Lecture
As was shown in Ch. 1, the need to make a management decision arises precisely when the state of the managed system (the control object) is unsatisfactory from the standpoint of the DM's (the controlling subject's) goals, i.e., precisely when there is a so-called problem situation (PS) .
Definition
The problem situation of a control object is defined as an unsatisfactory state of the managed system from the standpoint of the DM's goals.
It is assumed here that every management decision made must ensure the transition of the managed system from an unsatisfactory state to an optimal (or best) one from the standpoint of the controlling subject's goals. In general, the process of finding, developing, adopting and implementing the optimal (or best) management decision is carried out in several stages, which we have called the «life cycle of a management decision» (see Section 1.3).
Definitions
A decision-making problem (DMP) for a specific problem situation is the problem of finding the management decision that is optimal (or best) from the standpoint of the DM's goals for transitioning the managed system from an unsatisfactory state to a state that satisfies the controlling subject.
A feasible solution (or feasible alternative) of a DMP is a management decision for the given problem that satisfies all the constraints specified in it (resource, time, logical, etc.).
An optimal (or best) management decision of a DMP is a management decision that transitions the managed system from an unsatisfactory state to an ideal state, i.e., to a state that satisfies the DM and is the goal of the decision being made.
The process of making a management decision involves the performance of a number of stages and procedures. These include, for example: analysis of information related to historical data and data on significant external and internal factors; identification of relationships between factors and the strength of their interaction with one another; forecasting the most probable scenarios for the development of external and internal conditions that significantly affect the state of the control object; generating possible options for changing the problem situation; determining the goals and criteria for the sought-after management decision; determining the feasible set of solutions; generating alternative solution options; refining the goals and criteria of management; evaluating the preferences of feasible alternatives of the DMP; substantiating and making the final choice of the optimal (or best) management decision .
In decision theory, various methods for modeling problem situations are often used to carry out a preliminary analysis of the PS and to correctly choose the goals and criteria of the sought-after management decision. In this context, by modeling a problem situation we mean the process of studying the state of a real managed system, involving the construction of some abstract or material model of it that is capable of adequately reflecting (replacing) the existing PS at certain stages of its study.
Please note!
The purpose of modeling a problem situation is to determine the goals, criteria and methods for forming the sought-after management decision on the basis of studying some model of it, which makes it possible to analyze historical and current data on the state of the control object, to identify significant external and internal factors and their relationships, and to determine possible scenarios for the development of external and internal conditions that significantly affect the state of the managed object.
The term «problem situation» is used in decision theory in two senses. First, a problem situation is usually understood as the fixed (initial) state of the control object, which does not satisfy the DM's goals and prompts him to seek an appropriate management decision to change the unsatisfactory state of the managed system to one that satisfies him. Second, a problem situation itself often becomes the object of special study using various modeling methods, with the aim of studying it in more detail in order to improve the quality of the management decisions made for a specific DMP.
When constructing mathematical models of problem situations, the first stage usually involves constructing a conceptual model that approximately describes the initial situation and serves as the basis for further refinement of its structure, properties and relationships. At the next stage, the model is formalized taking into account the identified properties, characteristics, relationships and operations of the original control object. In the resulting mathematical model, the corresponding symbolic operations and constraints are introduced and objective functions are specified, which makes it possible to move on to studying it in the abstract. The next stage of researching and refining the mathematical model is checking it for correctness and adequacy with respect to the original problem situation in a specific DMP. After the necessary adjustment of the mathematical model being formed and a final check of its adequacy, it is simplified. The process of simplifying the mathematical model provides for the possibility of excluding from it non-essential elements and (or) their relationships, which makes it possible to optimize resources (time, cost and means) while preserving the adequacy of the model. On the basis of a mathematical model of the problem situation formed in this way, and using various methods (simulation modeling, mathematical modeling, functional modeling, expert systems, cognitive modeling , data mining, etc.), it is studied and the goals, criteria and methods for forming the sought-after management decision of a specific DMP are determined.
Note that the choice of methods for modeling problem situations largely depends on the specific DMP. In particular, it depends on the conditions (certainty or uncertainty) under which the modeling takes place and on what kind of initial information it is based (for example, for weakly structured data). Thus, for example, when choosing the simulation modeling method , we must understand that this approach, as a rule, requires a large amount of data, complex algorithmization to describe the behavior of complex objects of the mathematical model, as well as significant computing power using a computer. In this sense, the simulation modeling method makes it possible to obtain good results in modeling, but it is quite labor-intensive and costly. Unlike the simulation modeling method, for example, when studying a small analytical model that is difficult to represent in a strictly formalized form, it is considered more appropriate to apply methods of expert forecasting or functional modeling based on decision tables , which are simpler to use and do not require significant resources.
Note that quite often, when modeling problem situations for a specific DMP, the modeling is carried out using several available methods, after which the results obtained are compared, and the one that, from the point of view of experts or the DM, most adequately describes the original situation is selected, which makes it possible to improve the quality of management decisions made.
Comments