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## WHAT IS IT?

CLOD (Computational Laboratory of Organizational Design) is a virtual laboratory of organizational design based on the March model on exploration and exploitation in organizational learning (1991) . The object of this work is verify in which environmental conditions a cognitive system capable of managing vague descriptions of reality is more effective than a formal system which instead provides precise descriptions. The hypothesis, certainly not original, is that under conditions of high turbulence, a vague description of the environment allowed by natural language gives rise to more effective performance than a precise description.
The contribution of the laboratory would be twofold: firstly, the cellular automata model of March is transposed in an agent-based environment and then extended to be used as a virtual lab supporting organizational design; secondly, a fuzzy version of the model is proposed in order to analyse, through generative experiments, the differences between crispy and fuzzy organizational learning approaches to environmental complexity.

## HOW IT WORKS

In the CLOD the main agents are the environment and the organization. The external environment is an unique agent, called "customer". While the organization is represented as a hierarchy of three levels. At the bottom, there is a class of agents called “members”. At the second layer, there is a subset of best performers among members, called “Elite”. Finally, at the top layer, there is the “leader”.

The leader is responsible to deliver the organizational answer to the customer, who expresses her/his needs through a string of 30 binomial choices (YES/NOT), randomlly assigned by 1 and -1.
Both members (Elite included) and the leader represent their beliefs about customer’s requisites through a string of 30 elements. In particular, beliefs of organizational actors could be each equal to 1, -1 or 0. Where, the value 0 in one of the dimensions of the vector representing an organizational actor means that she/he is not able to express any belief on the corresponding dimension of the customer representative vector.

The objective of the organization in the CLOD is the achievement of the maximum level of agreement between customer's needs and the answer the organization produces to meet customer requisites. In this kind of framework, the performances of the organization are evaluated by the customer and are measured in terms of fitness between the vector of customer's needs and the vector representing the answer of the organization (the vector of leader's beliefs). In order to figure out the customers needs two types of mechanisms partially resume the learning mechanisms of March’s model, contribute to spread the knowledge throughout the organization. On the one hand, there is a top-down learning based upon the principle of conformity: the knowledge of each member of the organization is compared with that of the leader; members beliefs change according to those of the leader with a probability called Members-conformity-degree%.
At the same time, best performing members (valuated on a Score defyned later) are selected as belonging to the Elite.
Just Elite members can interacts with the leader through an additional learning mechanism: the disagreement between beliefs of the majority of the Elite and those of the leader leads to a modification of the latter with a different probability named Leader-listening-ability%. According to the March’s model, if leader differs from the Elite view on a single dimension, the probability that it will be unchanged is (1-(Leader-listening-ability% )/100)k , where k (k > 0) is the number of members (within the Elite) that share the leader beliefs minus the number who do not. The probability that the beliefs of leader (on any particular dimension) will be adjusted to conform to the majority beliefs of the Elite depends not only on his ability to listen, but also on the level of agreement among the Elite members. Over time, the leader affects the beliefs of its organizational members, even while the leader itself is being affected by the beliefs of those members. Through these two mechanisms, the leaders and the members become more homogenous and converge over time to a stable equilibrium.

The organizational performances are evaluated depends on the agreement between members or leader beliefs and customer’s requisites. All members and the leader are aware of their overall fitness represented in term of Score. The Score is given by the number of beliefs that match customer’s requisites minus the number of disagreements, normalized on the number of dimensions. A different concept is that of Knowledge. The Knowledge is measured at any time as the proportion of customer’s requisites correctly represented in the beliefs of leader and on average in members’ beliefs. Neither the members nor the leader have any information of customers' requisites. In this context, both leader and the members can reproduce false beliefs in their processes of exploration and exploitation.
Therefore, the Score produces an assessment of performances that takes into account both accordance and disagreements of beliefs with customer’s requisites; the Knowledge is an external performance measure and has been conceived as normalized Hamming’s distance between beliefs of members and of the leader from customer’s requests.

Moreover, the model provides that the environment could be characterized by a certain level of turbulence, which is implemented as the probability of changes of customer's needs, happening according to a probability named turbulence-degree. The turbulence represents the complexity of the environment, in terms of intensity of surprises coming from technology, regulations, and markets. The turbulence is modeled through a change of the customer requisites that happens according to a probability named turbulence-degree. Additionally, it is possible to define the frequency of turbulence and the life span of this phenomenon: two parameters are introduced named respectively Turbulence_span and Stability_span, corresponding to two sliders in the NetLogo interface.The Turbulence_span is expressed in number of ticks and represents the length of the period in which the customer vector could be affected by the turbulence. Conversely, the Stability_span represents the number of time periods in which the external environment can be considered stable. By setting the values of Turbulence_span and of Stability_span, it is possible to define the frequency of periods of turbulence and their impact in terms of time. Furthermore, the complexity of external environment is taken into account. In our proposal, the number of dimensions characterizing the customer’s needs is a parameter that can be modified through a slider in the lab interface. Increasing the size of customer requirements’ vector simulates a more demanding market. Accordingly, the increase in customer dimensions implies a corresponding increase in the number of leader and members vector dimensions.

