general are a very powerful mod-eling language and GSPN specifically are very well suited forthe simulation of supply chains. Compared to other languagesgives the graphical representation of the model an extremelygood overview and a quick insight of the dynamics of the model.In addition of these PN-benefits, it was possible to build thisvery complex and large model in a short time. This because theauthor started from the methodology provided in [2] and [5].This methodology allows the user to built models on a incre-mental and systematical way by coupling basic components bywell defined rules. Several experiments were performed on themodel. From their results we can conclude that on this model,the most important disturbance factor on the performance mea-sures is the random transport time. If the objective is to mini-mize costs, spoilage has to be reduced. Plant breakdowns haveonly a minor influence. When there are more reliable suppliersused, cost increase but the service factors don’t. When we cutthe total number of suppliers, costs drop without the loss of per-formance. Best results were gained with a minimum of low-costsuppliers.

REFERENCES

[1] C. A. Petri, Nets, time and space, Theor. Comput. Sci., vol. 153, number1-2, p. 3-48, Elsevier Science Publishers Ltd., Essex, UK, 1996

[2] Carmen-Veronica Bobeanu and Eugene J.H. Kerckhoffs and Hendrik VanLandeghem, modeling of Discrete Event Systems:A Holistic and Incremen-tal Approach Using Petri Nets, Ghent University, Delft University of Tech-nology, ACM Transactions on modeling and Computer Simulation, p. 389-423, vol. 14, number 4, ACM Press, New York, NY, USA, okt. 2004

[3] Prof.dr.ir. Hendrik Van Landeghem, Advanced Methods in Production &Logistics, Universiteit Gent, 2006

[4] Carmen-Veronica Bobeanu, Modelling and Simulating Manufacturing andService Systems using Petri Nets, Universiteit Gent, 2005

[5] Rik Van Landeghem and Carmen-Veronica Bobeanu, Formal Modelling ofSupply Chain: An Incremental Approach Using Petri Nets

[6] Markus Bundschuh and Diego Klabjan and Deborah L. Thurston, Mod-elling Robust and Reliable Supply Chains, University of Illinois at Urbana-Champaign, journal????, 2003, June

[7] Ester Massons Vila, Supply Chain modeling: Optimization Versus Simula-tion, Ghent University, jul. 2004

[8] GreatSPN User’s Manual v. 2.0.2, Universita di Torino, Dipartimento diInformatica, Performance Evaluation group, July 2004

[9] Gianfranco Balbo and Jorg Desel and Kurt Jensen and Wolfgang Reisigand Grzegorz Rozenberg and Manuel Silva, Introductory Tutorial PetriNets, 21st International Conference on Application and Theory of PetriNets, Aarhus, Denmark, June, 2000

Contents

Overzicht iii

Overzicht iv

Extended abstract v

List of Abbreviations x

1 Introduction 1

2 Supply Chains 2

2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2 The Supply Chain in case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.3 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Petri Nets 5

3.1 Petri Net Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 Elementary Net Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2.1 The static structure of EN-Systems . . . . . . . . . . . . . . . . . . . . . . . 5

3.2.2 The dynamic behaviour of EN-Systems . . . . . . . . . . . . . . . . . . . . 6

3.3 Place/ Transition Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.3.1 The static structure of Place/ Transition-Nets . . . . . . . . . . . . . . . . . 7

3.3.2 The dynamic behaviour of P/T-Nets . . . . . . . . . . . . . . . . . . . . . . 7

3.4 Timed Petri Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.4.1 Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.4.2 Timed PN terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.5 Stochastic Petri Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.6 Generalized Stochastic Petri Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.7 Motivation for modeling with GSPN . . . . . . . . . . . . . . . . . . . . . . . . . . 9

vii

CONTENTS viii

3.8 GreatSPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 The Model 11

4.1 The Overall Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.2 Supplier level 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3 Supplier level 2 and 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.4 Supplier level 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.5 Ordering and Delivery Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.5.1 Simple Queue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.5.2 Advanced Queue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.6 Adaptation of the Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5 Optimization at strategic level 24

5.1 Basic serial model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.2 Basic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.3 High Reliability model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.4 60% source limit model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

6 Simulation 28

6.1 Performance indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6.2 Target Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6.3.1 Analysis of the models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6.3.2 Analysis between models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

7 Control Layer Model 33

7.1 Implementation in the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

8 Conclusion 36

Appendix A 37

Appendix B 41

Bibliography 43

List of Figures 45

List of Tables 46

List of Abbreviations

CT Cycle Time

cu currency unit

DES Discrete Event Systems

DTPNs Deterministic Timed Petri Nets

ENS Elementary Net Systems

GreatSPN GRaphical Editor and Analyzer for Timed and

Stochastic Petri Nets

GSPN Generalized Stochastic Petri Net

GUI Graphical Users Interface

MTBF Mean Time Between Failures

MTTR Mean Time To Repair

PN Petri Net

P/T Nets Place/ Transition Nets

SC Supply Chain

SPNs Stochastic Petri Nets

SS Safety Stock

STPN Stochastic Timed Petri Net

SWN Stochastic Well Formed Net

TPPN Timed Places Petri Net

TS Target Stock

TTPN Timed Transitions Petri Net

ix

Chapter 1

Introduction

It is the intention of this mastersthesis to obtain a better insight in supply chains and to optimize

them by simulation. Simulating a supply chain by running a computer model is a support tool

to optimize supply chains at tactical level. In the preceding research a computer model has been

made of a supply chain. This model was made in the modeling language Petri Nets . Petri Nets

are a mathematical and a graphical environment and are fundamentally different than textual

languages. Supply Chains are often modeled with textual languages. This approach could result

in new insights then those gained by textual languages.

The two most important parameters/measures through the whole project are:

The price The total cost of production, transport, spoilage and stock.

The performance at customer level Service level is measured at the end consumer.

Supply Chains are a very interesting subject because they are hard to predict and they have a

difficult dynamic behaviour. They are also very interesting because everyone has to deal with

them daily. Only think at all those times a certain product is not in stock at the hypermarket or

at the local grocery.

1

Chapter 2

Supply Chains

2.1 General

A supply chain is a coordinated system of companies which purpose it is to bring products or

services to their final customers. These companies can deliver as well services as goods. It is the

intention of supply chain management to intervene in the supply chain in such way that the perfor-

mance is raised. The performance of a supply chain is not defined by one single parameter: There

is cost, lead-time, reliability, robustness, capacity, spoilage,. . . Optimizing all those performance

indicators and making good trade-offs is the difficulty of supply chain management.

2.2 The Supply Chain in case

In practice every supply chain for every product is different. As we can model only one supply

chain (but run several scenarios on that model), choices have to be made. To make comparison

possible, the supply chain modeled in this mastersthesis is one used in previous research. See

Bundschuh et al. (2003) and Vila (2004). The supply chain in case has to conform to the next

requirements:

• The supply chain has 4 levels of suppliers:

– First level: Production of raw materials

– Second level: Production of semi-finished products

– Third level: Production of finished products

– Fourth level: Distributor of the products

• Every level of suppliers has several competitors at several locations:

2

CHAPTER 2. SUPPLY CHAINS 3

– 6 Suppliers of the first level: 2 in Asia, 2 in Eastern Europe and 2 in Western Europe

– 6 Suppliers of the second level: 3 in Asia, 1 in Eastern Europe and 2 in Western Europe

– 6 Suppliers of the third level: 2 in Asia, 1 in Eastern Europe and 3 in Western Europe

– 1 distributor located in Western Europe

• Orders are transmitted from one level to the other level only once per week

• The suppliers of the first three levels can all break down and have their own MTBF an

MTTR

• Spoilage: When a product is produced or has arrived at one of the first three levels, there is

a possibility that the product is wasted

• Orders are sent to their customers only when the order is complete

• Orders can be processed directly or they can be backlogged

• Cycle times, customer order intervals, transportation times, MTBF and MTTR are random

numbers, all with their own probability density function

See Figure 2.1: The complete supply chain.

Figure 2.1: The complete supply chain

2.3 Parameters

For the parameters (eg. MTBF, lead times, . . . ), values are used from previous research (See Vila,

2004). The values used are summarized in table 2.2. Transport costs are summarized in table 2.1.

In table 2.1 it doesn’t matter between which level the transportation is.

