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

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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


  • 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.


The DM Model

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

The Interacting DM Model

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

Interactions from DMi to DMj

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

Solution Space

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

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)

Problem Setting


  • 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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