An introduction to Systems Dynamics. by Corrado lo Storto

Transcription

1 1 An introduction to Systems Dynamics by Corrado lo Storto

2 2 Main questions: Why? What? How?

3 Why? 3 The project delivery system Goaloriented Open has / requires external inputs Complex uncertainty, many requirements, technically and from business perspectives Dynamic Nonlinear causeeffect relationships

4 Why? 4 The current project delivery system Starting point with some flaws Based on PERT and CPM from 40 s Critical Path Method neglects resources Risk Management includes risk in all tasks Measurement based on Cost vs Throughput If it didn t work you weren t detailed enough

5 What? 5 A new project delivery system Systems Thinking (Systems Dynamics) Jay Forrester Industrial Dynamics, 1961 MIT Perspective of whole and how parts interact Tools for mapping dynamic complexity Causal loop diagrams Stock and Flow

6 What? 6 System variables: system input 1 output input 2 To every system there correspond two sets of variables: Input variables. They originate outside the system and are not affected by what happens in the system Output variables. They are the internal variables that are used to monitor or regulate the system, resulting from the interaction of the system with its environment and are influenced by the input variables

7 What? 7 System Thinking Process Specify Issue (dynamic, holistic thinking) Construct Hypothesis / model (causal relationship thinking) Test Hypothesis / model (scientific thinking) Implement Changes Model reality to understand a system s behaviour not specific performance

8 What? 8 Hypothesis and Stock & Flow Diagram an example Add Work Work Common Variance Work In Progress Special Variance Work Complete Hypothesis: excessive task estimate padding decreases project delivery efficiency Percieved Schedule Pressure Padding Adjustment Define Schedule Allotted Time Schedule Used Employee Performance Measure

9 9 simulation a very powerful and widely used management science technique to analyze and study complex systems a technique that imitates how a realworld system behaves as it evolves over time adopts a simulation model., i.e. a model that usually takes the form of a set of assumptions about the behavior of the system, either expressed as mathematical or logical relations between the objects of interest in the system allows to better understand the expected performance of the real system and to test the effectiveness of the system design

10 What? 10 Accelerometer: Consider the massspringdamper (may be used as accelerometer or seismograph) system shown below: FreeBodyDiagram x x u f s f s M M f d f d f s (y): position dependent spring force, y=xu f d (y): velocity dependent spring force Newton s 2nd law Mx M y u f ( y) f ( y) Linearized model: My by ky d Mu s

11 11 jumping ball

12 12 Several simulation paradigms: System Dynamics, Discrete Event and Agent Based High Abstraction Less Details Macro Level Strategic Level Middle Abstraction Medium Details Meso Level Tactical Level Aggregates, Global Casual Dependencies, Feedback Dynamics, Discrete Event Entities (passive objects) Flowcharts and/or transport networks Resources Agent Based Active objects Individual behavior rules Direct or indirect interaction Environment models System Dynamics Levels (aggregates) StockandFlow Diagrams Feedback loops Low Abstraction More Details Micro Level Operational Level Mainly discrete Individual objects, exact sizes, distances, velocities, timings, Mainly continuous (source: PoChing, C. DeLaurentis, 2007, adapted from: Borshchev A, Filippov A. From System Dynamics and Discrete Event to Practical Agent Based Modeling: Reasons, Techniques, Tools. Proceedings of the 22 nd International Conference, July 2529, 2004, Oxford, England, UK)

13 13 systems dynamics a methodology to explore complexity, interconnectedness, and change over time that provides a framework in which to apply the idea of systems theory to social and economic problems developed at MIT in the late 1950s (based cybernetics, industrial dynamics, control theories) uses 2 analysis tools Causalloop diagrams (i.e., causeeffect diagrams CLD) Stockflow diagrams (SFD) the system is modeled as a set of continuous variables differential equations hydraulic models analogy availability of several models since1956 easy to model, effective as a communication and sharing tool limited development time and cost

14 14 systems dynamics The study of informationfeedback characteristics of industry activity to show how organizational structure, amplification (in policies), and time delays (in decisions and actions) interact to influence the success of the enterprise (Jay Forrester 1958 and 1961)

15 15 Basics of system dynamics StockandFlow Stock A Rate Stock B Casual Loops Decision Rules (source: PoChing, C. DeLaurentis, 2007)

16 16 Basics of system dynamics an example (source: PoChing, C. DeLaurentis, 2007) Brownies_in_Stomach(t) = Brownies_in_Stomach (t dt) (eating digesting) * dt eating = 1 digesting = 1/2 INIT Brownies_in_Stomach = 0 DOCUMENT: Initially Andy s stomach is empty. UNITS: brownies DOCUMENT: Andy eats a brownie every hour. UNITS: brownies/hour DOCUMENT: Andy digests 1 brownie every 2 hours. He therefore digests a half a brownie every hour. UNITS: brownies/hour

17 17 steps in system dynamics modeling Identify a problem Develop a dynamic hypothesis explaining the cause of the problem Create a basic structure of a causal graph Augment the causal graph with more information Convert the augmented causal graph to a system dynamics flow graph Translate the system dynamics flow graph into equations and a SD software modeling program Use computer simulation to infer the behavior of the system