CHAPTER 2. SUPPLY CHAINS 4

to West-Europe East-Europe Asia

from 1 2 3 1 2 1 2 3

1 42 42 42 47 47

West-Europe 2 44 49 49

3 46

1 27 27 27 35 35 35

East-Europe 2 29 29 29 24 24

1 35 30 17 17 17

Asia 2 36 31 18 18 18

3 32 19 19

Table 2.1: Transport costs in cu

parameter value

reliability

West-Europe

East-Europe

Asia

98%

96%

96%

lead-time

same continent

between continents

Uniform distribution: [1− 3] weeks

Uniform distribution: [3− 5] weeks

spoilage 5%

source limit percentage 40%

MTBF 25 weeks

MTTR Uniform distribution: [2-5] weeks

demand West-Europe 1.000.000 per year

simulation horizon

one year

= 50 weeks

= 250 days

Table 2.2: Model parameters

Chapter 3

Petri Nets

3.1 Petri Net Formalism

Petri nets (PNs) are a mathematical language which is defined by CA Petri in 1962. The dynamic

behaviour of systems can be modeled in PNs. Petri Nets were designed as a language where it

is possible for some events to occur concurrently. PN are typically strong at describing systems

with synchronisation and resource sharing. Petri Nets have a graphical representation wich is very

helpful for the comprehention of the dynamic stucture.

There are several levels of petri nets. In the next sections some of the relevant classes of PNs for

this mastersthesis are discussed.

3.2 Elementary Net Systems

3.2.1 The static structure of EN-Systems

Definition 3.1 (Elementary Net System) (Petri, 1996) A triple N = (S, T, F ), with:

• S the set of state-elements

• T the set of transition-elements

• a relation F for “flow”

is called a net iff S, T and F fulfill the following conditions (net axioms):

N1: S ∪ T 6= �

N2: S ∩ T = �

N3: domF ∪ ranF = S ∪ T

5

CHAPTER 3. PETRI NETS 6

N4: F ∩ F−1 = �

A net is used to represent the underlying static structure (potential dynamics). From the definition

of Petri Nets, Petri Nets can be visualized as an ordered bipartite graph without isolated nodes;

this results in a nice graphical representation:

• S-elements: circles © (Storage places)

• T-elements: bars or boxes � (Servers)

• Flow relation: arcs −→ (connection elements)

Additional concepts

For a given net N = (S, T, F ), XN := S ∪ T (the set of all net elements), and for x ∈ XN :

•x = {y ∈ XN : (y, x) ∈ F}, Input of a net element

x• = {y ∈ XN : (x, y) ∈ F}, Output of a net element

•x• :=• x ∪ x•, Environment of a net element

3.2.2 The dynamic behaviour of EN-Systems

PNs incorporate a notion of state which is denoted by a function M , called marking. For a given

net N = (S, T, F ):

M := {m : m ⊆ S}, (The class of conceivable markings);

E := {e : e ⊆ T, e 6= �}, (The class of all conceivable events)

The dynamic behaviour of the net is the evolution of the state of the net.

The firing rule (Petri, 1996)

The firing process is the evolving from one state to the other state. The firing rule indicates when

it is possible for a transition to fire, and what the changes are on the marking:

1. An event transforms a marking M into a different marking M ′.

2. An event is a set E of transitions; events are the only source of change.

3. Transitions in the same event E have disjoint neighbourhoods •t• (transitions may individ-

ually occur without interfering with each other).

4. The preconditions •t of each transition t ∈ E belong to M but not to M ′ and the postcon-

ditions t• of each t ∈ E belong to M ′ but not to M .


3.3 Place/ Transition Nets

3.3.1 The static structure of Place/ Transition-Nets

The elementary net systems of the previous section are PNs of the lowest level: A marking at a

place is a boolean variable. Place/ Transition Nets (P/T Nets) are an example of PNs at a higher

level. A marking at a place is now allowed to be an integer variable.

Definition 3.2 (Place/ Transition Net) (Desel & Reisig, 1998): A P/T-net is a 6-tuple N =

(P, T, F, K,W, M0) that consists of:

• the finite sets of places (P) and transitions (T) (P ∩ T = �), and a set of arcs F ⊆

(P × T ) ∪ (T × P ),

• capacitiesK : P → N+0 ∪ {∞}

• arc weights defined by W : F → N+0

• the initial marking M0 : P → N+ such that for each p ∈ P,M0(p) ≤ K(p).

Additional relations

Input and output of S-elements can be described by:

I := F−1 ∩ (S × T )

O := F ∩ (S × T )

3.3.2 The dynamic behaviour of P/T-Nets

1. A transition is enabled when there are at least as much tokens in all the inputplaces of that

transition as the weight of the arc corresponding to that inputplace, and when the capacity

of the outputplaces is lager then the amount of tokens at those corresponding output places

added with the amount of tokens that the firing of this transition would generate at these

outputplaces.

2. Only enabled transitions may fire

3. If an enabled transition fires at marking M. The state of the net evolves to M’.

(a) There are as much tokens removed from every inputplace as the corresponding weight

of the arc between the inputplace and the firing transition.

(b) There are as much tokens generated in every outputplace as the corresponding weight

of the arc between the firing transition and the outputplace.


3.4 Timed Petri Nets

The simulating of processes in the time can return valuable performance results of those processes.

The class of Petri Nets wich includes time specifications are called Timed Petri Nets (TPM).

3.4.1 Approaches

Several approaches are possible for the implementation of time in PN. There are Timed Places

(TPPN), timed tokens, timed arcs and Timed Transitions (TTPN). For the experiments in this

mastersthesis, TTPN are used.

With TTPN, when a transition is enabled, the delay starts. When the delay has elapsed, the

transition will be fired. Two firing policies are possible: Three-phase firing and Atomic firing.

Our tool uses atomic firing. This means that tokens are kept in the inputplaces until the delay

has elapsed. When the transition is fired tokens are generated in the output places.

3.4.2 Timed PN terminology

Conflicts and selection rules With atomic firing, it is possible that one token enables multiple

transitions. This is called a conflict. In this case, selection rules decide which one of the enabled

transitions is going to fire. Again there are several approaches. There is preselection and race.

GreatSPN uses race. This means that when a conflict arises, the transition is fired with the

shortest firing delay.

Server semantics Transitions can be seen as servers which are processing sets of tokens. With

TTPN, servers need a certain amount of time to process these sets. Sets of tokens can be processed

one-by-one, all the sets can be processed concurrently or a maximum of K sets can be processed

concurrently. We speak of respectively: Single-server semantics, Infinite-server semantics and

Multiple-server semantics.

3.5 Stochastic Petri Nets

TTPN with atomic firing in which all transitions delays are random variables with negative expo-

nential distributions are called Stochastic PN(SPN). The dynamic behaviour of a SPN is described

through a stochastic process.

Definition 3.3 (Stochastic PN) A SPN is a 7-tuple SPN = (P, T, I(.), O(.),H(.),W (.),M0)

where:

• P (.), T (.), I(.), O(.)


• H(.) Inhibitor arc: Arcs from a place to a transition. The arc has a parameter attached, his

weight. When there are as many tokens in the place as the weight of the arc, the transition

is disabled. Tokens are never consumed by inhibitor arcs. The graphical representation is a

line ending in a circle.

• W (.) is the function defined on the set of transitions that associates a rate with each transi-

tion; this rate is the inverse of the average firing time of the transition.

• M0 The initial marking

3.6 Generalized Stochastic Petri Nets

A Generalized Stochastic Petri Net (GSPN) are SPNs where some of the transitions fire in zero

time. These transitions are called immediate transitions. Immediate transitions have a higher

priority then timed transitions. This means that when more than one transitions are enabled,

the immediate transition will fire first. Between immediate transitions, there are also priorities.

Priority numbers are attached to every transition with the priority function π : T −→ N. A GSPN

model is defined as an 8-tuple (P, T, I, O, H,W, π, M0).

3.7 Motivation for modeling with GSPN

The purpose of a supply chain is to bring products towards the customer within a specified delivery

time. Because we want to compare performance indicators of several simulations of supply chains

with different transportation times, it is clear that we choose for a class of petri nets where temporal

specifications are implemented. As we do not which to ad a time stamp to every transition in the

model, the choice is easily made to use Generalized Stochastic Petri Nets to model supply chains.

