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					Supply Chain Management
              Lecturing SS 2011




   helmut.merkel@prologue-asia-pacific.com




                                             1
Supply Chain Management
1. Why Supply Chain Management ?
   1.1. Learning Curve Concept
   1.2 Innovation
   1.3 Specialization, Globalization, Cooperation
2. Supply Chain Model
   SCOR, DCOR, CCOR of the International Supply Chain Council
3. Communication Architectures
   3.1   The Marathon Principle
   3.2   The Domino Principle
   3.3   The Shared Information Principle
   3.4   The Architecture behind
4. Design Principles
   4.1 “Vision” of the entire Process Chain
   4.2 Company overlapping Process Design (Vision of the entire Process Chain)
   4.3 Decision Making - Feedback Loops as basic Process Elements
   4.4 Self-Similarity – the Formula for Growth
   4.5 Shared Information Communication Architecture
   4.6.Central- or decentralized control of Supply Chains ?


                                                                            2
Supply Chain Management (2)


5. Implementation
   5.1. Top Down Approach
   5.2 Business Re-engeneering
   5.3 Aris Business Process Modelling
   5.4 Business Process Modelling and Project
        Management

6. Total Cost of Ownership
   6.1 How to calculate Implementation Projects ?
   6.2 Cost Curve Models
   6.3 Total Cost of Ownership – Approach




                                                    3
1. Why Supply Chain Management
 1.1. Learning Curve Concept
 1.2 Innovation
 1.3 Specialization, Globalization,
 Cooperation




                                      4
1.1 The Learning Curve Model

 In competition an individual company has to proof its advanced learning
 curve, which leads to competitive advantages, before at all to improved
 “Total Costs per Unit” (Gesamtstückkosten)

costs per unit
(c/u)
                                                  Unit price (1)



                            In a world with fixedUnit price (2)
                           terms, the first movers
                           are always on the save
                                    side


                                                                   Company B

                                      Company A



                          Output(0)                       Accumulated Volume   5
                                                                               5
1.1 The Learning Curve Model


costs per unit       The Learning Curve “Theory” was heavily
(c/u)                researched in the 1970’s – Economies of Scale,
                     Economies of Scope etc.

                     Division of Labor and all kind of specialization are
                     the reason to discuss related “Transaction costs”




                                                   Accumulated Output Volume




                                                                               6
in the real world, many things can be changed


                       Costs per      Transaction   Total Costs
                       Unit           Costs         per Unit

  Innovation


 Re-Engineering

 Specialization


 Globalization

 Horizontal
 Cooperation                                                    in
                                                             Theory !
  Vertical
  Cooperation              -
                                                                        7
1.3 Innovation is „Change“ - How does „Change“ work ?

    Product Innovation, Business Model Innovation, Process Innovation
    and Infrastructural Innovation impact each other

    Costs per unit (c/u) can be significantly impacted by“Innovation” –
    the learning curve model shows the details

    Innovation also triggers “Productivity” and “Structure” – i.e.
    productivity advantages and structural advantages



             Innovation
                                              Structural Change
  (Re-Engineering, Specialization,            (horizontal and vertical
  Globalization)                              Cooperation)




                                                                          8
1.2 Innovation is Change
    „the destructive power in the struggle for the better“




      “Innovation” in 1870 (Schumpeter):
      -   Introduction of a new product or a new quality of
          an existing product
      -   Implementation of a new production system in an
          industry (…to improve costs per unit (cpu))
      -    A new sales-/distribution channel
      -   Discovery of a new source for raw material or
          product components
      -   Implementation of a new organization




                                                              9
1.2 Innovation is „Change“ - How does „Change“ work ?

                                                            Business Modell
                                                              Business Process
                                                          Systems/Infrastructure



                        Strategy   Operations   Tactics


                             Business Model
                             Business Model



                            Business
                            Business       Process
                                           Process



                        Systems/Infrastructure
                        Systems/Infrastructure




                                                                                   10
1.2 Innovation is „Change“ - How does „Change“ work ?



                 Business
                  Model

                            Process             Process
                            Model               Model

                                                             Systems/
                                                          Infrastructure




                                                                           11
1.2 Innovation is „Change“ - How does „Change“ work ?




                                                        12
1.3 Innovation is „Change“ - How does „Change“ work ?


                                       Idea

                                Product Innovation
                        Idea
       Business Model
         Gesch äftsmodell                               Geschäftsmodell
                                                        Geschäftsmodell



       Process Model
        Gesch äftsprozesse                                            Idea
                                                        Geschäftsprozesse
                                                        Geschäftsprozesse



       Systems/Infrastructure
       Informationssysteme                            Informationssysteme
                                                      Informationssysteme

                                                               Process Innovation
                                 Geschäftsmodell
                                 Geschäftsmodell



Systems Innovation              Geschäftsprozesse
                                Geschäftsprozesse


                                           Idea
                                Informationssysteme
                                Informationssysteme
                                                                               13
1.3 Innovation reduces Costs per Unit

              Innovation
   c/u

                                          The assumption, c/u are shifted in parallel,
                                          implies the same process integration level.
                                          change of the transaction costs posssible




          Innovation lowers c/u




                                  Same Volume                       Accumulated Volume


                                                                                         14
1.3 Innovation is „Change“ - How does „Change“ work ?

      In economies with an increasing degree of specialization,
   communications and logistics transactions are rapidly growing.
  Infrastructure: ports, airports, highways telecommunication and
     education are becoming key success factors in an economy.



                               Additional elements,
                               additional relations




    The car manufacturers reduced their own share of production from
                    70% in 1970 to only 17 % in 2005

                                                                       15
  1.3 Specialization lowers the Costs per Unit

                    Specialization/Division of Labor (sharing of
                    work)
Cost per unit
c/u
                                             The assumption, c/u and transaction costs
                                             are shifted in parallel, implies the same
                                             process integration level.

                             1.



                       Supply Chain Management has to control
                                                    … but
                       Transaction Costs. The increaseincreases transaction costs
                Sepicialization reduces C/U
                                                          in
                                        2.       2.
                       “Transaction costs” must be lower then
                       the decrease of the “Costs per Unit”.1.



                                    Same output                       Accumulated Output


                                                                                           16
  1.3 Globalization lowers the Costs per Unit

                    Globalization
Cost per unit
c/u
                                             The assumption, c/u and transaction costs
                                             are shifted in parallel, implies the same
                                             process integration level.

                             1.



                       Supply Chain Management has to control
                                                    … but
                       Transaction Costs. The increaseincreases transaction costs
                Globalization reduces C/U
                                                          in
                                       2.        2.
                       “Transaction costs” must be lower then
                       the decrease of the “Costs per Unit”.1.



                                    Same output                       Accumulated Output


                                                                                           17
  1.3 Horizontal Cooperation lowers the Costs per Unit

                (horizontal) Cooperation/Concentration
Cost per unit
c/u
                                         The assumption, c/u and transaction costs
                                         are shifted in parallel, implies the same
                                         process integration level.

                         1.




                                              but
                 Supply Chain Management…hasincreases transaction costs
                                                  to control
                                          2.
                 Transaction Costs. The increase in
                 “Transaction costs” must be lower then1.
                 the decrease of the “Costs per Unit”.
                                           2.

                                      Cooperation reduces C/U

                                      Increasing Output           Accumulated Output


                                                                                       18
  1.3 Vertical Cooperation changes Transaction Costs

                   (vertical) Cooperation/Concentration
Cost per unit
c/u
                                         The assumption, c/u and transaction costs
                                         are shifted in parallel, imply a higher process
                                         integration level.

