Chaos and complexity inSMEs networks andinnovation ecosystems:
post-pandemic challenges
International Conference on Production
Research Americas – ICPR 2022 –UTFPR, Curitiba, Brazil

Production and Systems Engineering
Graduate Program - PPGEPS

Prof. Dr. Miguel Sellitto

Dottorato di Ricerca in Ingegneriadell´Innovazione Industriale DISMIAgenda•Complexity theory:•General Systems Theory;•Chaos Theory;•Information Theory;•Strategy in Networks•Typology;•Complexity Influence in the Strategy.

Complexity Theory: Systems,Chaos, Information

Complexity Theory• Elements of complexity theory are already found in the work of Greekphilosophers, such as Plato (cybernetics) and Aristotle (teleology) andmedieval philosophers, such as Roger Bacon (nature laws are shownby observation, not contemplation);• The theory is currently considered to draw on key elements fromthree other theories developed in the 20th century:• General systems theory;• Chaos theory;• Information theory.

4Systems Theory• The main subject encompasses the so-called CAS (complex adaptivesystems);• CAS evolve according to the auto-organization principle, in which partsexchange energy, materials, and information seeking for a suitablescheme that allows efficiently achieving their goals;• The search can be controlled by a central intelligence or according tospontaneous, trial and error attempts.

5Systems Theory• Systems theory studies fundamental properties of networks based on
non-linear interactions that can be direct or feedback (closed-loops);• While negative feedback stabilizes the system, positive feedback cangenerate complex behavior that, if exceeding certain limits, generates
chaotic behavior;• An initial scheme, under uncertainty, engenders alternative schemes
chosen by the intelligence, or unexpected schemes that emerge fromthe parts, stimulated by external information.

6

Elements of CAS• Regular or unexpected interaction patterns are characterized by:• Variety: is the probability that any two agents can fulfill different missions;• Flexibility: is the probability that a single agent can fulfills more than one mission;• Redundancy: is the probability that more than one agent can fulfill a givenmission;• Availability: is the probability that an agent will be idle when required for amission;• Reliability: is the probability that at least one agent successfully accomplishes agiven mission;• More variety, more flexibility, more redundancy, more availability amplify thecomplexity and increase system´s reliability but also increase cost: a trade-off
problem.

Linear and non-linear (complex) relationships
AAZ

Linear multiple

ZB
linear simple
AZ

Y

cybernetics
Y partially causes itself(triggered processes)

BZBY

circularity
Y causes itself,
self-sustained processManufacturing as a CAS
Marketing

Maintenance, industrial
engineering

Inputs: raw
material, energy,
information,

TransformationOutputs:
products andcustomers

Chaos Theory• Chaotic behavior originates from extreme responses of CASs which, underborderline conditions, exhibit unexpected behavior;• Usually such behaviors are characterized by more than proportional variations in
the output in response to small variations in the input;• Such behaviors, at first sight, seem random but, observed in more depth, they
result from a hidden, deterministic process;• Therefore, one must consider that chaos is not synonymous with disorder, butwith behavior that is difficult to decipher at first sight;• The expressions “chaos out of order” and “deterministic chaos” are used insituations of extreme behavior of CASs.

Extreme behavior of systems• First order: only negative
feedback and quickly reachstability;• Second order: negative as wellas positive feedback may or
may not reach stability;Extreme behavior of systems• Chaotic: positive feedback loops may eventually convey tounstable states if a certain threshold is surpassed, the chaosedge;• Theoretical models may be the only method of identifying
chaotic behavior. If a chaotic trajectory can be described by awell-known model, with a given probability, it is possible topredict the next occurrence of the phenomenon.

Some well-known Chaotic Models•Logistic Map (a second-order model, possibly the simplest);•Tent Maps;•Bernoulli Attractor;•Hénon Attractor;•Mackey-Glass Attractor;•Lorenz Attractor.
• Application of the logistic map(https://www.sciencedirect.com/science/article/pii/S2405896318316161)

Logistic Map•

Logistic Map•

Logistic Map•

Logistic Map•

Logistic Map•

Logistic Map•

Logistic Map•
Randomsequence

Chaotic
sequence

Information Theory• Information is the opposite of uncertainty;• The greater the uncertainty a message dissipates, the more information themessage contains;• Therefore, the more unlikely the content of the message, the greater the chance iteliminates and the greater the amount of information it contains;• “Man who bites a dog” and “airplane that crashes” have more information than “dog that bitesa man and “airplane that completes the trip”;• In the manufacturing, it is more important for informational intelligence to save,recover, and dispose of failure data than normal operation data.

Information Quantity• Try to guess the right word (not a possible word, but the exact word, i.e. themissing letter):• B_EF;• SIN_;• The easiest word is the one in which the least amount of information is missing;• For p possible messages, with probability distribution P(s), the average
information content in the source is given by the so-called Shannon entropy.

Information Quantity• BEEF;• If p = 2 and the probabilities are [E = 99%, other = 1%], than the missing information quantity is:• I = -[0,9 * log(0,9) + 0,1 * log(0,1)] = 0,08 bits (almost nothing new);• SINK or SING or SINC or SINS;• If p = 4 and the probabilities are [A = E = I = O = 25%], than the missing information quantity is :• I = -[4 * (0,25 * log(0,25)] = 2 bits;• As the odds in the second word are greater, the second missing letter dissipates
more uncertainty and the amount of information is greater than the first.