3.8 GreatSPN

Petri Nets can be executed automaticly with computer software. Several packages are available

and GreatSPN, developped at the university of Torino, is one of those Petri Net software kits.

GreatSPN is a tool with a Graphical Users Interface (GUI). The Nets can be drawn on a canvas

similar to a vector oriented drawning tool. GreatSPN allows the user to built GSPN and Stochastic

Well Formed Nets (SWN). After building the models can be analysed at tw levels: The sructural

level, this is an anlysis of the model where the initial marking is not considered, and on the

behavioural level, here the initial marking is considered. Simulation runs can be made, always

whith the choice for timed or untimed simulations. Also is it possible to choose for automatic

firing or to let the operator decide wich enabled transition to fire.


In this mastersthesis GreatSPN is used to examine supply chains by a GSPN model.

Chapter 4

The Model

In this chapter we describe the model. First we take a short look at the overall model and

afterwards every component of the model will be explained

4.1 The Overall Model

In Figure 4.1 there is a plot of the overall model built in GreatSPN, used for all the experiments.

The the model consists of six suppliers of each of the first three levels and one supplier of the

fourth level. The supplier of the fourth level is the one who delivers at the customer. It is also on

this level that the performance of the supply chain is measured.

11

CHAPTER 4. THE MODEL 12P7

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4.1:

The

over

allm

odel

CHAPTER 4. THE MODEL 13

4.2 Supplier level 1

Suppliers of level one are those at the beginning of the supply chain. So, these suppliers don’t

have any suppliers, only customers. In the model description there are six suppliers of level one

(Bundschuh et al., 2003). That is two in West-Europe, two in Eastern-Europe en two in Asia. As

we will only need at maximum 3 suppliers of level 1 per simulation (Vila, 2004), there are in the

overall model 3 of them. When different suppliers are needed, only their parameters are changed.

In this way the model is kept small.

The PN model associated to a supplier of level 1 is displayed in Figure 4.2. A short description

of every component of Figure 4.2 is provided for the transitions in Table 4.1 and for the places in

table 4.2.

Notation Interpretation Type and Mean Time or

Priority

t1, t2 & t3 Receiving incoming orders from customers

1,.. 3

immediate, 1

t4 Direct processing from stock immediate, 4

t5 Producing goods immediate, 1

t6 Storing conform goods immediate, 1

t7 Demolishing non conform goods and placing

a new order

immediate, 1

t8 Backlogging immediate, 1

t9 Processing backlogs immediate, 7

t10 Releasing order to ship immediate

t11, t12 & t13 Goods are assigned for customers 1,.. 6 immediate, 1

t14 The factory breaks down Stochastic, MTBF

t15 Repairing of the factory Stochastic, MTTR

Table 4.1: The transitions of a supplier of level 1 from Figure 4.2

4.3 Supplier level 2 and 3

Suppliers of level two and three are those in the middle of the supply chain. So, these suppliers have

at the left side six suppliers and at the right side six customers. In the model description, there

are six suppliers of level two (One in West-Europe, two in Eastern-Europe and three in Asia)and


Notation Interpretation

P1 Incoming orders

P2 Orders waiting for production (backlogs, direct processed and spoiled products)

P3 Available products (conform and non conform specifications)

P4 Goods in stock

P5 Backorders

P6 Orders waiting to be released for shipping

P8 Factory is up

P7 Outgoing Goods

P9 Factory is down, orders can not be produced

Initially there are s goods stored, s is also the target stock

Table 4.2: The places of a supplier of level 1 from Figure 4.2

P3 P1

P2 P7

P5

P8

P9

P4

s

P6

t15t14t5

t12

t11

t13t10

t8

t7

t6

t3

t2

t1

t9

4π

t4

4π

Figure 4.2: A supplier of level 1

six of level three(three in West-Europe, one in Eastern-Europe and two in Asia).As we will only

need at maximum 3 suppliers of level 2 and at maximum suppliers of level 3 per simulation (Vila,

2004), there are in the overall model 3 of them. When different suppliers are needed, only their

parameters are changed. In this way the model is kept small. A close-up of one of the suppliers

of level 2 or 3 is seen in Figure 4.3. Now a short description of every element of the supplier in

Figure 4.3 follows. An explication of the transitions elements of Figure 4.3 is listed in Table 4.3

the places are listed in 4.4.


Notation Interpretation Type and Mean Time

or Priority

t1, t2 & t3 Incoming orders from customers 1,.. 3 immediate, 1

t4 Processing orders immediate, 1

t5, t6 & t7 Sending orders to suppliers 1,.. 3 immediate, 1

t8, t9 & t10 Goods entering from suppliers 1,.. 3 Stochastic, (Table 2.2)

t11 Storing conform goods immediate, 1

t12 Demolishing non conform goods and placing a new

order

immediate, 1

t13 Backlogging immediate, 1

t14 Processing backlogs immediate, 1

t15 granting orders to be sent immediate, 1

t16, t17 & t18 Sending goods to customers 1,.. 3 immediate, 1

t19 Setting state to: send orders deterministic, 5 days

t20 Setting state to: don’t send orders immediate, 1

t21 Initializing state to: don’t send orders determ., 10−9 days

t22 The factory breaks down Stochastic, MTBF

t23 Repairing of the factory Stochastic, MTTR

t24, t25 & t26 Ungrouping 1 token in 100 Immediate (take 1,

give 100)

t27, t28 & t29 Grouping 100 tokens in 1 Immediate (take 100,

give 1)

Table 4.3: The transitions of a supplier of level 2 or 3 from Figure 4.3

4.4 Supplier level 4

The supplier of level four is the supplier at the end of the supply chain. This is the supplier who

delivers directly to the customers. It is at this supplier where the performance is measured. There

is only one supplier at this level, located in Western Europe. A close-up of this suppliers is shown

in Figure 4.4. Now a short description of every element of the supplier in Figure 4.4 follows. An

explication of the transitions of Figure 4.4 is listed in Table 4.5 the places are listed in 4.6.1In GreatSPN, it is not possible to store more then 255 tokens per place



P1 Incoming orders

P2 Outgoing orders

P3 Available products

P4 Stock of goods 1

P5 Backorders

P6 Stock of assigned goods 2

P7 Outgoing goods

P8, P9 & P10 Maximum 40% of the orders can been sent to the same supplier. All the

six suppliers have their own place who receives 2 tokens when an order is

sent to an other supplier and 3 tokens are removed when an order is sent to

the corresponding supplier. When there are no tokens left in the place, the

supplier reached his 40% limit3.

P11 State: Do not send orders

P12 State: Send Orders

P13 State: Shipping department is up

P14 State: Shipping department is down

P15, P16 & P17 Token storage per 100

1 Initially there are s goods stored, s is also the target stock

2 This stock is only used when the shipping department is down

3 The initial amount is P = 3 tokens

Table 4.4: The places of a supplier of level 2 or 3 from Figure 4.3

4.5 Ordering and Delivery Mechanism

The suppliers of different levels are connected in such a way that orders can be sent and products

can be received. The orders and products have to be transmitted by a certain mechanism that

meets certain specifications:

• Every supplier has to be able to send orders to every supplier one echelon upstream.

• The mechanism has to remember which customer ordered which amount of goods

• An order is only shipped when the order is complete


P10P

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2π

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2π

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_2 _2_3

_2 _2 _3

Figure 4.3: Supplier of level 2 and 3

P11P

P7P8

P10PP9P

P2

P1P4

P6

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P12 P13 P14

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_100_100

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_3

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_50 _50_50

Figure 4.4: Supplier of level 4


Notation Interpretation Type, Mean Time or Prior-

ity

t1 Generating demand Stochastic, parameter

t2 Processing orders Immediate, 1

t3 Backlogging orders Immediate, 1

t4, t5 and t6 Sending orders to suppliers 1, 2 and 3 Immediate, 5

t7, t8 and t9 Goods entering from suppliers 1,.. 6 Stochastic, (see Table 2.2)

t10 Storing conform goods Immediate, 1

t11 Demolishing non conform goods

(spoilage)

Immediate, 1

t12 Processing backlogs Immediate, 1

t13 Delivering goods to the customer Immediate,

t14 Setting state to: send orders Deterministic, 5 days

t15 Setting state to: Block until next week Immediate, 1

t16, t17 & t18 Ungrouping 1 token in 1001 Immediate (take 1, give 100)

t19, t20 & t21 Grouping 100 tokens in 1 Immediate (take 100, give 1)

Table 4.5: The transitions of a supplier of level 4 from Figure 4.4

• Separate orders have to be shipped separate, orders have to be queued

• Transport times have to be proportional with distances between the suppliers

4.5.1 Simple Queue

First we consider the transportation and ordering mechanism proposed in Figure 4.5: Ordering

and Delivery (Simple). Every supplier has such a mechanism per customer. Thus, in the whole

model there are 3× (3 + 3 + 1) = 21 of these queues (every customer has 3 suppliers, there are 3

customers of level 2, 3 of level 3 and 1 of level 4). This mechanism satisfies all the specifications

enumerated above. Now a short description of every element of the mechanism proposed in Figure

4.5 follows. An explication of the transitions of Figure 4.5 is listed in Table 4.7. The Places are

listed in Table 4.8.