18 18 some critical aspects Determining the appropriate boundaries to define what should be included within a system Thinking in terms of causeandeffect relationships Focusing on the feedback linkages among components of a system

19 19 Causal Loop Diagram (CLD) Represent the feedback structure of systems Capture The hypotheses about the causes of dynamics The important feedbacks salary performance tired sleep salary VS performance salary performance performance salary tired VS sleep tired sleep sleep tired

20 20 Labeling Link Polarity Signing: Add a or a sign at each arrowhead to convey more information A is used if the cause increase, the effect increases and if the cause decrease, the effect decreases A is used if the cause increases, the effect decreases and if the cause decreases, the effect increases salary performance tired sleep

21 21 Determining Loop Polarity Positive feedback loops Have an even number of signs Some quantity increase, a snowball effect takes over and that quantity continues to increase The snowball effect can also work in reverse Generate behaviors of growth, amplify, deviation, and reinforce Negative feedback loops Have an odd number of signs Tend to produce stable, balance, equilibrium and goalseeking behavior over time salary performance tired sleep

22 22 Reinforcing loop and balancing loop salary performance tired sleep Behavior Over Time Behavior Over Time performance level supportive behavior sleep amount unsupportive behavior unsupportive behavior supportive behavior time time

23 23 Loop Dominance There are systems which have more than one feedback loop within them A particular loop in a system of more than one loop is most responsible for the overall behavior of that system The dominating loop might shift over time When a feedback loop is within another, one loop must dominate Stable conditions will exist when negative loops dominate positive loops

24 CLD with Combined Feedback Loops 24 birth rate population death rate

25 25 CLD with Nested Feedback Loops (SelfRegulating Biosphere) Evaporation clouds rain amount of water evaporation Earth s temperature Sunshine Evaporation A mount of water on earth Clouds Rain

26 26 Exogenous Items Items that affect other items in the system but are not themselves affected by anything in the system Arrows are drawn from these items but there are no arrows drawn to these items Sunlight reaching each plant Density of plants Sunlight

27 27 Delays Systems often respond sluggishly From the example below, once the trees are planted, the harvest rate can be 0 until the trees grow enough to harvest delay # of growing trees Harvest rate Planting rate

28 28 Flow Graph Symbols Level Rate Flow arc Auxiliary Causeandeffect arc Source/Sink Constant

29 29 Level: Stock, accumulation, or state variable A quantity that accumulates over time Changes its value by accumulating or integrating rates Changes continuously over time even when the rates are changing discontinuously Rate/Flow: Flow, activity, movement Change the values of levels The value of a rate is Not dependent on previous values of that rate But dependent on the levels in a system along with exogenous influences

30 30 Auxiliary: Arise when the formulation of a level s influence on a rate involves one or more intermediate calculations Often useful in formulating complex rate equations Used for ease of communication and clarity Value changes immediately in response to changes in levels or exogenous influences Source and Sink: Source represents systems of levels and rates outside the boundary of the model Sink is where flows terminate outside

31 31 Example: Population and birth Births Population Births Population

32 32 Example: Children and adults Births Children Children maturing Adults Births children Children maturing Adults

33 33 Building construction Problem statement Fixed area of available land for construction New buildings are constructed while old buildings are demolished Primary state variable will be the total number of buildings over time Causal Graph Industrial Construction Demolition buildings Construction fraction Fraction of land occupied Land available for Industrial buildings Average area per building Average lifetime for buildings

34 34 Building construction: simulation model Flow Graph Equations Construction (C) Demolition (D) db l /dt = C r D r Industrial Buildings (B) C r = f1(cf, B l ) D r = f2(al,b l ) Construction fraction (CF) Fraction of land occupied Average lifetime for buildings (AL) CF = f3(flo) FLO = f4(la,aa,b l ) Land available for industrial buildings (LA) (FLO) Average area per building (AA)

35 Software Modeling & Simulation (VenSim, Powersim, Ithink, etc.) 35 The modeling process starts with Sketching a model Writing equations Specifying numerical quantities Then simulate the model Examine the simulation output and discover the dynamic behavior of variables in the model

36 The CLD of a project management model 36 quality of work Work to do Project Model Work To Do required workforce hiring delay actual workforce fatigue overtime hours required work done productivity

37 Flow Graph: The Rabbit Population Model 37 births Rabbit Population deaths birth rate average lifetime

38 38 Equations: The Rabbit Population Model average lifetime = 8 Units: Year birth rate = Units: fraction/year births = Population * birth rate Units: rabbit/year deaths = Population / average lifetime Units: rabbit/year Population = INTEG(births deaths,1000) Units: rabbit

39 The Rabbit Population Model: simulation output (source: MIT System Dynamics in Education Project Under the Supervision of Dr. Jay W. Forrester by Leslie A. Martin) 39

40 40 The system dynamics modeling process Mental Models, Experience, Literature Perceptions of System Structure Diagramming and Description Tools Comparison and Reconcilation Structure Validating Processes Representation of Model Structure Empirical Evidence System Conceptualization Model Formulation Behavior Validating Processes Empirical and Inferred Time Series Comparison and Reconciliation. Deduction Of Model Behavior Literature, Experience Computing Aids

41 41

42 Thank you! 42