System Design and Complexity

Unidirectional: A => B

    Feedback: A ⇔ B

    Indirect: A => B, B => C

Positive causation:  +A => +B   => positive feedback, reinforcement, leads to instability

Negative causation +A => -B    => negative feedback, damping effect, leads to stability

\(Y=F[K(t),L(t)]\)

\(Y(t)=C(t)+I(t)\)

\(I(t)=sY(t)\) and \(C(t)=(1-s)Y(t)\)

Dynamics:

\({dK(t) \over dt}=I(t)-\delta K(t)=sY-\delta K(t)\) Depreciation

\({dL(t)\over dt}=nL(t)\) Population growth, immigration

\(y={Y\over L}=f[k(t)]=Ak(t)^{1-\alpha}=Ak(t)^\beta\)

See image

initiation, planning, execution, closure

\(K={r\over (k_b+k_d)}\), K: carrying capacity

\({df(t)\over dt}=rf(t)(1-{f(t)\over K})\)

\(f(t)={K\over 1+\eta e^{-rt}}\)  with \(\eta={K\over f(0)}-1\)

SE is an interdisciplinary field of engineering and engineering management that focuses on how to design and manage complex systems over their life cycles.

Structural perspective, representative agents, macroscopic dynamics

Systems engineering is about defining the system:

→ structural (elements), organizational (shape), functional (what does system do) perspective.

Systems design is about defining the structure and dynamics of a system such that a desired outcome is obtained

• Setting the objective

  • Situation analysis

  • Formulation of the objective

• Search for solutions

  • Concept synthesis

  • Concept analysis

• Selection of solutions

  • Evaluation of concepts

  • Decision

    Solution neutrality, state requirements (normative)

Operability, Measurability

Completeness and Balance

Contradiction–free, Redundancy–free

Prioritization

PEST: Sociological, Technological, Economic, and Political

    → external analysis of macro-environment

    SWOT: Strengths, Weaknesses, Opportunities, and Threats

    → external and internal analysis

    Structured methods to analyze the situation.

    => Setting the objective; situation analysis

    Analyze what do we have and look at future trends

Project management is the discipline of organizing and managing resources in such a way that these resources deliver all the work required to complete a project within defined scope, time, and cost constraints.

On-time endeavor.

Two objectives: deliver results within prespecified constraints, optimize allocation of resources to meet predefined objectives

Unidirectional: A => B

    Feedback: A ⇔ B

    Indirect: A => B, B => C

Positive causation:  +A => +B   => positive feedback, reinforcement, leads to instability

Negative causation +A => -B    => negative feedback, damping effect, leads to stability

Inventory correction (alpha) and workforce correction (theta) have different time

scales, which lead to oscillations.

    An increase in sales leads to an overshooting in inventory/production and increased

hiring.

    Lower inventory coverage leads to larger oscillations.

Introduction, Growth, Maturity, Decline

    Question Marks, Stars, Cash Cows, Dogs

    BCG Matrix: market share vs. market growth

beta/delta > 1 => unstable, explosion

    beta/delta = 1 => oscillations

    beta/delta < 1 => stable, approaching an equilibrium

    Beta and delta: price derivative of demand / supply.

Single market, linear supply and demand, competitive market

    Demand reacts immediately to price, no future expectations, market clearing

Technology diffusion → spatial process

    New technology is exogenous

    Technology doesn’t fail

    Empirics show asymmetric S-curve

    Effect of competition unclear

x_n+1 = r * x_n * (1-x_n)

    Control parameter r

    0 < r < 1 => x => 0

    1 < r < 3 => x = 1-1/r, stationary regime

    3 < r < 4 => oscillations

Period doubling happens in 3 < r < 4, where cycles of solutions exist, with increasing r the cycles get longer (by doubling of the cycle length due to bifurcation)

Simple problem: = trivial problem; few, weakly or uncorrelated criteria, perfect Solution.

Complex problem: = nontrivial problem; many, strongly correlated optimization Criteria, frustrated system with several (non optimal) solutions.

Difference to cubic eq.: procedure for solution is unclear BUT also well defined due to given information and specified goal.

Difference to airport: airport has unclear goals/information (undefined problem space)TSP (travelling salesman problem) = well-defined, non-trivial

Not all solutions can be determined within a finite time. Many criteria are strongly Interdependent and influence the solution. As not all solutions can be investigated. One probably doesn’t find the perfect one, or at least one doesn’t know if one did.

1: what is the problem? Define cost function;

2: what is the solution? Evolutionary Optimization;

3: select solution. Best solution is known, Improving by random deviations

Complexity is given, can’t be simplified. Complexity stems from the different criteria Which are interlinked

Setting the objective, search for solution, selection of solutions The steps are prerequisites of the following step, proper preparation helps (Roli: maybe it not only helps but is crucial?) for following tasks

Inner system: part of the system which is affected by the problem and its possible solutions. Environment: contains system. Inner system can be enlarged (size can be corrected due to the effect of the solution)

Solution neutral, describe requirements, operable, measureable, complete, no contradictions, no redundancy, prioritized.

Types: procedural, system, mandatory, desired

As a help to formulate objectives (compatibility, dimensions of objectives)

1. Order: modification within system, 2. Order: modification of system rules

Synthesis: generate solutions, analysis: evaluate solutions, Create variety vs. reduce variety, Iterative process

Need to know time needed for an activity, cope with uncertainty of activity duration, dependencies between activities

Relationships between activities are not shown in Gantt, impact of delay is not shown, CPM shows critical path, allows capacity planning

Longest path through schedule, no float