An example of the simple queue working In this Example (see Figure 4.6)there is a sequence

of orders leaving and entering the queue.



P1 Incoming orders

P2 Outgoing Orders

P3 Backorders

P4 Incoming Goods

P5 Stock of Goods 1

P6 Outgoing Goods

P7 State: Do not send orders

P8 State: send orders

P9, P10 & P11 Maximum 40% of the orders can been sent to the same supplier. All the

six suppliers have their own place who receives 2 tokens when an order

is sent to an other supplier and 3 tokens are removed when an order is

sent to the corresponding supplier. When there are no tokens left in the

place, the supplier reached his 40% limit.2

P12, P13 & P14 Token storage per 100

1 Initially there are s goods stored, s is the target stock

2 The initial amount is P = 3 tokens

Table 4.6: The places of a supplier of level 4 from Figure 4.4


Notation Interpretation Type, Mean Time or Priority

t1 Sending orders from the customer to the sup-

plier’s control mechanism

Immediate, 4

t2 Orders are received by the supplier Immediate, 1

t3 Order moving from third in row to second Immediate, 3

t4 Order moving from third in row to second Immediate, 1

t5 Order moving from 2nd in row to first Immediate, 3

t6 Order moving from 2nd in row to first Immediate, 2

t7 Orders are assigned to the customer Immediate, 1

t8 Orders are released to the customer when the

complete order is fulfilled (when P39 is empty)

Immediate, 1

t9 Goods are shipped Stochastic, infinite server, 10

or 20 days

Table 4.7: The transitions of a simple queue from Figure 4.5


P1 Orders

P2 Last order in row

P3 Place to keep the third and the second order separated

P4 Second order in row waiting until the first order is complete and released

P5 Place to keep the first and the second order separated

P6 First order in row

P7 Assigned products for the first order, waiting until the order is complete (= until

P6 is empty)

P8 Goods on their way to the customer

Table 4.8: The places of a simple queue from Figure 4.5

• 3 orders are waiting to be served. First order is an order of 4 products, second order has

products an the third order 3. 3 product of the first order are already assigned.

• When the last product of the first order is added, the first order is released

• The second and the third order move up


P8

P2P3P4P5P6

P7

P1

t9

t7t4

t2

t6

2π

t5

3π

t3

3π

t8

4π

t1

4π

Figure 4.5: Ordering and Delivery (Simple)

• A new order of 2 products enters the line

4.5.2 Advanced Queue

In the previous subsection a queue was proposed. This queue was used to explain the basic idea

of the queue in a simple straightforward way. But, there is a problem with this simple queue:

When a new order enters an empty queue, the whole order should move to the first place. This is

not the case with the simple queue, because the first order is split in two at transition t53. The

first token moves directly to front of the queue (P39)where it blocks the rest of the tokens by the

inhibitor arc. This way the order is shipped at two different moments. This is contrary to initial

problem description. An example is shown in Figure 4.7.

To cure this, the next queue is proposed. See Figure 4.8. When the queue is empty and an order

arrives, the first token that enters the queue is split of by transition t6 and moves to place P6

where its is blocked until the whole order is arrived at place P3. After that the queue works just

like the simple queue. It has to be said that this more advanced queue doesn’t work different when

the queue is not empty.

4.6 Adaptation of the Description

In Bundschuh et al. (2003), there are some prescriptions that were not possible to implement with

the tool GreatSPN. It was not possible to model a uniform probability distribution and a demand

of 20000 per week. Instead there is a negative exponential probability distribution used for the

transportation times and the demand is limited to 10 per week. For more information about this

subject, see the discussion about GreatSPN at ??.


P8

P2P3P4P5P6

P7

P1

t9

t7t4

t2

t6

2π

t5

3π

t3

3π

t8

4π

t1

4π

(a) 3 separate orders in the queue

P8

P2P3P4P5P6

P7

P1

t9

t7t4

t2

t6

2π

t5

3π

t3

3π

t8

4π

t1

4π

(b) First order ready, waiting to be shipped

P8

P2P3P4P5P6

P7

P1

t9

t7t4

t2

t6

2π

t5

3π

t3

3π

t8

4π

t1

4π

(c) First order is shipped

P8

P2P3P4P5P6

P7

P1

t9

t7t4

t2

t6

2π

t5

3π

t3

3π

t8

4π

t1

4π

(d) Second order moves to intermediate state

P8

P2P3P4P5P6

P7

P1

t9

t7t4

t2

t6

2π

t5

3π

t3

3π

t8

4π

t1

4π

(e) Third order moves to intermediate state

P8

P2P3P4P5P6

P7

P1

t9

t7t4

t2

t6

2π

t5

3π

t3

3π

t8

4π

t1

4π

(f) The -initially- second order can now be served

P8

P2P3P4P5P6

P7

P1

t9

t7t4

t2

t6

2π

t5

3π

t3

3π

t8

4π

t1

4π

(g) Third order moves to second place

P8

P2P3P4P5P6

P7

P1

t9

t7t4

t2

t6

2π

t5

3π

t3

3π

t8

4π

t1

4π

(h) One order of two products arrived and is waiting

at the end of the row.

P8

P2P3P4P5P6

P7

P1

t9

t7t4

t2

t6

2π

t5

3π

t3

3π

t8

4π

t1

4π

(i) The supplier accepted the new order.

Figure 4.6: Ordering and Delivery


P28

P30

P39 P40

P41 P42 P43

P51

t39

t54t29

t27

t40

2π

t53

3π

t55

3π

t64

4π

t38

4π

(a) An order of 4 products enters the empty queue

P28

P30

P39 P40

P41 P42 P43

P51

t39

t54t29

t27

t40

2π

t53

3π

t55

3π

t64

4π

t38

4π

(b) The order proceeds

P28

P30

P39 P40

P41 P42 P43

P51

t39

t54t29

t27

t40

2π

t53

3π

t55

3π

t64

4π

t38

4π

(c) Only the first token moves up

P28

P30

P39 P40

P41 P42 P43

P51

t39

t54t29

t27

t40

2π

t53

3π

t55

3π

t64

4π

t38

4π

(d) Only the first token moves up

P28

P30

P39 P40

P41 P42 P43

P51

t39

t54t29

t27

t40

2π

t53

3π

t55

3π

t64

4π

t38

4π

(e) The first token arrives at the end of the queue

P28

P30

P39 P40

P41 P42 P43

P51

t39

t54t29

t27

t40

2π

t53

3π

t55

3π

t64

4π

t38

4π

(f) The remaining tokens are blocked by the first

token

Figure 4.7: Simple Queue: Split of the order

P9

P7

P5

P4 P3 P2 P1

P8

P6

t11

t10

t8

t7

t6

t3t5

2π

t4

3π

t2

3π

t9

4π

t1

4π

Figure 4.8: Advanced ordering and delivery mechanism

Chapter 5

Optimization at strategic level

In the previous chapter a PN model of a supply chain was proposed. Before we have a look

at the experiments, some strategic level decisions have to be made. The model can simulate

several scenario’s. This means that at a higher decision-level, there can be decided that some less

desired suppliers are not considered. This can result in a Supply chain with a very high reliability

or a scenario where only the cheapest suppliers are used. The results obtained in this chapter

are calculated with the linear programming method. The total cost was always minimized with

constraints on the reliability and the robustness. These calculations are outside the scope of this

mastersthesis, for details see Vila (2004).