## HOW TO USE IT

The interface of CLOD lab consists of buttons, sliders, choosers and other output displays elements. Each of these elements permits to start a procedure or to set the value of a variable in order to define specific experimental sets. On the center of the user interface there is a window in which the “world” of the model is made visible. The simulation environment is represented by concentric circles of different radius (growing radius implies gradually decreasing in knowledge of members and of the leader). At the center of these circles there is the customer whose position is stable during simulation time. At the set-up each agent (members and leader) is located in the space at a certain distance from the center according to its level of knowledge. Once the simulation is started, learning and organizational processes allow members and leader to learn and change their beliefs seeking to move closer to customer requirements.
To start the simulation, therefore, it is necessary to define ininterface:
1) environmental parameters
2) learning parameters
3) choose the simulation stop conditions
4) organizational parameters
5) choose the evaluator
6) choose the extension
Finally throught the buttons of Setup and Go the simulation runs. According to the March model the simulation ends when an equilibrium is reached (all members and the leader share the same belief with respect to each dimension (March, 1991)). In the CLOD it is also possible to set a maximum number of ticks as a stop condition.

## THE FUZZY EXTENTION

In the Fuzzy extention:
1. The concept of stratified organization on three levels remains unchanged in this extension. There is a group of organizational members, one leader and one sub-group of members called Elite.

2. There is a customer to which it is assigned a vector with the same characteristics described for the Crisp CLOD Laboratory.

3. Members estimate the reality dimensions through fuzzy beliefs represented through the dual truth model (for an extensive presentation of the dual truth model see Iandoli and Zollo, 2008). Each member tries to forecast which is the value of each dimension of the customer’s requisites vector (Requisites(i)). The jth member’s guesses are represented by dual fuzzy beliefs (lvij, rvij) where lvij and rvij are computed as follows.:
lvij = (c + 2 – p)/(c + 2)
rvij = (p + 1) / (c + 2)
where c is the cardinality of the term set, p is the position of the term in the term set starting from the lowest term.
So to the jth member is computationally represented by two arrays LVj and RVj , of length #dimensions, containing, respectively, the left and the right values of the truth couples. This is the major difference between the fuzzy extension of CLOD and the crisp one. In the crisp CLOD model, as in March, members’ guesses are represented by binary beliefs, i.e. an agent bets that the ith event will either occur or not. In the fuzzy extension, the guess about the occurrence of the ith event can be described by sentences like “I am pretty confident that the event will occur” or “I am not very sure this event will occur”, etc.
At each tick, members can modify their beliefs about customers’ requisites through the conformity process (learning form the leader with probability equal to the member-conformity-degree%, except when the label “I don’t know” appears ) as we describe at point 9.

4. Also the leader is represented by a couple of two vectors of #dimensions elements lv_l and rv_l, containing, respectively, the left and the right values of the truth couples. This leader will represent the organizational knowledge about the customer and will be determined by aggregating the beliefs of the members as described below;

5. We define for each member and for the leader a new vector called respectively orientation_m and orientation_l. These vectors define the orientation of members’ and leader’s beliefs. This is one of main conceptual and computational differences of the present extension of the March’s model and that proposed in the paper of Iandoli et al of 2009. In particular, considering the jth member, if his left value on the ith element of the customer vector is lvij > rvij (lvij < rvij ), the ith element of orientation vector of the member will be -1 (1). Only when lvij = rvij ,the ith element of the orientation vector will be 0.

6. Orientation vectors are used to compute the scores of the members and of the leader. In fact, the scores are calculated taking into account the agreements and the disagreements between orientation vectors and the customer’s requisites vector. This mechanism is used to model the aggregation of preferences and beliefs of the agents and represents an additional important improvement of the previous fuzzy extension of Iandoli et al. (2009).

7. Furthermore, members' orientation vectors are used to calculate the majority of elite's beliefs. In fact, to build the majority vector of the elite beliefs, the fuzzy code uses the orientation vectors of the members by counting the majority of 1 or -1 inside them for each dimension. This means that the majority concept is not based on a close convergence about a belief (represented by a truth couple), but instead on the same orientation (left or right) on that belief. This mechanism can be conceived as a sort of voting mechanism.

8. The values of truth couples depend on the cardinality of the chosen term set. The cardinality indicates the degree of precision with which the agents express their judgments (increasing cardinality corresponds to fine grained belief).

9. The learning mechanisms of members and leader have been also amended with respect to the crisp and to the previous fuzzy version. Assuming a disagreement between leader's orientation vector and a member's orientation vector on the ith dimension, the latter will change its dimension with probability member-conformity-degree%. The member will change its couple values (lvij , rvij) moving towards his closest fuzzy function in the direction of leader orientation. The same happens when the leader learns from the Elite. This mechanism implies that learning itself is slow and gradual and that, while agents move in the direction of a new orientation, they continue in maintaining their differences in perceiving external reality.

10. The equilibrium is reached and the simulation stops when the orientation vectors of members and of the leader are characterized by the same values.

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