                           1.




                Supply Chain Management has…to controltransaction costs
                                                 but decreases
                Transaction Costs. The decrease in
                                             1.
                “Transaction costs” will lower the overall
                “Costs per Unit”.                              2.




                                 Same Output                        Accumulated Output


                                                                                           19
2. Supply Chain Model

The leading “Supply Chain Reference Model” from the international
Supply Chain Council, 2005-2007: SCOR; DCOR and CCOR




                         What is a Supply Chain ?
         A supply chain is a well organized Process to
         serve and supply a specific market, using
         global resources and global logistics
         infrastructure, IT systems, human skills etc.
         Competition in all markets force companies to
         develop time to market advantages, flexibility
         abilities as well as competitive “Costs per Unit”
  The Supply Chain Operations Reference Model (source: Supply Chain Council, 2005a)
         (Stückkosten).
                                                                                      20
 2. Supply Chain Model
   „Vision“ of the entire Process Chain                      Push: SCOR/TOGAF


                 Plan
                P1 Plan Supply Chain

                 P2 Plan Source        P3 Plan Make       P4 Plan Deliver       P5 Plan Return



                Source                         Make                         Deliver
                S1 Source Stocked             M1 Make-to-Stock              D1 Deliver Stocked




                                                                                                   Customers
                Product                                                     Product
    Suppliers




                S2 Source Make-               M2 Make-to-Order              D2 Deliver Make-
                To-Order Product                                            To-Order Product


                S3 Source Engineer-           M3 Engineer- To-              D3 Deliver Engineer-
                To-Order Product              Order                         To-Order Product




                           Source Return                               Deliver Return
                           SR1 Return Defective                        DR1 Return Defective
                               Product                                     Product
                           SR2 Return MRO Product                      DR2 Return MRO Product
                           SR3 Return Excess Product                   DR3 Return Excess Product




The Supply Chain Operations Reference Model (source: Supply Chain Council, 2005a)
                                                                                                               21
2. Supply Chain Model




                        22
2. Supply Chain Model




                        23
2. Supply Chain Model




                        24
2. Supply Chain Model




                        25
      2. Supply Chain Model

 1.     Design Process
 2.     Product Development
 3.     Sampling
                                      Focus: Product Management
 4.     Order placement
 5.     Inline Production
 6.     Packaging
 7.     Sourcing Overlapping processes not covered !!!
                   Supplier/Vendor Management
 8.     Consolidation               Focus:
                       Quality ManagementBuying, Sourcing
 9. Quality Checks Risc Management (ISO 28000)
 10. Booking             Finance missing
 11. Document Handling
 12. Transportation
 13. Importmanagement
 14. Haulage                         Focus: Logistics, Supply Chain Management
 15. Distribution Centre/Crossdock
 16. Distribution
 17. Storelogistics
26
3. Communication Architectures
   3.1 Marathon Principle
   3.2 Domino Principle
   3.3 Shared Information Principle
   3.4 The Architecture behind




                                      27
3. Communication Architectures

  What is a Supply Chain ?
  A supply chain is a well organized Process to serve and
  supply a specific market, using global resources and global
  logistics infrastructure, IT systems, human skills etc.
  Competition in all markets force companies to develop
  time to market advantages as well as “cost per unit”
  (Stückkosten) advantages.
  The key to gain time and cost advantages is the Process
  Design of a Supply Chain. The key of Process Design is the
  “Communication Architecture”. The Communication
  Achitecture describes how regular communication between
  hundreds of participants of a Supply Chain is organized.
  How are “order information” forwarded ? Who has actual
  information ? How are Exceptions (Alerts) organized etc. ?
                                                                28
3. Communication Architectures
3.1 Marathon Principle – Trigger concept   Phidippides or Pheidippides (or
                                           Philippides) 570 bC., when the
                                           Persians (Darius I) landed at
                                           Marathon, was send by the
                                           Athenians to Sparta as fast as
                                           possible he can, to ask for help. The
                                           Spartans said that they will help
                                           after the moon was full (probably
                                           in order to let the Athenians alone
                                           with the Persians and not only for
                                           religious reasons). Phidippides
                                           came back running the 147 miles
                                           distance with the disappointing
                                           news for the Athenians.
                                           Phidippides then returned to
                                           Marathon in time to fight in the
                                           battle. He was ordered to run to
                                           Athens to bring the news of victory.
                                           In one week he had to run more
                                           than 300 miles.
                                                                           29
3. Communication Architectures
3.2 The Domino- or Chinese Wall Principle

                                            221 bC, Qin Shi Huang
                                            completed the first part
                                            of the Chinese wall, to
                                            protect “Zhong Guo”
                                            against the Barbarians.
                                            Whenever the wall was
                                            attacked, a fire was set
                                            up on the nearest watch
                                            tower – and all other
                                            watch towers followed to
                                            do the same.
                                            So the message of an
                                            attack was much faster
                                            then a messenger.




                                                              30
    3.2 The Domino Principle
Even in 2010, many companies organize their process after the „Domino Principle“


                        Order
                                                            Order
    Manufacturer    Order-Status         Agent                              Product Mgmt
                                                      Confirmation




                           „Pier to Pier” Information flow
                                  (Domino Principle)




                          Arrival Date                          Shippment
    Consolidation                          Distribution           Advice       Store
        Hub                                Centre


   31
3. 2 The Domino Principle
Even in 2010, many companies organize their BPR after the „Domino Principle“
Buying                               Order              Label

Agent                                           Order
                                                                                        Confec-
Vendor                                                    Order           Production
                                                                                         tion

Manufacturer                                                      Order   Production

                                                                                                                          Docu-
Forwarding Agent                                                                       Haulage                            ments

Carrier                                                                                      Shipment

                                                                                                                         Fax
Holage Agent                                                                                            Haulage

                               Price competition,
QC                                                                                                                QC
                               Time Pressure,
Cross Docking                                                                                                          Distribution
                               Need for Flexibility
Store                          … the Domino Principle is obsolete
Sales     2.
          2.   Vertikalisierung und Versorgungsketten
               Logistik (Supply Chain Management)



32
3.3 Shared Information Principle



                                   This principle was
                                   developed by “nature”.
                                   All geese watch the top
                                   goose ahead and not
                                   their direct predecessor.

                                   What would happen, if
                                   they all follow only their
                                   direct predecessor ?




                                                         33
 3.3 The Shared Information Principle

        IT-based Information         Information-      Control-
        In Advance                                 System                 Database


                                        Order,
        Product Managmt        Labels, Pkcklist,
                                     QC
                                                                                     Information in advance
        Manufacturer                      Production                                 (Shared Information
                                                                                     Services) saves time, costs
        Pre-Supplier                                                                 and increases flexibility of all
                                   Production
                                                                                     involved parties

                                                            Transpor-
        Forwarding Agent                                      tation


        Carrier                                                   Shippment



        Transportation                                                  Haulage
        Agent                                                                                       ... Same process
        Distribution Centre                                                       Distribution
                                                                                                    structure for QC,
                                                                                                    AZO etc.