Four scenario’s are under investigation.

basic serial model The cost is minimized

basic model Because the basic serial model proposes only one path, the whole supply chain

is extremely vulnerable for complete disruptions. In the basic model suppliers can order

maximum 40% to the same supplier.

high reliability model As the number of suppliers decreases, the reliability drops. Here a cer-

tain higher reliability is guaranteed by using high reliable suppliers. The 40% source limit

is still set.

60% source limit model To obtain a higher reliability with less costly suppliers, the total num-

ber of suppliers will be dropped.

5.1 Basic serial model

For this optimization, the only important feature is the cost. This results in the supply chain where

only the cheapest suppliers of each echelon are used. This supply chain has a high reliability

24

CHAPTER 5. OPTIMIZATION AT STRATEGIC LEVEL 25

((96%)3 = 88%), 88% of the time are all the elements of the supply chain operational. The

disadvantage of this cheap and high reliable supply chain is the robustness. When one of the

elements is down, the entire supply chain is down. No bypasses are possible. The total minimum

cost of this supply chain is 69, 3 ∗ 106 currency units. See Figure 5.1.

Figure 5.1: Basic serial

5.2 Basic model

To meet the disadvantages of the previous scenario (the low robustness), a source limit of 40%

is introduced. This means that a supplier can order maximum 40% of all his orders to the same

supplier With this extra restriction every supplier has to order to at least three suppliers at a

higher level. See Figure 5.2. The reliability is has dropped to (96%)9 = 69% and the total cost

for one year has increased to 77.7 ∗ 106 currency units. But robustness has also increased.

5.3 High Reliability model

The disadvantage of the basic model is that the reliability has dropped. Therefore a restriction to

the LP problem is added: The reliability must be greater than 75%. The result of the calculation

is shown in Figure 5.3. The reliability is has raised to (98%)6(96%)3 = 78% and the total cost for

one year has increased to 115 ∗ 106 currency units.


Figure 5.2: Basic

5.4 60% source limit model

It is also possible to obtain a high reliability with cheaper suppliers by using less suppliers. This

is why the source limit is raised to 60%, allowing only 2 suppliers per level. See Figure 5.4. The

reliability is has raised to (96%)6 = 78% and the total cost for one year has dropped to 71.2 ∗ 106

currency units. The price which has to be paid for these good Figures is that the robustness has

dropped.


Figure 5.3: High Reliability

Figure 5.4: 60% source limit

Chapter 6

Simulation

When the optimization at strategic level is completed, the tactical planning begins. In this case this

is: When the suppliers are chosen, there has to be decided how service levels have to be attained.

The parameters we can manipulate are the target stocks for every supplier. The simulation of

several models will support us to find appropriate parameters with their resulting service levels.

6.1 Performance indicators

As supply chains have more then one level of interest, we now define the several supply chain

performance indicators used in the discussion below.

Stockout periods It indicates the number of periods that the deliveries where not met at the

last echelon (the echelon of the customer).

Service level P1 It is the percentage of the periods that there was no stockout:(1− StockoutPeriods

TotalPeriods

)× 100%

Service level P2 or fill rate It is the percentage of the fulfilled demand to the total demand:(1− DemandCovered

DemandTotal

)× 100%

Transport cost See Table 2.1

Average Inventory The sum of the average inventory of every supplier.

Total Cost The sum of the transportation costs, the fixed cost per transportation route, the

inventory costs and the backlog costs. With an inventory cost of 1 cu per period and a

backlog cost of 2 cu’s per period.

28

CHAPTER 6. SIMULATION 29

Average breakdown The total time of all the breakdowns compared to the simulation duration.

Spoilage The amount of product spoiled per day.

6.2 Target Stock

Target stock is the stock every supplier tries to attain. The average stock at a supplier will always

be lower than the target stock. This because of the transport times, the time orders have to wait

until submitted to a supplier, stockouts of a supplier, etc.

The level of the target stock which has to be set depends on the demand during leadtime (LT) and

the service levels we want to attain. The demand during LT is a distribution δ (µδ, σδ) which is the

result of two distributions: The demand (µD, σD) and the lead time (µLT , σLT ). Because we want

to examine the impact of the target stock on the service level, we simulate every scenarios with

different z-factors z = 0, 1, 2, 3, 4, this is the number of times we use σδ as safety stock (SS). The

target stock is calculated using next formula for the suppliers of level 2, 3 and 4 (See Landeghem

(2005)):

TS = µδ + Z × σδ =µD × µLT

n× spoilech+ Z ×

√µLT × σ2

D + µ2D × σ2

LT

with:

TS The Target Stock

µδ Average demand during LT

Z The number of times σδ we use as safety stock (SS)

σδ The standard deviation on the demand during LT

µLT Average Lead Time or transport time

µD Average Demand

n The total number of suppliers in the echelon

spoil The amount wasted per echelon1

ech The number of times spoilage has to be count in 2

Z The z-factor

σD The standard deviation on the Demand1standard spoil = 0.952For echelon 1,2,3 & 4 ech is respectively 4, 3, 2 & 1


σLT The standard deviation on the Lead Time or transport time3.

Suppliers of the 1st echelon have unlimited stocks (see Bundschuh et al. (2003)). For the simulation

target stocks of 50 at the 1st echelon could be replenished fast enough, so it seemed like they were

infinite.

Every scenario was simulated with and without uncertainty factors. If we calculate for the same

scenario the Target Stock for different levels of uncertainty, Target Stocks will be different. To

make comparison easier, Target Stocks are for every level of uncertainty the same for same scenarios

and same values of Z.

Target stocks for uncertainty factor Z from 0 to 4 are shown in the appendix on p. 42 Table 1.

6.3 Experiments

Several scenarios were simulated with the PN-model. In Table 6.1, 6.2, 6.3 and 6.4 are the results

presented.

6.3.1 Analysis of the models

to be continued . . .

6.3.2 Analysis between models

to be continued . . .

3Because the lead time is simulated as a exponential distribution, σLT = µLT . When a supplier has n multiple

supplier, σ lowers with a factor 1√n

.


Experiment: Z P1 P2 Average Average Transport Total

Basic Inventory Backlog Cost Cost

Model (%) (%) (103 prod.) (103 prod.) (106c.u.) (106c.u.)

With ev-

ery uncer-

tainty

0

1

2

3

19.7

.

.

.

98.8

100.0

.

.

32.7

145.3.

.

.

34.1

1.1.

.

.

76.9

78.3

.

.

84.0

85.7

.

.

Without

Any Un-

certainty

0

1

2

29.5

99.9

.

97.35

99.7

100.0

33.7

146.0

277.1

26.8

4.3

9.3

70.4

70.8

73.1

75.6

83.5

87.8

Without

Random

Leadtimes

0

1

29.6

89.4

93.3

100.0

26.7

106.3

42.7

2.1

74.2

88.7

81.9

96.3

Without

Plant

Break-

downs

0

1

2

14.4

.

100.

100.0

26.8

180.2

3.9

0.1

81.1

80.5

88.5

89.5

Without

Spoilage

0

1

2

.

.

100.0

100.0

38.8

151.3

17.0

0.3

72.0

72.0

75.7

79.6

Table 6.1: Results for the Basic Model


Basic Inventory Backlog Cost Cost

Serial (%) (%) (103 prod.) (103 prod.) (106c.u.) (106c.u.)

With ev-

ery uncer-

tainty

0

1

2

18.5

100.0

100.0

98.7

100.0

100.0

14.4

137.8

274.8

37.7

0.088

0.0

71.3

72.6

71.4

76.1

79.8

85.4

Without

Any Un-

certainty

0

1

28.4

100.0

100.0

100.0

19.4

191.2

18.5

0.0

67.6

66.5

70.7

76.4

Table 6.2: Results for the Basic Serial Model



High Inventory Backlog Cost Cost

Relia. (%) (%) (103 prod.) (103 prod.) (106c.u.) (106c.u.)

With ev-

ery uncer-

tainty

0

1

2

11.1

.

.

98.6

.

.

31.6

.

.

35.3

.

.

116.5

.

.

123.7

.

.

Without

Any Un-

certainty

0

1

2

29.5

99.9

100.0

96.6

100.0

100.0

37.9

140.1

272.5

19.7

0.1

0.0

107.1

102.3

107.0

113.1

109.3

111.4

Table 6.3: Results for the High Reliability Model


60% Source Inventory Backlog Cost Cost

Limit (%) (%) (103 prod.) (103 prod.) (106c.u.) (106c.u.)

