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Computational Models of Multi-National Organizations Alexander H. Levis Smriti Kansal A. E. Olmez Ashraf AbuSharekh Phoenix, AZ 1 April 2008
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A. H. Levis

2. 12/6/2018
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.
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A. H. Levis

3. Outline Decision Maker Models Lattice Algorithm Cultural Attributes
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Outline
Decision Maker Models
Lattice Algorithm
Cultural Attributes
C-Lattice Algorithm
Example using CAESAR III
Results
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4. 12/6/2018
The DM Model
A five stage, model was postulated as an extension of Herbert Simon’s stimulus – response model:
Situation
Assessment
Response
Selection
Two stage S-R model of Simon SA CI TP IF RS
Five Stage DM Model
IF: Information Fusion
TP: Task Processing
CI: Command Interpretation
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A. H. Levis

5. The Interacting DM Model
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The Interacting DM Model
The additional stages were necessary for creating different types of interactions among decision makers SA CI TP IF RS
Results
Sharing
Information
Command
Input
Problem:
Algebra of Interactions
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A. H. Levis

6. Interactions from DMi to DMj
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Interactions from DMi to DMj
DMi
Output/
Response
Input/
Stimulus
DMj
The matrices of Interactions:
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A. H. Levis

7. 12/6/2018
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
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A. H. Levis

8. Lattice Algorithm Universal & Kernel Nets Incidence Matrix
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Lattice Algorithm
Universal & Kernel Nets
Incidence Matrix
Simple Paths
MINOs and MAXOs
User defined Constraints
Structural Constraints
From user defined constraints to feasible structures identified by boundary elements
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A. H. Levis

9. 12/6/2018
Solution Space
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A. H. Levis

10. Using Cultural Attributes
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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.
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A. H. Levis

11. Modeling Cultural Attributes
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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.
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A. H. Levis

12. Modeling Cultural Attributes
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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
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A. H. Levis

13. C-Lattice Algorithm 12/6/2018 A. H. Levis Get MINOs and MAXOs
Build Lattices
For each Lattice
MINO connections  CC upper boundaries? No
Yes
Generate C-MAXO and C-MINO
Next Lattice?
Yes No
Build C-Lattices
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A. H. Levis

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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)
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A. H. Levis

15. Problem Setting The following command structure is proposed
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Problem Setting
The following command structure is proposed
Hofstede Dimensions for the three countries
Country
PDI
IND
MAS
UAI US 40 91 62 46 A 38 80 14 53 B 66 37 45 85
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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
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A. H. Levis

17. Results ESG/CC – MEU/CC – ACE – GSE - CSSE
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Results
ESG/CC – MEU/CC – ACE – GSE - CSSE
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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A. H. Levis