Dr. Tsygichko V.N., Popovich A.U.

Institute for Systems Analysis of Russian Academy of Sciences

Synthesis of Organizational Structures

Synthesis of Organizational Structures is one of fundamental interdisciplinary problems of modern science. An organization’s chances for success in attaining it’s goals significantly relies on the capabilities of it’s structure. Nowadays, when the world is changing with an increasing rate, issues concerning synthesis and dynamic modification of organizational structures come to the foreground.

Thanks to a broad variety of studies that reveal features of real organizations (and especially works of Henri Mintsberg [9,58], which generalize principle researches on organizational structures, dominant concepts and rich empirical data), we have a comprehensive fundament for a formal theory.

However till now there was no formal theory for synthesis of organizational structures, nothing that could be applied to real organizations and provide us with analytical decision making support tools. Existing formal theories are mostly focused on a research of hypothetical idealized structures with formal inter-element relations given and are rather alienated from the studies of real organizations [5, 33]. The main problem and the cause of most failures is the absence of basic parameters that determine structure formation. Without an explicit definition of these parameters it’s impossible to form a reasonable formal theory for Synthesis of Organizational Structures.

The approach we are going to present derives from fundamental axioms and principles of systems analysis and decision making theory and is based on an analysis of features of organizational systems, those genesis and operation.

Let us examine functioning and development of organizational systems.

Structurization of management and control processes constructs a hierarchic entity of interlinked subsystems. A control subsystem can be defined as a multilevel structure consisting of interlinked subsystems the elements of which are empowered to make decisions. The subsystems and elements form a hierarchy. Higher level element states a problem to a lower-level element and influences it by changing problems, introducing limitations or restrictions, or enumerating alternative actions. A low-level element is free in its actions in executing assigned tasks within the framework of specified restrictions or alternatives. A higher-level element organizes interaction of elements (subsystems) subordinated to it for the purpose of achieving goals (performing tasks) assigned to it by a higher-element. A lower-level element influences a decision by a higher-level element by informing it on its state and the consequences of the decision it makes. A higher-level element can correct or alter its decision in conformity with this information. Thus there occurs coordination of lower-level decisions with the goals of the entire organization.

The informational structure of the hierarchic control subsystem in question reflects the hierarchic nature of the organization. In an actual control subsystem this is reflected in the fact that a specific level of description of system state corresponds to each control component. Higher-level control elements deal with larger subsystems and broader aspects of system activity. Description of system state at higher levels is less detailed than at lower ones, while the problems (tasks) resolved at higher levels contain more uncertainty and are more difficult to solve.

Formally control bolls down to coordination of the activities of lower-level subsystems, which in practice is accomplished by formulating tasks for subsystems of all levels.

Formulation of tasks by higher-level elements takes place in the language of the parameters of these elements, which per se gives certain freedom of choice of control parameters for lower-level elements. The temporal structure of control system functioning is also heterogeneous. The higher the level of control, the greater the period of decision-making and the overall duration of execution of assigned tasks.

The enumerated properties of interlevel relations determine in large measure the nature of functioning of a control system as a hierarchic structure.

Incomplete information on the situation developing at any given moment in the activities of target systems is one of the principal features of processes in these systems. This means that decision-making in all control components takes place in conditions of a different degree of uncertainty, which substantially affects the quality of decisions and, consequently, the course of functioning processes.

Let us analyze this aspect in a more detailed way. Decision making is based on a goal-oriented process of uncertainty resolution. Precise values of decision-targeted parameters () are rarely known, but decision maker can always operate ranges of possible values ().

For each decision there exists an allowable accuracy of input information, i.e. minimal allowable ranges of decision-targeted parameters -- . Specification of for all defines allowable region of uncertainty . Introduction of allowable range of accuracy makes it possible to convert a continuous set of numerical values of state description parameters to a bounded finite set and to perform practical calculations. Let the allowable ranges of accuracy be determined for all parameters of description of a certain social entity, and let the ranges of determination of these parameters be known (where is the region of determination of the state of the target entity. We shall divide the ranges of possible values of components of vector into segments of length . There will be segments in each interval.

(1)

The probability that the numerical value of parameter will fall within the segment, , shall be designated . Then, by virtue of the independence of components of vector , full entropy of decision will be written as

. (2)

Analytical process of uncertainty resolution that constitutes the core of decision making is directed on reduction of initial region to a certain final region, i.e. reduction if initial entropy (full entropy at the beginning of the decision making process) to residual entropy (full entropy at the end of the process). Entropy approach allows us to introduce quality of decision as a function of uncertainty resolution degree:

,

, (3)

where is time given for the certain decision making.

(determines the degree of risks the decision maker takes if he makes a decision at the moment . )

The most effective process of uncertainty resolution is based on the principle of sequential resolution of uncertainty. This principle states that the process of systems analysis should consist in movement from determination of the goals and conditions of development of an organization as an integral entity toward determination of objectives, mechanisms of functioning, conditions and criterions in detail and for each subsystem and element. In the process of this movement, at each level of system representation, beginning with the highest level, one selects for further examination from the many possible development alternatives only those which merit attention from the standpoint of system goals, while the remainder are discarded and no longer considered. Correctness of selection of alternatives at each level of synthesis is verified by means of analyzing them at a lower, more detailed level of representation. The initial alternatives are refined based on the results of this analysis, and their number is reduced. Such organization of analytic process makes it possible to isolate for analysis only a small portion of the infinite number of possible sets of parameters values and to determine the most rational ones from this limited number of alternatives.