With ev-

ery uncer-

tainty

0

1

2

3

15.9

.

.

.

93.1

.

.

.

13.4

.

.

.

100.5

.

.

.

75.3

.

.

.

87.0

.

.

.

Table 6.4: Results for the 60% Source Limit

Chapter 7

Control Layer Model

In the previous chapter several scenario’s are proposed and simulated. All those scenario’s use the

same model based on the supply chain described by Bundschuh et al. (2003). In that description,

the state of a customer’s suppliers is not considered when that customer decides where he sends

his orders to. In this case it is possible that a customer sends orders to a supplier with many

backlogs. If the customer would have the appropriate information of his suppliers to send his

orders only to those suppliers who can deliver directly from stock, supply chain performance can

possibly be raised. In this chapter we implement a control layer in the model so that customers

have more information about the status of their suppliers at the ordering moment.

7.1 Implementation in the model

The only modification that has to be added in the model are inhibitor arcs between the backlog

places (e.g. place P5 in Table 4.1 and Figure 4.2) and the send-order transitions (e.g. transitions

t230, t232, ..t240 in Table 4.3 and Figure 4.3). Weights can be added to each inhibitor arc to

permit a certain level of backlogs at each supplier. There were simulation runs with weights of 0,

2 and 5. In Figure 7.1 a close-up is shown of the Control Layer Model. Note the inhibitor arcs

from P63, P75 & P48 to respectively t65, t377, & t48.

7.2 Results

Results of the simulation are shown in Table 7.1. Best results are with inhibitor arc weight of

. . . If comparison is made with the results of Chapter 6 . . .