Supply Chains, Networks,
Ecosystems, Tecnosystems,
Industrial Districts, Short
Supply Chains: strategy andcomplexity

Networks: complexity• Networks appear when several companies, spontaneously or not,cooperate to achieve priorities, or individually take advantage of fractors
due to the existence of the network;• It is not possible to explain a network by explaining only the relationships
between the parts, two by two; it is necessary to explain relationships
between all parts;• Every part affects and is affected by every other part, and as the network
grows, the number of relationships grows more than linearly.

Primitive meta-strategies in networks• Efficiency: stable environment, defined and regular demand, littleinnovation; focus on smooth, continuous flows;• competition priorities: low price, on-time delivery, conforming quality;• Responsivity: unstable environment, uncertain demand, majorinnovation; focus on fast and discontinuous flows;• competition priorities: ability to change the product (flexibility), innovation.

Matching Life Cycle and Strategy
Throughput

maturity

Efficiency

Responsivenessevolution
introduction

End of lifetimeComplex Methods in Networks• In the early days of industrialization, artisanal manufacturing wascomplex, as it depended on combinations of factors, such as machines,materials, product design, and mainly operator skills;• Rationalization and management methods, particularlyinterchangeability of parts and automation, have consistently reduced
the complexity;• Recently, the need to achieve multiple strategic objectives at the sametime (cost, quality, flexibility, delivery) has again increased thecomplexity of manufacturing.

Complex Methods in Networks• To manage the complexity, it is necessary to measure and modify it
accordingly, there is, to measure and modify the amount of
information needed to run the strategy;• A stable and functional, efficient SC generates few anomalies andneeds little information, which implies low complexity• An unstable and innovative, responsive SC, requires handling newsituations to handle, which implies high complexity.

Shannon´s Entropy: H(p)•30IssuePlanning andscheduling

Framework:
information neededto manage
uncertainties in thefootwear industry(empiricallycollected)

Logistics

Labor
FinanceTechnologyandinnovation

Tag
I1
I2
I3
I4
I5
I6
I7
I8
I9
I10
I11
I12
I13
I14
I15
I16
I17
I18
I19
I20Information
Forecasting
Manufacturing capacity
Scheduled maintenanceLead-times and deadlines
Scheduled shipments
Scheduled arrivals
Shared inventory situation
Shared transportation situation
Availability of skilled operators
Availability of skilled designers
Cash-Flow
Shared purchases
Credit, payments, and loans
Shared Financing
Product development
Process development
Shared investments
Shared machineTechnology transfer
Technical support31

Application 1, eﬃciency: safety shoes
Metallic parts

Syntheticparts

Institutional
clients

Distributor 2

R1
Manufacturing

R21
R11R2
R12R13R3

Leather parts

R22

Distributor 1RetailersApplication 1, eﬃciency: safety shoes
R1I1
I2
I3
I4
I5
I6
I7
I8
I9
I10
I11
I12
I13
I14
I15
I16
I17
I18
I19
I20

R2R3

R11R12R13

R21 R22
10% 50%30% 60%50%
60%
30% 60%

10%
10%
10%
20% 10% 40%
50% 20% 50%

10% 50%
30%
30%
20%

10% 20%40% 60%10%20%
20% 40%

10% 10%Application 1, eﬃciency: safety shoes
Metallic parts

Syntheticparts

Institutionalclients

Distributor 2

R1
Manufacturing

R21R11R2
R12

R13R3Leather parts

R22

Distributor 1

RetailersComplexity sources:• Redundant channels; and• Dependability for localdeliveries.

Application 2, responsivity: luxury shoes
Aesthetic parts
R1

Manufacturing

Leatherparts

R31
R21R2

R22

R3

R32
R11
R12Atelier 1

R13Atelier 2

R14
Designcenter

Foreignerclients

Distributor 2

R15

Distributor 1

R16
Atelier 3

Domestic
retailersApplication 2, responsivity: luxury shoes
Aesthetic parts
R1

Manufacturing

Leatherparts

R31
R21

R2

R22

R3

R32
R11R12

Atelier 1

R13
Atelier 2

R14
Designcenter

Foreignerclients

Distributor 2

R15

Distributor 1

R16
Atelier 3

Domestic
retailersComplexity sources:• innovation; and• flexibility.

Comparison
Competitive
dimension

Importance
N1

ImportanceN2

CostHigh

Low

Quality

HighLow

Intermediate (*)

Intermediate

Flexibility

LowHigh (*)

Innovation

Low

High (*)

Relative Complexity

15%

28%

Dependability

Source of complexity (*)

Complexity and Performance•Initial studies by GEEP (PPGEPS UNISINOS) and DISMI(UNIMORE) indicate strong non-linearity in the relationshipbetween complexity and performance in manufacturing
networks;•They also indicate that such non-linear relationships
depend on the competitive priority that the networkchooses.

Complexity and Performance•A proposition to verify in further studies.
performance

Efficiency

Responsivity
complexity

Post-pandemic scenario•In pandemic times, industry has been severely affected bydisruptions in supply chains;•A new source of complexity arises, how global supply
chains should deal with disruption risk;•Two new strategic scenarios that were already proposed in
SC strategic studies seems to enhance relevance: agility(not only responsivity), and resilience (not only efficiency).

Post-pandemic scenario
Demand uncertainty
Supply uncertainty
low(stable process)high(unstable process)low(functional product)high(innovative product)

Efficiency

Responsivity

Resilience

AgilityComplexity and Performance: the next step
•How should such a relationship be?
performance

Efficiency

Responsivity/
resilience?

Agilitycomplexity

Some initial publications

sellitto@unisinos.br