        Store                                                                              Sales
34
 3.3 The Shared Information Principle

     Paradigm Shift: The Shared Information Principle

     Manufacturer                       Agent           Buyer



                      QC



     Consolidation
                                         WWW
                                        Database




                                    Bypass

      Carrier                      Conditioner           Store
                                 Cross Docking

35
3. Communication Architectures



       3.4 The Architecture behind
            3.4.1 Feed back loop Model, Feed forward Model, Growth
                   Model – Definition of “System, Structure, Behavior
                   (Performance), Process”, Second order System
           3.4.2 Connecting “Feed back loop Models” as a Domino Chain
           3.4.3 Connecting “Feed back loop Models” with a Shared
                  Information Hub
           3.4.4 Exchanging Capacity Information
           3.4.5 Matching “goals”
           3.4.6 Merging loops to avoid redundant functions
           3.4.7 Forced self-similarity




                                                                        36
 3.4 The Architecture behind
     3.4.1 Feed-back-loop Model (first order, linear system)


           Plan: replenish bucket until line (Ziel)



                        Plan

            Control
                            Feed Back



                      Manage            Report
                                        “gap”



                   Watch process realtime and
Open water tap     measure “gap” (target-level)

                                                               37
   3.4 The Architecture behind
        3.4.1 Feed-back-loop Model (first order, linear system)

                                                                     Manage
                             Plan
                                                   Control

            Control
                                   Feed Back
                                                                    Feed Back

                       Manage                        Plan



                      Ressourcen
- First Order Control Loop
                                                  Plan
                                    Control                          Target
                                                                  Feed Back

                                               Manage


                                                                                38
3.4 The Architecture behind

        System: Set of elements and relations
        S :=      e1, e2, e3, … en; r1, r2, r3, … rn, r11, r12, rnm

        The “e’s” are elements, the “r’s” are relations. Relations are connecting
        elements. Elements perform “Functions”. Relations can be information-,
        energy-, materials- moneyflow etc. The Structure of a system is a frozen
        picture of all elements and connections in a one moment. Behavior of a
        system is the measurable performance of a system during a period of time.
        All Systems serve a purpose – they are following a target. A target can
        have several sub-targets. In nature the central target of a system is
        survival, and improving living conditions. Living conditions can only be
        improved, if the usage of the systems resources is efficient.
        To follow a target, systems use the Functions of their elements. Using the
        functions, is using up limited resources. The limitation of resources
        determines the capacity of an element.
        In order to reach a specific target (sub-target), the usage of the functions has
        to be coordinated. Coordination means, to organize the sequential or parallel
        use of all functions (i.e. resources) efficiently.
        Efficient means: to reach a given target with a minimum use of resources;
        or: to reach the best level (maximum) of a target with given resources.
                                                                                    39
3.4 The Architecture behind
        Performance of a system is the measurable behavior of a system during a
        period of time. Performance has to be defined in relation to the given
        targets. If the target is a quantity, for example: “efficient production of
        1000 units in one month”, an adequate performance measuring would focus
        on the progress of production during the period of time and on the cost
        level to measure “efficiency”.
        Performance measurement can be a complex task, because sub-targets have
        to be measured and the functions of many elements have to be observed.
        Therefore we use so called: KPI Systems. An intelligent set of all Key
        Performance Indicators.

        Process is an expression, which is widely used in all areas of Science and
        Practice. We define “Process” as “System”. A Process is a System ….


        Live systems in Nature have five basic process patterns:

        1.   All processes to build up a living infrastructure
        2.   All processes to maintain survival levels
        3.   All processes to expand living conditions for growing populataions
        4.   All processes to overcome emergency (Exceptions) situations
        5.   All processes to recover and come back to normal survival levels
                                                                                     40
3.4 The Architecture behind

      „Feed Forward Model“ (Steuerung)

         Decision: 1(l)/0.1 (l/sec) =
         10 sec. water flow

                                                                     Plan
         Control

                                        Check pressure and
                                        capacity of the water tap


                                          Plan: 1(l)/0,1 (l/sec)
                                          10 seconds water flow

               Manage
                                                                     Feed Back,
                                          Target: Fill the bucket    after the entire
                                          with 1 l water !           process is
               Manage                     There is no water in the   completed
                                          bucket now.



                                                                                        41
3.4 The Architecture behind

      „Growth“




                     Das mathematische Modell eines linearen, positiven Regelkreises kann als
                 Exponentialfunktion entwickelt werden:
                 (31) level (t) = e r
                 e selbst entwickelt sich nach der Gleichung
                                           n
                                 1
                 (32)   limn  1 + n 
                                      
                                               =e
                 Diese Darstellung zeigt, daß sehr viele Rückkopplungen nötig sind, bis exponentielles
                 Wachstum erreicht wird.

                                                                                                         42
3.4 The Architecture behind
      Second „order“ system


                            Goal                                             Goal

              A Supply Chain is at least a “second order system” or a
                    System
                                  Re gle r
                                                                  System
                                                                              Re gle r

              “higher order system”. The self similar loops represent
                                  Rückwärts-
                                  übertragungs-
                                                                              Rückwärts-
                                                                              übertragungs-
                                                                              funktion h2
              legal independent companies, with intedpendent
                                  funktion h2

                  Stellgröße                      Regelgröße    Stellgröße                      Regelgröße
              goals/targets and non transparent capacities for the
                                  Re ge lstre cke                             Re ge lstre cke
                                                     Input xe                 Vorwärts-
              participants. From a birds perspective, there are
       Input xe

                     +
                                  Vorwärts-
                                  übertragungs-
                                  funktion h1                      +
                                                                              übertragungs-
                                                                              funktion h1                Output xa
                                                           Output xa
              multiple redundant functions (like planning/decision
              making). The communication between the different
              loops is1 “Domino like” – Every loop puts a Purchase
                     PAGE EINFACHES BEISPIEL FüR EIN SYSTEM ZWEITER ORDNUNG 04/18/93 18:54
                     L       L2.K=L2.J+DT*R2.JK                      L2:=Zustandsgröße2 (Level)
              Order (PO) to the predecessor loop. The predecessor
                     R       R2.KL=L1.K/D                            R2:=Flußgröße 2 (Rate)
                     L       L1.K=L1.J+DT*(R1.JK-R2.JK)              L1:=Zustandsgröße 1
              is delivering what is requested in the PO, according to
                     R       R1.KL=(ZIEL-L2.K)/AT                    R1:=Flußgröße 1
                     C       D=2                                     D:=Verzögerungskonstante
              the terms of the PO. According to the terms, the
                     C       AT=1                                    AT:=Verzögerungskonstante
                     C       ZIEL=10
              paymentL1=5 arranged after theZiel:=Zielzustand für L1
                     N         is                                     same terms.
                                                                     L1=5:=Anfangswert
                  N    L2=2                             L2=2:=Anfangswert für L2
                  SAVE L1,L2,R1,R2,ZIEL                 Speicher f. Variable res.
                  SPEC DT=0.25/LENGTH=30/SAVPER=1       Systemanweisungen




                                                                                                                     43
 3.4 The Architecture behind
      3.4.2 Connecting “Feed back loop Models” as a Domino Chain
A Value Chain as higher order system with Domino connected decision
loops is not efficient … The Inefficiency is Delta “R, Ressources” and
Detlat “T, Time”
- Higher Order Control
  Loop
                                      This (delayed) behavior results from the design
                                      of the “communication architecture”


                    R What    are the “natural                                 Target


                         reasons” of R and T
                               The “mathematics” behind is a (linear) differential
                               equation model higher world
                         delays in the ofrealorder
                                                                                Time




                                                       T
                                                                                        44
3.4 The Architecture behind
    3.4.2 Connecting “Feed back loop Models” as a Domino Chain


                      2.                                                                2.                                                          2.
                      Goal                                                             Goal                                                         Goal

               System                                                         System                                                         System
                           Re gle r                                                       Re gle r                                                       Re gle r

                           Rückwärts-                                                     Rückwärts-                                                     Rückwärts-
                           übertragungs-                                                  übertragungs-                                                  übertragungs-
                           funktion h2                                                    funktion h2                                                    funktion h2

              Stellgröße                     Regelgröße                      Stellgröße                     Regelgröße                      Stellgröße                     Regelgröße
                           Re ge lstre cke                                                Re ge lstre cke                                                Re ge lstre cke
   Input xe                Vorwärts-                              Input xe                Vorwärts-                              Input xe                Vorwärts-
                           übertragungs-                                                  übertragungs-                                                  übertragungs-
                 +         funktion h1                                          +         funktion h1                                          +         funktion h1

                                             1.                                                                                                                          1.
                                                      Output xa                                                      Output xa                                                      Output xa


                                                                                                            1.