33

CHAPTER 7. CONTROL LAYER MODEL 34

P347

P346P355

P354

P353

P352

P351

P350

P349

P348

P334

P333 P342

P341

P340

P339

P336

P335

P264

P263

P340

P339

P338

P337

P336

P335

P270

P269

P332

P331

P330 P329

P328

P327

P315

P321

P316P317P318

P319P320

P324 P323

P322 P321 P320

P319

P318

P317 P316

P315 P314 P313

P312

P311

P310 P309

P308P307 P306

P305

P304

P258

P296

P303

P302

P301P300

P299

P298

P295

P294 P293

P292 P291 P290

P289

P288

P287 P286

P285 P284 P283

P282

P281

P280 P279

P278 P277 P276

P275

P219

P221

P222P223

P224

P22550

P226

P227

P220

P260

P259

P258

P257

50

P256

P255P254

P253

P252

P251

P250

P249

P248

50

P247

P246P245

P244

P243

P78

P76P77P79

P80P82

P81

P314

P313 P312

P311P310 P309

P308

P307

P306 P305

P304 P303 P302

P301

P61

P166

P167

P181

P180

P179 P178

P183

P182

P160

P159

P158

P157P162

P161

P163

11

P164

P165

P66

P67

P68

P65

P63

P64

P6215

P60

P156

P155

P154

11

P153

P152

P151

P150

P149

P148

P147

P146

P145

11

P144

P143

P142

P141

P140

P139

P79

P78

P80

P77

P76

P69

P70

P138

P137

P136

P135

P134

P133P132

P131

P130

P129

P128

P127

P126 P125

P124

P123

P122

P121

P120

P119 P118

P117

P116

P115

P114

P113

P112 P111

P110

P109

P108

P107

P106

P105 P104

P103

P102

P101

P100

P99

P98 P97

P96

P95

P94

P93

P92

P91P90

P89

P88

P87

P86

P85

P84

P83

P1474

P295

P1677

P1475

P1476

P1478

P1473

P73

P72

P25

P26

P979

P75

P74

P71

P1477

P1479

P4338

P137 P1024

P290

P291P292

P293

P294

P439

43

P42

P43

P44

P45

P46

P47

P48

P49

P508P51

P52

P53 P54

P55 P56P57

P58

P59

P81

P82

P83

P84

P85

P86

P87

P88P168P169

P170

P171

P172

P173

P174

P175

P176P177

P184

P185

P186

P187

P188

P189

P190

P191

P192

P193P194

P195

P196

P197

P198

P199 P200

P201

P202

P203

P204

P205

P206

P207

MTBF=0.040000MTTR=0.285714

EA=0.050000

AE=0.050000

WA=0.050000

AW=0.050000

EW=0.050000

WE=0.050000

Demand=2.000000CT=2.000000

order=5.000000

WW=0.100000

EE=0.100000

AA=0.100000

spoil=0.050000nspoil=0.950000

first_time_order=0.000010first_time_order_II=0.000020

T211

T210

T205

T388

T287

T345

T272

T378

T302

T209

T208

T207

T206

T212

T213

t49

t376

t66

T387

T386

T383

T377

T376

T373

T347

T346

T340

T256T257

T258

T291T290

T289

T276 T275T274

T245

t218

T184T183

T244

t222

t220

T243

t72t71

T175 T174

T166 T165

t33 t34

t29T28

t378T948

t393 t392t401

t400

t399

t398t397t396

t395 t394

t381 t382 t390t389t388t387

t384 t383

t389

t379

t359

t358

t368

t367

t361

t360

t354

t353

t349

t337

t336

t330

t329

t323

t322

t261

t262

t263

t264

t265

t266

t267

t268

t269

t270

t303

t302

t301

t300

t299

t298

t297

t296

t295

t294

t288t287

t286

t285

t284

t283

t282

t281

t280

t279

t89

t90

t352

t351

t345

t344

t219

t235 t230

t231t232

t234

t233

t163

t164t154

t155

t145

t146

t188

t190

t189

t191

t241t240

t239t238

t237

t236

t229

t228

t227t226

t225t224

t223

t221

t55

t53t51

t69

t182

t181

t180

t179

t173

t172

t171

t170

t68

t63

t57

t56

t162

t161

t153

t152

t144

t143

t137

t136

t135

t134

t128

t127

t126

t125

t119

t118

t117

t116

t110

t109

t108

t107

t101

t100

t99

t98

t92

t91

t78

t77

t76

t75

t74

t73

t32

t37

t46

t43

t42

t41

t39

t36

t1164

t1163

t60

t59

t344t962

t979

t961

t9491

t362

t968

t364

t379

t362

2π

t366

2π

t359

2π

t352

2π

t333

2π

t326

2π

t319

2π

t88

2π

t355

2π

t348

2π

t61

2π

t160

2π

t151

2π

t142

2π

t133

2π

t124

2π

t115

2π

t106

2π

t97

2π

t44

2π

t1167

2π

t360

3π

t361

3π

t365

3πt364

3π

t358

3πt357

3π

t351

3πt350

3π

t335

3π

t334

3π

t328

3π

t327

3π

t321

3π

t320

3π

t84

3π

t85

3π

t354

3πt353

3π

t347

3πt346

3π

t64

3π

t62

3π

t157

3πt156

3π

t148

3πt147

3π

t139

3πt138

3π

t130

3πt129

3π

t121

3πt120

3π

t112

3πt111

3π

t103

3πt102

3π

t94

3πt93

3π

t47

3π

t45

3π

t1165

3π

t1166

3π

t364

4π

t363

4π

t370

4π

t369

4π

t363

4π

t362

4π

t356

4π

t355

4π

t339

4π

t338

4π

t332

4π

t331

4π

t325

4π

t324

4π

t260

4π

t292

4π

t277

4π

t86

4π

t87

4π

t357

4π

t356

4π

t350

4π

t349

4π

t186

4π

t52

4π

t177

4π

t168

4πt67

4π

t58

4π

t159

4π

t158

4π

t150

4π

t149

4π

t141

4π

t140

4πt132

4π

t131

4π

t123

4π

t122

4πt114

4π

t113

4π

t105

4π

t104

4πt96

4π

t95

4π

t38

4π

t50

4π

t35

4π

t1162

4π

t1161

4π

t343

4π

t363

4πt292

5π

t390

5π

t385

5π

t307

5π

t380

5π

t375

5π

t277

5π

t348

5π

t343

5π

t215

5π

t216

5π

t217

5π

t200

5π

t199

5π

t198

5π

t197

5π

t196

5π

t214

5π

t65

5π

t48

5π

t377

5π

t259

7π

t293

7π

t278

7π

t187

7π

t54

7π

t178

7π

t169

7π

t40

7π

t345

7π

t365

7π

_5

_2

_2

_3

_5

_2

_2

_3

_5

_2

_2

_3

_5

_2_2

_3

_5 _2

_2

_3

_5

_2

_2_3

_5

_2_2 _3

_5

_2_2_3

_5 _2_2_3

_5

_2_2

_3

_5

_2_2_3

_5

_2

_2 _3

_5

_2 _2_3

_5

_2_2 _3

_5

_2_2 _3

_5

_2_2

_3_5

_2_2

_3

_5

_2

_2_3

_5

_2_2

_3

_5

_2

_2 _3

_5

_2

_2

_3

_100

_50_100

_50_100

_100

_100

_50_100

_50_100 _100

_50_100

_100_50

_100_100

_50_100 _100

_50_100 _100

_50_100

_100

_50 _100

_100

_100_50_100

_100

_50_100

_100_50 _100

_50_100

_100 _50_100

_100_100_50

_100

_100_50

_100

_100 _50_100

_100_50_100

_50_100

_100_100_50

_100

Figure 7.1: A close-up of the Control Layer Model, suppliers of level 3 and 4

CHAPTER 7. CONTROL LAYER MODEL 35


Control Inventory Backlog Cost Cost

Layer (%) (%) (103 prod.) (103 prod.) (106c.u.) (106c.u.)

Inhibitor

Weight =

0

0

1

19.8

.

96.6

.

29.5

.

49.0

.

79.6

.

88.1

.

Inhibitor

Weight =

1

0

1

.

.

.

.

.

.

.

.

.

.

.

.

Inhibitor

Weight =

5

0

1

.

.

.

.

.

.

.

.

.

.

.

.

Table 7.1: Results for the Control Layer Model

Chapter 8

Conclusion

It was the goal of this thesis to model and simulate supply chains by Petri Nets (PN). First we

have to say that these goals are reached. A model of a supply chain was constructed and several

simulation runs were performed successfully.

During the building of the model there were no obstacles found that PN couldn’t overcome. For

this reason it is the author’s belief that Petri Nets in general are a very powerful modeling language

and GSPN specifically are very well suited for the simulation of supply chains. Compared to other

languages gives the graphical representation of the model an extremely good overview and a quick

insight of the dynamics of the model. The graphical representation has a great added value to

the reader in terms of the understanding of the model. In addition of these PN-benefits, it was

possible to build this very complex and large model in a short time. This because the author

started from the methodology provided in Bobeanu et al. (2004) and Landeghem & Bobeanu

(2002). This methodology allows the user to built models on a incremental and systematical way

by coupling basic components by well defined rules. While building the supply chain model in the

tool GreatSPN, only one hard restriction could not been overcome: It is not possible for a place to

contain more than 255 tokens. Therefore 2000 products had to be modeled by one token. Several

experiments were performed on the model. From their results we can conclude that on this model,

the most important disturbance factor on the performance measures is the random transport time.

If the objective is to minimize costs, spoilage has to be reduced. Plant breakdowns have only a

minor influence. When there are more reliable suppliers used, cost increase but the service factors

don’t. When we cut the total number of suppliers, costs drop without the loss of performance.

Best results were gained with a minimum of low-cost suppliers.

36

Appendix A

37

APPENDIX A 38

50

50

50

11

11

11

2π

2π

2π

2π

2π

2π

2π

2π

2π

3π 3π

3π 3π

3π 3π

3π 3π

3π 3π

3π 3π

3π 3π

3π 3π

3π 3π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

4π

5π

5π

5π

5π

5π

5π

5π

5π

5π

7π

7π

7π

7π

7π

7π

_2_2_3

_2 _2 _3

_2 _2_3

_2

_2

_3

_2_2

_3

_2

_2_3

_2_2

_3

_2

_2

_3

_2

_2_3

_100_50 _100

_50

_100

_100 _50

_100

_100_100_50

_100

_100_50

_100

_100 _50

_100

_100

_50

_100

_50

_100

_100

_100_50

_100

Figure 1: The overall model Part I: Suppliers of Level 1 & 2

APPENDIX A 39

15

8

8

2π

2π

2π

2π

2π

2π

2π

2π

2π

3π 3π

3π 3π

3π 3π

3π 3π

3π 3π

3π 3π

3π 3π

3π 3π

3π 3π

4π

4π

4π

4π

4π 4π

4π 4π

4π 4π

4π 4π

4π 4π

4π 4π

4π 4π

4π

4π

4π

5π

5π

5π

5π

5π

5π

5π

5π

5π

7π

7π

7π

_2_2

_3

_2

_2_3

_2

_2

_3

_2_2

_3

_2

_2_3

_2 _2

_3

_2_2_3

_2 _2_3

_2

_2_3

_50

_100 _100

_50

_100_100

_50_100

_100

_50_100

_100

_50_100 _100

_50

_100

_100

_50_100

_100

_100_50_100

_100

_50

_100

Figure 2: The overall model Part II: Suppliers of Level 3

APPENDIX A 40

43

MTBF=0.040000

MTTR=0.285714

EA=0.050000

AE=0.050000

WA=0.050000

AW=0.050000

EW=0.050000

WE=0.050000

Demand=2.000000

CT=2.000000order=5.000000

WW=0.100000

EE=0.100000

AA=0.100000

spoil=0.050000

nspoil=0.950000

first_time_order=0.000010

first_time_order_II=0.000020

2π

2π

2π

3π 3π

3π 3π

3π

3π

4π

4π

4π

4π

4π

4π

4π

5π

5π

5π

7π

_2

_2

_3

_2

_2

_3

_2

_2

_3

_100

_50_100

_50_100

_100

_100

_50_100

Figure 3: The overall model Part III: Suppliers of Level 4

Appendix B

41

APPENDIX B 42

Des

crip

tion

zSu

pplie

r1 1

Supp

lier

1 2Su

pplie

r1 3

Supp

l.2 1

Supp

l.2 2

Supp

l.2 3

Supp

l.3 1

Supp

l.3 2

Supp

l.3 3

Supp

l.4

Bas

ic0

5050

5011

1111

158

843

150

5050

1818

1825

1313

682

5050

5024

2424

3418

1893

350

5050

3131

3143

2323

118

450

5050

3838

3852

2828

143

Seri

al0

5050

5024

2343

150

5050

4845

852

5050

5071

6812

83

5050

5095

9017

04

5050

5011

911

321

3H

igh

050

5050

1113

1313

1313

22R

elia

ble

150

5050

1822

2221

2121

352

5050

5024

3030

2929

2947

350

5050

3138

3836

3636

604

5050

5038

4646

4444

4473

60%

050

5050

1212

1212

43so

urce

150

5050

2121

2020

732

5050

5030

3028

2810

33

5050

5039

3937

3713

44

5050

5047

4745

4516

4C

ontr

ol0

5050

5011

1111

158

843

laye

r1

5050

5018

1818

2513

1368

250

5050

2424

2434

1818

933

5050

5031

3131

4323

2311

84

5050

5038

3838

5228

2814

3

Tab

le1:

Tar

get

Stoc

ksfo

rev

ery

Supplier

Ech

elon

Su

ppli

er

for

ever

yex

peri

men

t(E

xper

imen

tsw

ith

diffe

rent

leve

lsof

unce

rtai

nty

have

the

sam

eva

lues

)

Appendix C

In this appendix a selection is made of interesting results of the several experiments. Token

distibutions are shown for several Stocks, Backlogs and transport delay places.

