Overview

04/19/23 1

SAL System Architectures Laboratory

Computational Modelsof Multi-National Organizations

Alexander H. LevisSmriti KansalA. E. Olmez

Ashraf AbuSharekh

Phoenix, AZ1 April 2008

04/19/23 2System Architectures Laboratory

Overview

• The problem of modeling multi-national organizations such as coalitions has received renewed attention.

• Coalition partners may have differences in equipment or material, differences in command structures, differences in constraints under which they can operate, and, last but not least, differences in culture.

• This paper focuses on the ability to introduce attributes that characterize cultural differences into the mathematical model for organization design and use simulation to see whether these parameters result in significant changes in structure.

• Specifically, the attributes or dimensions defined by Hofstede are introduced in the design process in the form of constraints on the allowable interactions within the organization.

• The Lattice algorithm is extended to the design of decision-making organizations subject to cultural constraints.


Outline

• Decision Maker Models• Lattice Algorithm• Cultural Attributes• C-Lattice Algorithm• Example using CAESAR III • Results


The DM Model

• A five stage, model was postulated as an extension of Herbert Simon’s stimulus – response model:

SituationAssessment

ResponseSelection

SA CITPIF RS

IF: Information FusionTP: Task ProcessingCI: Command Interpretation

Two stage S-R model of Simon

Five Stage DM Model


The Interacting DM Model

• The additional stages were necessary for creating different types of interactions among decision makers

SA CITPIF RS

ResultsSharing

InformationSharing

InformationSharing

CommandInput

• Problem:

– Algebra of Interactions


Interactions from DMi to DMj

00

10C

00

10H

00

10G

00

10F

11s 11e

The matrices of Interactions:

DMi

DMj

Input/Stimulus

Output/Response

SA IF RSCI s i

SA IF RSCI

e j

C ij

H ij

F ij

G ij

e i

s j

TP

TP


The Lattice Algorithm

• Remy and Levis (1988) introduced a computational framework for designing organizational architectures based on Petri Nets and Lattice Theory.

• The Lattice Algorithm– A set of structural constraints was established– Additional problem-specific constraints were possible– The DM model was expressed in Petri Net form– For a given number of DMs, the algorithm determines all possible

organizational structures that meet the constraints– The algorithm does this in a constructive way – not by

enumeration– The algorithm is based on the invariant theory of Petri Nets – The solution set has the structure of a Lattice with the minimally

connected organizations (MINOs) as the lowest solutions and the maximally connected ones (MAXOs) as the highest ones.

– Since a Petri net formulation is used, the model is executable; consequently, it can be used to analyze performance


Lattice Algorithm

0x

x0C

0x

x0H 1x s

0x

x0G

0x

x0F x1 e

p2

p3

p4

p5

p6

p7

p8

p9

p10

p11

p12

p13

p14

p15

p16 p17

p18

p19p20 p21

DM1

DM2

RSSA IF TP CIt11 t21 t31 t41 t51

t12 t22 t32 t42 t52

t0 t5

p2

p18

p22

DM1

DM2

RS

SAt11

t52

t0 t5

m1 m2 m3 m4 m5

M1 M2 M3 M4 M5

User defined Constraints

Universal & Kernel Nets

Incidence Matrix

Simple Paths

MINOs and MAXOs

From user defined constraints to feasible structures identified by boundary elements

Structural Constraints


Solution Space

Org41 Org40

Org39Org38 Org37Org36

Org35 Org34Org33 Org32Org31

Org29 Org26

Org24 Org23Org22Org21Org20

Org19

Org18

Org17Org16

Org15

Org14

Org13 Org12 Org11

Org10(M5)

Org9(M4)

Org8(M3)

Org7(M2)

Org6(M1)

Org5(m5)

Org4(m4)

Org3(m3)

Org2(m2)

Org1(m1)

1

32

831

2

81

4134

4 31

32

631

2

61

4134

4 31

4 413 11

75 12 104

3

8 3

3

63

8 6

7 5213 11

8 6131112 10

8 6313 112 12

2

2 10

2

7 5 3 213 11Org28 Org30 Org27 Org25

m1 m2 m3 m4 m5

M1 M2 M3 M4 M5


Using Cultural Attributes

• Interactional constraints help a designer determine classes of physically similar feasible organizations by setting specific conditions that limit the number of various types of interactions between decision makers.