 The reasons for „Inefficiency“ in Domino connected Supply Chains are:


- No exchange of “capacity” information/restrictions (walking bottle neck…) 1.
- No procedure to match “goals” 2.
- No exchange of information about critical process situations (exception management)
- Redundant functions
- No forced self-similarity

                                                                                                                                                                                                45
3.4 The Architecture behind
     3.4.2 Connecting “Feed back loop Models” as a Domino Chain




                               Insufficient Communication

 Non synchronized capacity of
 Ressources; bottle-necks (Oliver Wight)
                                                     MRP, MRP II, ERP, SC(R)M

 Non synchronized „goals or targets“ –               Reduce Complexity – merge Loops
          („Bullwhip-Effekt“)
 Redundancy of Functions

 Lacking control of „critical“                       Consequent closed-loop Architecture
 Developments – missing feedback links               self-similarity
 Quality of Information                              Standardization


                          Shared Information – Instead of Domino Architecture




                                                                                       46
3.4 The Architecture behind
       3.4.3 Connecting “Feed back loop Models” with a Shared
             Information Hub


                                                             … only the “Shared
                                                         Information” Architecture
                                                             allows an efficient
                                                                 operation


                                                                                      Shared
                                                                                    Information
                                                                                        DB


              System                                                         System                                                         System
                          Re gle r                                                       Re gle r                                                       Re gle r

                          Rückwärts-                                                     Rückwärts-                                                     Rückwärts-
                          übertragungs-                                                  übertragungs-                                                  übertragungs-
                          funktion h2                                                    funktion h2                                                    funktion h2

             Stellgröße                     Regelgröße                      Stellgröße                     Regelgröße                      Stellgröße                     Regelgröße
                          Re ge lstre cke                                                Re ge lstre cke                                                Re ge lstre cke
  Input xe                Vorwärts-                              Input xe                Vorwärts-                              Input xe                Vorwärts-
                          übertragungs-                                                  übertragungs-                                                  übertragungs-
                +         funktion h1                Output xa                 +         funktion h1                Output xa                 +         funktion h1                Output xa




                                                                                                                                                                                               47
3.4 The Architecture behind
    3.4.3 Connecting “Feed back loop Models” with a Shared
          Information Hub




                                                             48
3.4 The Architecture behind
        3.4.6 Merging loops to avoid redundant functions




                                                                                          Goal


             System                                                         System                                                         System
                         Re gle r                                                       Re gle r                                                       Re gle r

                         Rückwärts-                                                     Rückwärts-                                                     Rückwärts-
                         übertragungs-                                                  übertragungs-                                                  übertragungs-
                         funktion h2                                                    funktion h2                                                    funktion h2

            Stellgröße                     Regelgröße                      Stellgröße                     Regelgröße                      Stellgröße                     Regelgröße
                         Re ge lstre cke                                                Re ge lstre cke                                                Re ge lstre cke
 Input xe                Vorwärts-                              Input xe                Vorwärts-                              Input xe                Vorwärts-
                         übertragungs-                                                  übertragungs-                                                  übertragungs-
               +         funktion h1                Output xa                 +         funktion h1                Output xa                 +         funktion h1                Output xa




                   In Supply Chains the successors and predecessors can agree to
                   merge multiple functions to avoid redundancy …


                                                                                                                                                                                              49
   3.4 The Architecture behind
           3.4.7 Forced self similarity



    The Process Design is following the “control loop” principles, which is supported by
    adequate Systems infrastructure (IT-Systems, Logistics)




                                                                   Understand, Plan

                                                    Control                                 Feed Back


Strategy   Operations    Tactics
                                                              Buy/Source, Move, Sell, Pay

       Business Modell
        Business Process
    Systems/Infrastructure




                                                                                                   50
3.4 The Architecture behind
    3.4.7 Forced self similarity




                                Self-Similarity is a key
                               principle in nature and
                             allows a structure to grow
                               systematically i.e. with
                                  high producitivity




                                                           51
3.4 The Architecture behind
    3.4.7 Forced self similarity


 Business Models/Process Models are decision process loops with high level
 Self-Similarity …




                                                   Plan
                                   Control                    Feed Back


                                                 Manage




                                                                             52
4. Design Principles

   4.1 “Design Principles” as elements of an SCM Architecture
   4.2 “Vision” of the entire Process Chain
   4.3 Company overlapping Process Design (Vision of the entire
       Process Chain
   4.4 Decision Making - Feedback Loops as basic
       Process Elements
   4.5 Self-Similarity – the Formula for Growth
   4.6 Shared Information Communication Architecture
   4.7.Central- or decentralized control of Supply Chains ?




                                                                  53
4. Design Principles
4.1 “Design Principles” as elements of an SCM Architecture




 Vitruvius, 30BC collected all knowledge of Greek and Roman architecture in 10
 volumes. The word “civil engineer” is developed from his works. The word
 “module” can be found there. Unfortunately there is not such a fundamental
 work: “How to construct a Supply Chain”

                                                                                 54
4. Design Principles
4.1 “Design Principles” as elements of an SCM Architecture
                                   An “Architecture” is a design plan. In this
                                   design plan, the Architect is figuring out his idea,
                                   how to carry out the order.

                                   The order he is requested to carry out can be a
                                   school building, a temple or such a nice arch.
                                   The purpose of the building determines the
                                   process how to use the building or the Arch

                                   The Architect has to study the purpose to
                                   define the needed functions (… of the
                                   structural elements) of the intended building or
                                   object. In the past functions (i.e. functions of
                                   the structural elements) were used to identify
                                   the tasks. Today we also study the process in
                                   parallel, which is using the structural elements
                                   (i.e. the performance or behavior of a
                                   process).

                                   For the needed functions the Architect has to
                                   know and to consider for which capacity
                                   and/or size dimensions his design has to go.
                                   To seize the capacity and/or dimensions,
                                                                                     55
4. Design Principles
4.1 “Design Principles” as elements of an SCM Architecture
                                        the Architect has to simulate all overlaying
                                        processes, in which the functions are used,
                                        in order to identify bottlenecks.

                                        As a lesson from the past, today we develop
                                        a picture of the needed and possible
                                        processes in parallel, to verify the functions
                                        and even to identify missing functions (i.e.
                                        structural elements).

                                        All these details are put together in
                                        construction plan which is the mathematial
                                        proof of stability under even heavy process
                                        performance of the planned functions.
                                        Furthermore he has to study the location
                                        and the environment where the building will
                                        be located.