43

APPENDIX C 44

01

Figure 4: Supplier of level 4 (P439). Basic model, Z = 0

APPENDIX C 45

Figure 5: Backlog of level 4 (P294). Basic model, Z = 0


APPENDIX C 46




APPENDIX C 47





APPENDIX C 48




APPENDIX C 49


APPENDIX C 50

02

APPENDIX C 51


APPENDIX C 52




APPENDIX C 53





APPENDIX C 54




APPENDIX C 55




APPENDIX C 56

04


APPENDIX C 57




APPENDIX C 58




APPENDIX C 59




APPENDIX C 60



APPENDIX C 61



APPENDIX C 62

06


APPENDIX C 63


APPENDIX C 64



APPENDIX C 65



APPENDIX C 66

07



APPENDIX C 67



APPENDIX C 68



APPENDIX C 69

08



APPENDIX C 70



APPENDIX C 71



APPENDIX C 72

11


APPENDIX C 73



APPENDIX C 74




APPENDIX C 75





APPENDIX C 76




APPENDIX C 77


APPENDIX C 78

12



APPENDIX C 79




APPENDIX C 80





APPENDIX C 81




APPENDIX C 82



APPENDIX C 83

13



APPENDIX C 84



APPENDIX C 85




APPENDIX C 86




APPENDIX C 87



APPENDIX C 88



APPENDIX C 89

16


APPENDIX C 90


APPENDIX C 91



APPENDIX C 92




APPENDIX C 93




APPENDIX C 94

17



APPENDIX C 95



APPENDIX C 96



APPENDIX C 97



APPENDIX C 98



APPENDIX C 99

18

APPENDIX C 100


APPENDIX C 101




APPENDIX C 102



APPENDIX C 103



APPENDIX C 104



APPENDIX C 105

21


APPENDIX C 106



APPENDIX C 107






APPENDIX C 108





APPENDIX C 109



APPENDIX C 110

22



APPENDIX C 111




APPENDIX C 112




APPENDIX C 113




APPENDIX C 114




APPENDIX C 115

23

APPENDIX C 116


APPENDIX C 117




APPENDIX C 118




APPENDIX C 119




APPENDIX C 120




APPENDIX C 121


APPENDIX C 122

26


APPENDIX C 123


APPENDIX C 124


APPENDIX C 125


APPENDIX C 126



APPENDIX C 127

27

APPENDIX C 128


APPENDIX C 129



APPENDIX C 130



APPENDIX C 131


APPENDIX C 132

31



APPENDIX C 133




APPENDIX C 134




APPENDIX C 135





APPENDIX C 136



APPENDIX C 137

32



APPENDIX C 138




APPENDIX C 139






APPENDIX C 140





APPENDIX C 141

33



APPENDIX C 142





APPENDIX C 143





APPENDIX C 144



APPENDIX C 145



APPENDIX C 146

36


APPENDIX C 147


APPENDIX C 148




APPENDIX C 149




APPENDIX C 150




APPENDIX C 151




APPENDIX C 152

37

APPENDIX C 153


APPENDIX C 154




APPENDIX C 155




APPENDIX C 156




APPENDIX C 157




APPENDIX C 158


APPENDIX C 159

41


APPENDIX C 160



APPENDIX C 161




APPENDIX C 162





APPENDIX C 163




APPENDIX C 164


APPENDIX C 165

42

APPENDIX C 166


APPENDIX C 167




APPENDIX C 168





APPENDIX C 169




APPENDIX C 170




APPENDIX C 171

46


APPENDIX C 172




APPENDIX C 173





APPENDIX C 174





APPENDIX C 175



APPENDIX C 176

47

APPENDIX C 177


APPENDIX C 178




APPENDIX C 179





APPENDIX C 180




APPENDIX C 181




APPENDIX C 182

51


APPENDIX C 183



APPENDIX C 184




APPENDIX C 185




APPENDIX C 186





APPENDIX C 187


APPENDIX C 188

56


APPENDIX C 189


APPENDIX C 190




APPENDIX C 191




APPENDIX C 192





APPENDIX C 193



APPENDIX C 194

57

APPENDIX C 195


APPENDIX C 196




APPENDIX C 197




APPENDIX C 198




APPENDIX C 199



APPENDIX C 200



APPENDIX C 201

61

Figure 358: Supplier of level 4 (P439). Basic model, Z = aaaresults/61

APPENDIX C 202

Figure 359: Backlog of level 4 (P294). Basic model, Z = aaaresults/61

APPENDIX C 203




APPENDIX C 204




APPENDIX C 205





APPENDIX C 206



Bibliography

G. Balbo, J. Desel, K. Jensen, W. Reisig, G. Rozenberg & M. Silva (2000). Introductory tutorial

petri nets. 21st International Conference on Application and Theory of Petri Nets, Aarhus,

Denmark.

C.-V. Bobeanu (2005). Modelling and Simulating Manufacturing and Service Systems using Petri

Nets. Universiteit Gent.

C.-V. Bobeanu, E. J. Kerckhoffs & H. V. Landeghem (2004). Formal Modelling of Discrete Event

Systems:A Holistic and Incremental Approach Using Petri Nets. ACM Transactions on mod-

elling and Computer Simulation, 14(4):389–423.

M. Bundschuh, D. Klabjan & D. L. Thurston (2003). Modelling Robust and Reliable Supply

Chains. journal????

P. Z. Chen, S. C. Bruell & G. Balbo (1990). Alternative Methods for Incorporating Non-

Exponential Distributions into Stochastic Timed Petri Nets. In PNPM89. Proceedings of the

Third International Workshop On Petri Nets and Performance Models, 1989, Kyoto, Japan,

pp. 187–197. IEEE Computer Society Press, Los Alamitos, CA, USA. NewsletterInfo: 36.

J. Desel & W. Reisig (1998). Place/Transition Petri Nets. In Petri Nets, pp. 122–173.

H. V. Landeghem (2005). Inleiding tot Bedrijfs- en Productiebeheer. Universiteit Gent.

H. V. Landeghem (2006). Advanced Methods in Production & Logistics. Universiteit Gent.

H. V. Landeghem & C.-V. Bobeanu (2002). Formal Modelling of Supply Chain: An Incremental

Approach Using Petri Nets. In Verbraeck, A. and Krug, W. (Eds.), Simulation in Industry,

Proceedings of the 14th European Simulation Symposium, ESS’2002, pp. 323–327. SCS European

Publishing House.

C. A. Petri (1996). Nets, time and space. Theor. Comput. Sci., 153(1-2):3–48. ISSN 0304-3975.

Universita di Torino (2004). GreatSPN User’s Manual, 2.0.2 edition.

207

BIBLIOGRAPHY 208

E. M. Vila (2004). Supply Chain modelling: Optimization Versus Simulation. Master’s thesis,

Ghent University.

List of Figures

2.1 The complete supply chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4.1 The overall model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2 A supplier of level 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.3 Supplier of level 2 and 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.4 Supplier of level 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.5 Ordering and Delivery (Simple) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.6 Ordering and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.7 Simple Queue: Split of the order . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.8 Advanced ordering and delivery mechanism . . . . . . . . . . . . . . . . . . . . . . 23

5.1 Basic serial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.2 Basic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.3 High Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.4 60% source limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

7.1 A close-up of the Control Layer Model, suppliers of level 3 and 4 . . . . . . . . . . 34

1 The overall model Part I: Suppliers of Level 1 & 2 . . . . . . . . . . . . . . . . . . 38

2 The overall model Part II: Suppliers of Level 3 . . . . . . . . . . . . . . . . . . . . 39

3 The overall model Part III: Suppliers of Level 4 . . . . . . . . . . . . . . . . . . . . 40

209

List of Tables

2.1 Transport costs in cu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4.1 The transitions of a supplier of level 1 from Figure 4.2 . . . . . . . . . . . . . . . . 13

4.2 The places of a supplier of level 1 from Figure 4.2 . . . . . . . . . . . . . . . . . . . 14

4.3 The transitions of a supplier of level 2 or 3 from Figure 4.3 . . . . . . . . . . . . . 15

4.4 The places of a supplier of level 2 or 3 from Figure 4.3 . . . . . . . . . . . . . . . . 16

4.5 The transitions of a supplier of level 4 from Figure 4.4 . . . . . . . . . . . . . . . . 18

4.6 The places of a supplier of level 4 from Figure 4.4 . . . . . . . . . . . . . . . . . . . 19

4.7 The transitions of a simple queue from Figure 4.5 . . . . . . . . . . . . . . . . . . . 20

4.8 The places of a simple queue from Figure 4.5 . . . . . . . . . . . . . . . . . . . . . 20

6.1 Results for the Basic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.2 Results for the Basic Serial Model . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.3 Results for the High Reliability Model . . . . . . . . . . . . . . . . . . . . . . 32

6.4 Results for the 60% Source Limit . . . . . . . . . . . . . . . . . . . . . . . . . . 32

7.1 Results for the Control Layer Model . . . . . . . . . . . . . . . . . . . . . . . 35

1 Target Stocks for every Supplier EchelonSupplier for every experiment (Experi-

ments with different levels of uncertainty have the same values) . . . . . . . . . . . 42

210

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