• If one could make a transition from cultural attributes to interactional constraints, one could use the Lattice Framework to generate the class of organizational structures preferred by a group.


Modeling Cultural Attributes

Hofstede distinguishes dimensions of culture that can be used as an instrument to make comparisons between cultures and to cluster cultures according to behavioral characteristics.

– Power Distance Index (PDI) focuses on the degree of equality, or inequality, between people in the country's society. A low power distance ranking indicates the society de-emphasizes the differences between citizen's power and wealth.

– Individualism (IDV) focuses on the degree the society reinforces individual or collective achievement and interpersonal relationships. A low individualism ranking typifies societies of a more collectivist nature with close ties between individuals.

– Masculinity (MAS) focuses on the degree the society reinforces, or does not reinforce, the traditional masculine work role model of male achievement, control, and power. A low masculinity ranking indicates the country has a low level of differentiation and discrimination between genders.

– Uncertainty Avoidance Index (UAI) focuses on the level of tolerance for uncertainty and ambiguity within the society - i.e. unstructured situations. A low uncertainty avoidance ranking indicates the country has less concern about ambiguity, hence is less rule-oriented, more readily accepts change, and takes more and greater risks.


Modeling Cultural Attributes

• Olmez (2006) used linear regression on the 4 Hofstede dimensions to compute additional constraints to be placed on the number of interactions allowed

dY = c + (PDI) + (UAI) + (MAS) + (IND)

where Y is #F or #G or #H or #C

For example:

#F ≤ 2, #G = 0, 1 ≤ #H ≤ 3, #C = 3

• These were introduced in the lattice algorithm as additional structural constraints.

• The extended lattice algorithm is called the C-Lattice Algorithm


C-Lattice Algorithm

Get MINOs and MAXOs

Build Lattices

For each Lattice

Generate C-MAXO and C-MINO

MINO connections CC upper

boundaries?

Build C-Lattices

Next Lattice?

No

Yes

No

Yes


A Hypothetical Case

• An island nation is in crisis due to an earthquake that caused substantial damage to the infrastructure.

• Timely Humanitarian Assistance & Disaster Relief is needed

• There are also security issues regarding US assets on the island

• PACOM directs and Expeditionary Strike Group that is in the area to proceed to the island

• Two other nations (A & B) have naval assets near the island and offer immediate support; they are willing to be part of a coalition force.

• The coalition is to be organized using a divisional structure consisting of five entities:

– ESG/CC (US)

– MEU/CC (US)

– ACE Air Combat Element (US, A)

– GCE Ground Combat Element (US, A, B)

– CSSE Combat Service Support Element (US, A, B)


The following command structure is proposed

Problem Setting

Country PDI IND MAS UAI

US 40 91 62 46

A 38 80 14 53

B 66 37 45 85

Hofstede Dimensions for the three countries


Approach

• Using the C-Lattice algorithm , organizational structures for the ACE, GCE, and CSSE for the countries that can support each element.

• The organizational structures reflected the cultural differences of US, A and B.

• All admissible combinations were implemented in CAESAR III and simulated for the given scenario

• One measure of performance was the number of tasks not served


Results

• ESG/CC – MEU/CC – ACE – GSE - CSSE

0 5 10 15 20 25

US-US-US-A-A

US-US-US-B-A

US-US-A-A-A

US-US-A-B-A

US-US-US-A-B

US-US-A-A-B

US-US-A-B-B

US-US-US-B-B

US-US-US-US-US

Series1

While US alone is the most efficient structure w.r.t. this metric, the US-US-US-B-A coalition force has good performance and is much preferable for this scenario. Note the decrease in performance, if the A and B roles are reversed (20 vs. 11%)

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