                                        The Architect will complete a visual draft of
                                        the building/object as a first step, showing the
                                        figuration/shape which serves the purpose
                                        and showing, how the functions can be used
                                        in all overlaying processes.
                                                                                   56
4. Design Principles
4.1 “Design Principles” as elements of an SCM Architecture
                                        Today and centuries ago, the design plans for
                                        the same purpose would be completely
                                        different. The use of light, energy, water,
                                        heating, aircondition, the use of materials
                                        (stone, wood, iron, artificial materials etc. are
                                        completely different. Security requirements
                                        (emergency exits f.e.), fire prevention,
                                        service and disposal aspects, washrooms,
                                        lifts etc. are also completely different.

                                        Every period of time had its own design
                                        principles which reflect the art expression
                                        and (architectural) knowledge of the sciences
                                        of the related period.

                                        Even for hundreds of centuries, the
                                        architecture of a building can be traced back.
                                        All details, even mathematics of the
                                        construction plans are still known.

                                        We also still know the project and execution
                                        plans of famous buildings. For sure there
                                        also many secrets, we only re-discover step
                                        by step.                                  57
4. Design Principles
                                        The architecture for
4.1 “Design Principles” as elements of an SCM Architecture a global supply chain is
                                        not obvious – there is no “documented”
                                        history. – IT Technology, which is driving
                                        the Design principles developed
                                        tremendously within the last 50 years.
                                        There are also no proven project plans,
                                        which could help to implement a global
                                        supply chain.
                                        Therefore we have to think about design
                                        principles of Supply Chains for the
                                        current time. In analogy, we define
                                        “Design Principles”:

                                        1. Integrity and Vision of an entire
                                           Supply Chain (Process)
                                        2. Company overlapping processes
                                        3. Definition of the structural Elements
                                        4. Self Similar Organization of the
                                           entire Supply Chain
                                        5. Shared Information as
                                           Communication Architecture
                                        6. Centralized/decentralized
                                           management of the Supply Chain


                                                                                     58
4.2 Integrity and „Vision“ of the entire Process Chain
   4.2.1   MRP (Materials Requirement Planning)
   4.2.2   MRP II (Manufcaturing Ressource Planning)
   4.2.3   ERP (Enterprise Ressource Planning)
   4.2.3   SCRM (Supply Chain Ressource Management)




                                                         59
4.2 Integrity and „Vision“ of the entire Process Chain
   (MRP – Materials requirement Planning)




                                           - No Feedbacks,
                                           - No Ressource plan




                                                                 60
4.2 Integrity and „Vision“ of the entire Process Chain
   (MRP – Materials requirement Planning - Phase II)




                                                     No Resource Plan




                                                                        61
4.2 Integrity and „Vision“ of the entire Process Chain
   (MRP – Materials requirement Planning - Phase III)




Unternehmens-
Ressourcen




                                                         62
4.2 Integrity and „Vision“ of the entire Process Chain (MRP II / ERP –
    Manufacturing Ressource Planning/Enterprise Ressource Planning
    ERP)



                                       Simulation
Unternehmens-
Ressourcen




                                                                         63
4.2 Integrity and „Vision“ of the entire Process Chain
   (MRP II/ERP – Manufacturing & Enterprise Ressource Planning)




                                                                  64
4.2 Integrity and „Vision“ of the entire Process Chain
   (SCRM - Supply Chain Ressource Management )




                                            Ressources
                                            Guidelines
                                            Manuals

                                                                                      Shared
                                                                                                               Order Network
                                                                                    Information
                                                                                        DB


              System                                                         System                                                         System
                          Re gle r                                                       Re gle r                                                       Re gle r

                          Rückwärts-                                                     Rückwärts-                                                     Rückwärts-
                          übertragungs-                                                  übertragungs-                                                  übertragungs-
                          funktion h2                                                    funktion h2                                                    funktion h2

             Stellgröße                     Regelgröße                      Stellgröße                     Regelgröße                      Stellgröße                     Regelgröße
                          Re ge lstre cke                                                Re ge lstre cke                                                Re ge lstre cke
  Input xe                Vorwärts-                              Input xe                Vorwärts-                              Input xe                Vorwärts-
                          übertragungs-                                                  übertragungs-                                                  übertragungs-
                +         funktion h1                Output xa                 +         funktion h1                Output xa                 +         funktion h1                Output xa




                                                                                                                                                                                               65
     4.2 Integrity and „Vision“ of the entire Process Chain: The entire Process View
                                                             of SAP ERP 2.0
 1.     Design Process
 2.     Product Development
 3.     Sampling
                                         Focus: Product Management
 4.     Order placement
 5.     Inline Production
 6.     Packaging
 7.     Sourcing      Overlapping processes not covered !!!
                         Supplier/Vendor Management
 8.     Consolidation                        Focus:
                              Quality Management Buying, Sourcing
 9.     Quality Checks   Risc Management (ISO 28000)
 10. Booking
 11. Document Handling
 12. Transportation
 13. Importmanagement
 14. Haulage                            Focus: Logistics, Supply Chain Management
 15. Distribution Centre/Crossdock
 16. Distribution
 17. Storelogistics
66
4.2 Integrity and „Vision“ of the entire Process Chain: Retail Loop

                                                                                                      1
                                                                              Strategic Marketing
                                                                                 Demand Plan
                                                                                   Sales Plan


                        4                                            3                                2
     Manufacturers,
        Vendor                              Strategic Buying                      Buying Plan
       Vendors



                            5                                        0                                4
                                                                                 Procurement,
     Consolidation                                                                 Sourcing,
          SCM                                        data
                                              Master Data                     Purchase Order (PO)
    Sea-/Air, Haulage                                                          Direct Distribution
                                                                                  Management


                            6                                        8                                7
     Cross Docking
     Warehousing                             Merchandise
                                           Merchandise Flow
                                                                                     Sales
                                                                              Stores – Sale (POS)
      Distribution                           Flow Control
                                                Control


                                Administrations Process (HR, Finance etc.)
                                Administrations Process (HR, Finance, etc.)


                                                                                                     67
     4.2 Integrity and Vision of the entire Process: Company overlapping
     Process Design – highly integrated

                                                 Web-Portals
                                                                  G
                                                               Understand, Plan
Supply Chain Mgmt
                                                 Data Warehouse/Mining
                             B                                                                                          D
         Manufacturers
                                                                                                          E
                                 Control Buy,
                                    Plan,
                                                                  CRM                      Admin Feed Back
                                     Control




                                                                                                              POS-Systese
                                                                                        (HR, Finance)
                             B




                                                                                                                Store&
              Logistcs
                                 A
              Provider
                                                     Merchandise Mgmt. System
                                                                                       C
                                        Org-
                                                    Merchandise            Inventory           Business
                                     Structure                            Management           Partners
                                                     Structure
                                 Manage: Buy/Source, Move, Sell, Pay
  Receiving




              Distribution             Purchase                 Sales,                 Price-, Markdown-
                 Centre                 Order                Stock-, Rack                Cross Marging
                                      Management            Supply Mgmt                      Control


                                                                      F
                                                                                                                 68
4.3 Integrity and Vision of the entire Process: Company overlapping
Process Design – highly integrated


     Company 1                      Company 2                            Company n



   Business Model                Business Model                        Business Model




          Business
      Geschäfts-                 Business
                             Geschäfts-                   Geschäfts-
                                                        Business
       prozesse
           Process Company overlapping Business Process Process
                                 Process
                              prozesse                     prozesse