Thus the principle of sequential resolution of uncertainty presupposes organization of an iterative procedure of analysis, downward through the hierarchy of descriptions of a organizational system, whereby one can avoid consideration of the complete set of development alternatives. The mechanisms of synthesis and detailing serve as the instrument of implementation of this procedure; these mechanisms ensure informational unity of multilevel systems description. Introduction of measure which reflects the requisite degree of aggregation of description of the system and its elements at different levels of generalization is one possible path of constructive continuation of the principle of sequential resolution of uncertainty. A complexity threshold [16] can be adopted as such a measure.

The procedure of systems analysis, organized with observance of the principle of sequential resolution of uncertainty, constitutes a certain invariant of the thought process. It is therefore natural that a constructive form of representation of this process is linked first and foremost with the properties of thinking. Such features of thought process as ability of purposeful multilevel abstract reflection of reality, ability to classify, plus others, involve one of its most important properties – limitedness of the number of factors and conditions with which consciousness can operate simultaneously in solving any problem. These properties are being actively studied at the present time, and the indicators of this limitation are extensively utilized in practice.

In decision making theory complexity threshold is a measure of allowable dimensionality of task which could be solved in a given period of time.

Complexity threshold obeys to the following axioms:

- a specific complexity threshold corresponds to every specific task;

- complexity threshold is a nondecreasing function of time given for the task solution.

The introduced above concepts complexity threshold and quality of decision allow us to advance a mathematical formulation for Synthesis of Organizational Structures.

Let be a graph that represents the structure of control in the given system, and let the function

(4)

be given.

The goal is to find a graph where function (1) finds its minimum on conditions that (or ) and

, _; (5)

, (6)

where - admissible quality of control problem solution,

- admissible uncertainty resolution degree (for the control problem),

- the ordinal number of problem in the sequence of problems being solved at the stage of decision making process,

- the number of such problems,

- a priory entropy for the stage of decision making process,

- a priory entropy for the stage of decision making process,

_{- complexity threshold,}

_{-the organization’s functional cycle.}

_{If the organization’s functional cycle is given a priori or is determined by technological process, than the synthesis problem could be formulated in the following way:}

_{Find structure of control}

, (7)

_{that satisfies the conditions (5) and (6).}

Synthesis of Organizational Structures is one of the most complicated problems systems theory has. Construction of functions (4) and (7), and calculation of complexity threshold for particular control problems arise the main difficulties.

The synthesis process can’t be determined by any general optimization scheme. This means that functions (4) and (7) are iterative procedures with human decisions involved at each step. These procedures could be described by algorithmic functions only. Our goal is in finding the algorithmic functions that approximate real processes in the most accurate manner. Principle of sequential resolution of uncertainty can help us ones again – we’ll start by modeling general features of the process, and then we’ll work on determination of precise details.

Our research of real organizations’ genesis has resulted in extraction of two main parameters that determine organizational structures. We’ve called these parameters “complexity” () and “payload” (). We must underline that each of these parameters has a complicated inner structure, and takes different forms in different organizations. Let’s illustrate these parameters by a simple example. What kind of tasks do we consider to be difficult? Typing, for example. It seems to be a very easy task. Every user of personal computer can do that. However if we need to type several hundreds of pages in a couple of hours, we think it to be impossible.

On the other hand, some mathematical problem. Let it be one of the problems that take about 5 minutes from a specialist to solve them, and let its solution fit in one page. However a person who doesn’t have any qualification in mathematics won’t be able to solve it, even if he has a lot of time in his hands.

This example illustrates two sides of difficulty. We called these sides “complexity” (it causes the sort of difficulties illustrated by the second example) and “payload” (this is what we run across in the first example).

An employee , who is assigned to a certain task , has to have enough time to be able to deal with the task’s payload and enough qualification to deal with its complexity . It’s convenient to handle sort of limit-parameters: complexity limit as the maximum complexity of task the employee can deal with, and payload limit as the maximum amount of time he can spare. Ability or inability to solve a problem is determined not by the problem’s and , but by the ratios .

We must underline that the meaning and inner structure of the parameter complexity differs between tasks of different types. If, for example, we consider tasks for security department, we bring to the fore requirements on tactical training and physical fitness. On the other hand, if we analyze work of sales department, we are much more interested in the employees’ abilities to work with customers. The more uncertainty of the tasks is, the more significant analytical and creative abilities of the employee are.

For the general case we can consider a set of types of tasks (or specializations) urgent for the certain organization. For each of the type we must construct an independent gradation of complexity. (Each level at each specialty has its own meaning.) In other words: , where -the set of specializations urgent for the studied organization.

Let’s introduce a function of expected effectiveness , which reflects the quality of task solution a manager can expect, if he entrusts employee with task .

At the current stage of approach, we can suggest the following approximation.

, (8)

where

,

-the number of specialization urgent for the organization,

,

- the number of tasks the employee is entrusted with at the current circle of the system’s functioning,

- the term that approximates manager’s contribution to the task solution (which reflects such functions of manager as formulation of tasks, consulting support, control and so on).

The approach presented above has brought us to development of the first general Synthesis of Organizational Structures Theory. The theory gave us a fundament for an applicable synthesis method, which has already resulted in a creation of program complex “HOSS” (“Hierarchical Organizational Structures Synthesizer”), a decision making support tool for an analysis, synthesis and reconstruction of organizational structures.

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