System Design and Complexity

beta/delta<1, price derivatives of supply and demand

• Only simple outcomes: damped, exploding, periodic oscillations.

• Real markets are irregular, “random looking” prices

• Suppliers: no simple expectations, but anticipatory effects

• No interaction between markets: consider inter-market influence

• Coupled cobwebs are looking at two markets, are sensitive to profits and costs

• Represent more realistic price dynamics

   

Profit is the trigger for suppliers on which market to go. They go where profit is higher. The sensitivity is the parameter which implies how strong suppliers react to profit differences.

Y=F(x1,x2,...xn)

Input factors of production x, output Y. Key inputs: Capital (K), Labour (L). Describes only technology, not economic behavior.

Substitute technology: Y=a+bx1+cx2+... => Sum

Complementary technology: Y=min{x1,x2,...} => Product

If output increases by more than that proportional change in inputs, there are increasing returns to scale.

If output increases by less than that proportional change in inputs, there are decreasing returns to scale

Specific form of Y=ALK

    Alpha + beta = 1 → constant returns to scale

Y=C+I → all output is spent as consumption or investment, C, I depend on the saving rate

2 feedback mechanisms: Change in capital (due to investment and depreciation) and growth in labour supply (immigration and/or reproduction)

Compare two equilibrium states

    Optimal saving rate: allows to maximize consumption → everyone is wealthier

Adopt the same saving rate → poor countries should increase saving, rich countries

    Should decrease saving

Explains some of the empirical data

Neglects benefits from human capital and technological progress

Business cycle: cyclic behavior around long term economic growth → therefore, no Contradiction.

    Boom - recession - depression - recovery

Linear functions can’t explain cyclicity (only possible by use of exogenous factors). Linear functions with an exact proportionality

    don’t represent reality

Hysteresis in class: cyclicity combined with quick changes to different states

Dynamics usually take time to adjust. IClassical example: more pig breeding due to high demand in pork meat. Pigs need to grow.

\({dx\over dt}=k_R x-x/a_R \)   kr: birth rate, ar: average lifetime

\(x(t)=x_0e^{rt}\)

\({dx \over dt}=k_Rx-f_R(x,y)\)  and \({dy \over dt}=k_Fy-f_F(x,y)\)

\(k(t)=ci{N_A (t)\over N}\)  and \(N=N_A(t)+N_P(t)\)

Dynamics

\({dN_P \over dt}=-k(t)N_P=-ci{dN_A(t) \over N}N_P\)  and \({dN_A \over dt}=-{dN_P \over dt}\)

c: contact rate, i: probability of adoption

General Form: \({df(t) \over dt}=\beta f(t)[1-f(t)]\) with solution \(f(t)={1\over 1+e^{-\beta (t-\mu )}}\)

\({df(t) \over dt}=\alpha [1-f(t)]\) => solution \(f(t)=1-e^{-\alpha t}\)

no S-Curve!

\({df(t) \over dt}=\alpha[1-f(t)]+\beta f(t)[1-f(t)]\)

=> S-Courve

\(x_{n+1}=rx_n(1-x_n)\)

r: length of time step

0 < r < 1: x_stat => 0

1 < r < 3: x_stat => 1-(1/r)

3 < r < 4: oscillations

\(s_t=\alpha+\beta p_{t-1}\)  supply responses to price with time lag

\(d_t=\gamma-\delta p_t\)

\(\alpha,\gamma\): basic supply/demand at p=0

\(\beta,\delta\) price derivatives

Market Clearing:

\(s_t=d_t\) => \(p_t={1\over \delta}(\gamma-\alpha)-{\beta \over \delta}p_{t-1}\)

if \({\beta \over \delta}\) <1  => Equilibrium

\({\beta \over \delta}\) >1  => unstable, explode

\({\beta \over \delta}\) =1  => oscillations

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

PEST: Sociological, Technological, Economic, and Political

    SWOT: Strengths, Weaknesses, Opportunities, and Threats

    Structured methods to analyze the situation.

    => Setting the objective; situation analysis

• 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

Operability, Measurability

Completeness and Balance

Contradiction–free, Redundancy–free

Prioritization

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

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