      Informations-
    Informations-              Informations-
                            Informations-                Informations-
                                                            Informations-
         systeme Company overlapping Systems (IT-/Logistics)systeme
                                  systeme
       systeme                  systeme                        systeme

      Integrated process links need standardized, integrated systems links
      Integrated systems links have impacts on business models

                                                                                        69
       4.4 Structual Elements; Decision Making Process: Feed-back-loop Model


                             Plan

            Control
                                   Feed Back


                       Manage



                      Ressourcen
- First Order Control Loop
                                                Plan
                                    Control                      Target
                                                              Feed Back

                                               Manage


                                                                               70
4.5 Self-Similarity




                         Self-Similarity is a key
                        principle in nature and
                      allows a structure to grow
                        systematically i.e. with
                           high producitivity




                                                    71
4.5 Self Similarity



  Business Models/Process Models are decision process loops with high level
  Self-Similarity …




                                                    Plan
                                Control                        Feed Back


                                                  Manage




                                                                              72
     4.6 Paradigm Shift: The Shared Information Communication Architecture

                        Shared Information Services


       Manufacturer                 Agent                      Buyer



                       QC



       Consolidation
                                     WWW
                                    Database




                                   Bypass

        Carrier                   Conditioner                   Store
                                Cross Docking

73
 4.7 Central- or decentralized control of Supply Chains ?
     Summary: Centralized and decentralized control/behavior


… Elements of an Supply Chain Management rule-set (Regelwerk), which
  allows cooperative and individual behavior at the same time
1. All process participants follow their individual business ideas, business models and
    process models such as MRP, MRPII, ERP etc.
2. All process participants acknowledge instructions from their predecessors in the
    process chain (domino) by “orders/contracts” – which are legally binding.
3. One Party (retailer or brand) normally takes initiative to use its power to “lead” the
    whole supply chain by instructions or sets of rules (Ordnungsinformationen).
4. A company overlapping communication infrastructure (Shared Information) is
    established, all process participants are asked to
    - share information about targets
    - share information about actual stati,
    - eliminate redundant functions,
    - match ressources and capacities to avoid bottle necks
5. All process participants accept the rule of immediate response and update about
    their own activities with accurate information to the Shared Information Hub
5. Implementation
  5.1. Top Down Approach
  5.2 Business Re-engeneering
  5.3 Aris Business Process Modelling
  5.4 Business Process Modelling and Project
       Management




                                               75
5. How is „Change“ going to be implemented in Companies



Case-Study: Company A & B decide to implement a new Business Model. To
implement the new Business Model, the companies decide to share resources:
A new Process Model needs to be implemented. The needed Infrastructure will
be shared.




        Company A                                         Company B




                                                                              76
5. How is „Change“ going to be implemented in Companies


     Company A & B decide to implement a new Business Model. To implement
     the new Business Model, the companies decide to share resources: A new
     Process Model needs to be implemented. The needed Infrastructure will be
     shared.




        Company A                                           Company B

                                    1.
                           A Project Team as a
                    temporary organization will organize/
                          Implement “Change”
                                                                                77
5. How is „Change“ going to be implemented in Companies

Company A & B decide to implement a new Business Model. To implement
the new Business Model, the companies decide to share resources: A new
Process Model needs to be implemented. The needed Infrastructure will be
shared.




         Company A                                           Company B

                     The Project Team will design the new
                     Business Process along the six Design
            2.          Principles: Vision of the entire
                       Process, Company overlapping….

                                                                           78
 5. How is „Change“ going to be implemented in Companies

Implementation Model

                                                           buttom up:
   3. Design & Implementation   Change
                                                           Workshop or
        follows a top down
                                                           Prototype
        Approach
                                                           Approach




                                                                         79
    5. How is „Change“ going to be implemented in Companies


Implementation Model          BPR Design & Implementation             Project Management




                                            Lösungs-
                                            (5% GA)
                                             Analyse
                                                           Strategy        Operations         Tactics


                                                                      Team, Role, Objectives




                                           (10-15%
                                            Konzept
                                             Grob-
                                             GA)
                                                                  Expected Results (Documents),
                                                                  As-Is Results, Ressources, Time




                                           (10-15%
                                            Konzept
                                             Fein-
                                             GA)
                                                                      Team, Role, Objectives
                                                                  Expected Results (Documents),




                                           (30-40%
                                            Sierung
                                             Reali-
                                              GA)
                                                                  As-Is Results, Ressources, Time




                                           (25% GA)
                                            Tierung

                                             Imple-
                                              men-
                                                                      Team, Role, Objectives
                                                                  Expected Results (Documents),
                                           Wartung                As-Is Results, Ressources, Time
                                           System,
                                           (5-10%)


                                             Lfd.


                                       GA: Gesamtaufwand



                          4. Design & Implementation follows
                            a “six” phases learning process
                                                                                                    80
  5. How is „Change“ going to be implemented in Companies

5. Many different BPR Design&Implementation (Re-Engineering) Models
                                                                                         Improve
                                                                        Implement        continuously
                                                       Design To-       Reengineer
                                      Map &            Be                                 Initiate
                      Prepare for                                       ed Process
                                      Analyze As-      Processes                           ongoing
                      BPR             Is Process                         Evolve           measure-
                                                        Benchmark        implementati     ment
                       Build cross    Create           processes        on plan         Review
                        functional      activity        Design To-      Prototype        performance
                        team            models           Be               and simulate     against
                       Identify       Create           processes        transition       target
                        customer        process         Validate To-     plans           Improve
                        driven          models           Be              Initiate         process
                        objective      Simulate and     processes        training         continuously
                       Develop         perform ABC     Perform          programs
                        strategic      Identify         trade-off       Implement
                        purpose         disconnects      analysis         transition
                                        and value                         plan
                                        adding
                                        processes




        BPR: The Surest Way to the Top (source: Muthu, Whitman and Cheragi, 1999, Figure 1)




                                                                                                          GA: Gesamtaufwand
                                 Grob-        Fein-          Reali-        Imple-          Lfd.
                 Lösungs-
                                Konzept      Konzept        Sierung         men-         System,
                  Analyse
                               (10-15%      (10-15%         (30-40%       Tierung        Wartung
                 (5% GA)
                                 GA)          GA)             GA)        (25% GA)        (5-10%)




                                                                                                                              81
6.2 Cost Curve Models




                        82
6.2 Cost Curve Models




                        83
5. How is „Change“ going to be implemented in Companies

BPR Re-Engineering
                                           Strategic Business Process
                                         Analysis and Target Conceptual
                                                     Design


                                                        Require-
                                                      ments Definition                    ARIS House

                                                    Design Specification
                                                 Implementation Description


                                 Requirements          Requirements           Requirements
                                   Definition            Definition             Definition
                                   Design                 Design                 Design
                                 Specification          Specification          Specification
                                Implementation         Implementation         Implementation
                                  Description            Description            Description
                                    Data                        Control         Function
                                                  Requirements Definition
                                                    Design Specification
                                                 Implementation Description

                                                          Output




                                                Information and
                                            Communication Technology




            The ARIS House of Business Engineering (source: Scheer, 1999b p 56 Figure 24)
                                                                                                       84
                 2000          2001           2002            2003          2004          2005        2006


          WPDL 1.0           Wf-XML 1.0                                      Wf-XML 2.0
                                                                             1.0
           WfMC                                                               Uses      Mapping



                                                              OASIS      ASAP             UDDI 3.0

                     IBM                IBM, Microsoft, BEA
                     WSFL                  BPEL4WS1.0          BPEL4WS 1.1         WS-BPEL 2.0       WS-BPEL

                                                               ebXML BPSS          ebXML BPSS         Mapping
                Microsoft                                         1.01                 1.1
                 XLANG

                                                              W3C     WSCL
                         BPMI
                                           Interface subset
                             BPML                                WSCI 1.0              WS-CDL


                            BPMN -0.9                                          BPMN 1.1              BPMN 1.1



          OMG
                                            UML 1.4                  UML 1.5                UML 2.0




Business Process Modelling (BPM)
Source: Zhou, Vera

                                                                                                                85
6.   Total Cost of Ownership
     6.1 How to calculate Costs of
     Implementation (COI) ?
     6.2 Cost Curve Models
     6.3 Total Cost of Ownership (TCO) –
     Approach




                                           86
6.1 How to calculate Costs of Implementation (COI)?




                                                      87
6.1 How to calculate Costs of Implementation (COI)?




                                                      88
6.1 How to calculate Costs of Implementation (COI)?




                                                      89
6.1 How to calculate Costs of Implementation ?




                                                 90
6.1 How to calculate Costs of Implementation (COI)?




                                                      91
6.2 Cost of Implementation (COI)




                                   92
6.2 Cost Curve Models




                        93
6.3 Total Cost of Ownership – Approach




                                         94
6.3 Total Cost of Ownership – Approach




                                         95
       Backup
Supply-Chain Management
      Systemtheorie




                          96
Beispiel für ein zielsuchendes „System“




-Struktur,
-Beziehungen,
-Prozess,
-Verhalten




                                          97
Relationen (Beziehungs) -Matrix



von - (e1)   (e2)   (e3)   (e4)   (e5)   (e6)   (e7)   (e8)   (e9)   (e10)
an
(e1)    -    r1,2    r1,3   -      -      -      -      -      -     r1,10
(e2) r2,1      -     r2,3   -      -      -      -      -      -       -
(e3) r3,1 r3,2         -  r3,4     -      -      -      -      -     r3,10
(e4)    -      -     r4,3   -     r4,5   r4,6   r4,7    -      -       -
(e5)    -      -       -    -       -      -      -    r5,8    -       -
(e6)    -      -       -    -       -      -      -    r6,8    -       -
(e7)    -      -       -    -       -      -      -    r7,8    -       -
(e8)    -      -       -    -     r8,5   r8,6   r8,7     -   r8,9
(e9)    -      -       -    -       -      -      -    r9,8    -  r9,10
(e10) r10,1 r10,2   r10,3   -       -      -      -      -  r10,9   -




                                                                             98
System und Subsystem – offen vs. geschlossen




                                               99
Cameron‘s Prozessbeispiel „Bibliothek“




                                         100
Datenmodell


              Identifizierer
                                     Attribute                        Attribute

                    KDNR                                                          PNR
                 Nam e, Vornam e                                            Prod.Bez., Preis
                                                                Attribute
                                                  KDNR    PNR
                                                     Menge




                       Kunde                        kaufen                  m     Produkt
                                       n



                        Entity-Typ                 Relationship                    Entity-Typ
                                                 (Beziehungstyp)
         K1, Müller, Franz                   K1, P1, 50              P1, Tel. 01, 85,-
         K2, Meyer, Fritz                    K1, P2, 30              P2, Telefax 248, 898,-
                                             K2, P1, 5
                                                                             
                Entities                          Beziehung                  Entities




                                                                                                101
Prozess-
Beispiel:
Produktionsplanungs
Prozess




                      102
zielsuchendes System erster Ordnung: Beispiel und Modell
Negativer Regelkreis
Architekturgesetz




                                                           103
linear „negative“ und - „positve“ Systemcharakteristika




   Rate                                          Rate

                                                            erzeugt lineares, positives
                                                            Systemverhalten
                   erzeugt lineares, negatives
                   Systemverhalten
              -m
                                                                  +m




          0                  Ziel   Level               0                          Level




                                                                                           104
System erster Ordnung – Regelkreis
Struktur: die zu einem Zeitpunkt beobachtbare Kopplung
Architekturprinzip: Rückkoppelung




                            System
                                       Regler

                                       Rückw ärts-
                                       übertragungs-
                                       funktion h2

                          Stellgröße                   Regelgröße
                                       Regelstrecke
               Input xe                Vorw ärts-
                                       übertragungs-
                             +         funktion h1                  Output xa




                                                                                105
Definitionsgleichung eines Systems erster (1.) Ordnung:*)

                     dx a (t)
(14)            a1             a 0 x a (t)  b 0 x e (t)
                       dt

Für den output des Systems ergibt sich:

                          b             a dx ( t )
(15)            xa ( t )  0 x e ( t )  1 a
                          a1            a 0 dt

Die Quotienten:

                     b0                       bm
(16)       KP =              allgemein: K G =               mit n=1,
                     a1                       an

für das System erster Ordnung heißen Verstärkungsfaktoren. Die Quotienten:

                     a1                                a
(17)       T1 =            ; allgemein           Tn = n 1
                     a0                                a0

heißen entsprechend Verzögerungsfaktoren.




   *) allgemeine Definition

          d2xa ( t )     dx ( t )                         dx ( t ) d2xe ( t )
... a2               a1 a  a0xa ( t )  b0xe ( t )  b1 e  b2             ...
            dt 2           dt                               dt       dt 2
                                                                                     106
 Dividiert man jetzt (15) durch T, dann folgt (mit T für T1) die elementare Beziehung:
                      1          K         dx (t)
 (18)                   x a (t)  x e (t)  a          oder:
                      T          T           dt

                             dx a ( t ) K           1
                                        x e ( t )  xa (t )
                               dt       T           T

 Von hier aus ergeben sich typische Wege, zur Lösung dieser Gleichung:
  analytisch, mit den Verfahren zur Lösung von Differentialgleichungen,
  simulativ bzw. rekursiv.
     Nach dem allgemein bekannten analytischen Verfahren zur Lösung von
Differentialgleichungen, zerlegt man Gleichung (16) in einen homogenen und in einen
inhomogenen Teil. Beide Gleichungen werden dann nach dem Verfahren der
"Trennung von Veränderlichen" gelöst.
     Als gedanklicher Startzeitpunkt linearer, zeitinvarianter Systeme wählt man stets
den (zeitlichen) Ursprung "0" im Koordinatensystem. Damit bleibt nur der
inhomogene Teil der Lösung übrig. Diese Beziehung ist in (19) dargestellt:
                                    t          a0
                                            ( s t )
                          K
                          T t0 0
(19)           x a (t )        xe ( s )e a1 ds
                              



oder
                                    t           1
                         K                (t s )
(20)           xa (t ) 
                         T t00 xe (s)e T ds
bzw. mit K=1
                             t                        (t s )
                                                1
(21)           xa (t )     
                           t0  0
                                        xe ( s ) e
                                                T
                                                        T
                                                                 ds


                                                                                         107
Mit der folgenden Vereinfachung:

                         s
                      1 T
(22)          h (s )  e
                      T

für s > oder gleich 0, bzw. h(s) = 0, für s < 0

lautet der Ausdruck (19), mit Hilfe von (20) umgeformt dann:
                            t                                              Faltungs-Integral
(23)          x a (t)     
                          t 0 0
                                   h (t  s)xe (s) ds


mit "xe(t)" als "Eingangs- oder Systemerregungsfunktion".
     "h(s)" heißt System-Antwort- oder Gesamtübertragungsfunktion (s.o.). Das
Systemverhalten xa(t) wird also berechnet, indem man die Systemeingangsfunktion
mit der Übertragungsfunktion "faltet". (21) nennt man auch: Faltungs-,
Superpositions- oder DUHAMEL1-Integral.
     Der rekursive Lösungsansatz2 entwickelt sich aus der oben dargestellten
Gleichung (18):




                                                                                               108
                dx a ( t ) K          1
(24)                       x e (t )  xa (t )
                  dt       T          T

     Im Gegensatz zur oben dargestellten Vorgehensweise beim analytischen
Verfahren, wird der Differentialquotient jetzt in einen zeitdiskreten Differenzen-
quotienten umgewandelt:
               x a ( t )  x a ( t  1) K                  1
(25)                                    x e ( t  1, t )  x a ( t  1, t )
                         DT             T                  T

     Die linke Seite der Gleichung wird als Netto-Veränderung der beobachteten
Ausgangsgröße bezeichnet. Die Netto-Veränderung läßt sich auch als Differenz
zwischen zwei Zuständen verstehen. Für "Zustand" wird die Bezeichnung xa(t-1) - vor
der Veränderung - und xa(t) - nach der Veränderung, beibehalten. Die
"Veränderungsrate" bei xa bzw. bei xe in der Zeit wird durch den Hinweis auf die
beiden betrachteten Zeitpunkte (t-1 und t) gekennzeichnet. Damit läßt sich (12) erneut
umformen:

                                  K                1               
(26)   x a (t)  x a (t  1)  DT  x e (t  1, t)  x a (t  1, t) 
                                  T                T               

Der Zeitabstand (t-1,t) entspricht hier genau : 1 DT.

Von hier aus werden zwei Strom- oder Flußgrößen (RATES [R]) definiert:
                           K
                   Re =      x e ( t  1, t )
(27)                       T                  für die Eingangsrate und
                                  1
                       Ra =         xa (t -1, t)
(28)                              T              für die Ausgangsrate.

Daraus wird dann schließlich:
                                                                                  Differenzen-
(29)           X Z (t) = X Z ( t  1)  DT( R e  R a )                           gleichung
                                                                                                 109
(30)        Bestand(Neu) = Bestand(Alt) + (Zugang-Abgang)

     DT (=1) wird in diesem Fall als Zeitmaß für eine Basis-Beobachtungsperiode
angenommen.


                                      Start
                        DT:=                  Zeit-Increment festl.
                        Level:=               initialisieren
                        AT:=                  Verzögerungskonstante festl.
                        t:=                   Zeit-Zählvariable initialisieren
                        L:=                   Zähl-Schranke festl.

                                  t          = t+DT

                         Rate.KL = (Ziel - Level.K)/AT


                         Level.K=Level.J+DT*Rate.JK




                   ja                    t<L?


                                      nein

                                      STOP
Abb. 3.4-6: Programm-/Prozeßablaufstruktur der rekursiven Lösu




                                                                                  110
„Verhalten“ im Zeitablauf für ein System erster Ordnung




     10                              Ziel
      9       Level, Ziel
      8
                                                         Systemzustand
      7

      6

      5

      4

      3                                                                          System 1. Ordnung
      2

      1                         Rate

      0
          0     1   2   3   4    5     6    7   8   9   10   11   12   13   14   15   16   17   18   19   20

                                                                                                     Zeit




                                                                                                               111
Positiver Regelkreis
Architekturgesetz




            Das mathematische Modell eines linearen, positiven Regelkreises kann als
        Exponentialfunktion entwickelt werden:
        (31) level (t) = e r
        e selbst entwickelt sich nach der Gleichung
                                  n
                        1
        (32)   limn  1 + n 
                             
                                      =e
        Diese Darstellung zeigt, daß sehr viele Rückkopplungen nötig sind, bis exponentielles
        Wachstum erreicht wird.


                                                                                                112
„Steuerung“
Architekturgesetz




                    113
System höherer Ordnung - Verzögerungen



                                        Zeit
                 Entscheidung       V


                                            V      Verzögerungen


                                            Abw eichungen
                                V
          V          Ziel

                                             e1             e0
                                        V              e2
                                        e3
                                                  e4
                     Ist
                                                                   e41
                                                             e43
                                                                   e42




                                                                         114
Gleichungssystem für ein System zweiter Ordnung




           PAGE 1 EINFACHES BEISPIEL FüR EIN SYSTEM ZWEITER ORDNUNG 04/18/93 18:54
           L    L2.K=L2.J+DT*R2.JK                    L2:=Zustandsgröße2 (Level)
           R    R2.KL=L1.K/D                          R2:=Flußgröße 2 (Rate)
           L    L1.K=L1.J+DT*(R1.JK-R2.JK)            L1:=Zustandsgröße 1
           R    R1.KL=(ZIEL-L2.K)/AT                  R1:=Flußgröße 1
           C    D=2                                   D:=Verzögerungskonstante
           C    AT=1                                  AT:=Verzögerungskonstante
           C    ZIEL=10                               Ziel:=Zielzustand
           N    L1=5                                  L1=5:=Anfangswert für L1
           N    L2=2                                  L2=2:=Anfangswert für L2
           SAVE L1,L2,R1,R2,ZIEL                      Speicher f. Variable res.
           SPEC DT=0.25/LENGTH=30/SAVPER=1            Systemanweisungen




                                                                                     115
Verhalten im Zeitablauf – System zweiter Ordnung


          14
                                                                                    Systemzustand
       Level, Ziel

          12




          10




           8




           6

                                                                                                                        System 2. Ordnung

           4                                                                 Ziel




           2




           0

               0     1   2   3   4   5   6   7   8   9   10   11   12   13     14    15   16   17   18   19   20   21    22   23   24   25   26   27   28    29    30

                                                                                                                                                            Zeit




                                                                                                                                                                        116
Sonderfall: Resonanz




                       117
Sonderfall: „Chaos“ (Verhulst Modell)

 Xn  B Xn 1(1  Xn 1)
 mit B als Wachstumsparameter
  0,6                                    0,8
  0,5                                    0,7
                                         0,6
  0,4
                                         0,5
  0,3                                    0,4
  0,2                                    0,3
                                         0,2
  0,1
                                         0,1
  0
        0   5   10   15   20   25   30   0
                                               0   5   10   15   20   25   30

   B=2.5                                       B=3.0




                                                                                118
Sonderfall: „Chaos“



           1
         0,9
         0,8
         0,7
         0,6
         0,5
         0,4
         0,3
         0,2
         0,1
           0
               0      5   10   15   20   25   30


           B=3.9999




                                                   119
Sonderfall: „Chaos“ - Bifurcation


                   Population



       Attraktor




                         B=3.0      Wachstumsrate




                                                    120
Sonderfall: „Chaos“ – andere bekannte Fraktaldarstellungen
Selbstähnlichkeit




                                                             121
Phasenraum und Darstellung des Systemverhaltens im Zeitablauf

                                               
                                                    Rate (+) max




               Level (-) min                                       Level (+) max
               Rate (-) min                                        Rate (+) min




                               Rate (-) max

                                   -2 -1,5-1 -0,50 0,5 1 1,5 2


                                              45

                                              90

                                              135

                                              180

                                              225

                                              270

                                              315


                                              360

                                                                                   122