Stanford L. Optner. Systems Analysis for Business and Industrial Problem Solving
Stages of Optner's systems analysis methodology:
- Identify symptoms.
- Determine whether the problem is relevant.
- Define the goal.
- Uncover the structure of the system and its defective elements.
- Determine the structure of possibilities.
- Identify alternatives.
- Evaluate alternatives.
- Select an alternative.
- Formulate the solution.
- Gain acceptance of the solution from executors and managers.
- Launch the implementation process.
- Manage the implementation process.
- Assess the results and consequences of implementation.
A problem is defined as a situation involving two states: one called the existing state and the other the proposed state. The existing state is represented by the current system; the proposed state is represented by a hypothetical or desired system. Each state contains a set of objects, properties, and relationships united within a process, and each can be described as a system. To move from the existing state to the proposed one, the current set of objects, properties, and relationships must be changed. A change in objects may mean replacing a piece of equipment rather than reorganizing personnel; a change in properties may take the form of increasing headcount; a change in relationships may introduce a new distribution of responsibilities.
A problem is characterized by the unknowns it contains and by its conditions. There may be one or many areas of the unknown. An unknown may be definable in qualitative but not quantitative terms. A quantitative characterization may take the form of a range of estimates representing the assumed state of the unknown. In the classical sense, unknowns are quantities to be determined. Defining one unknown in terms of another may therefore be contradictory or redundant. Unknowns can only be expressed in terms of what is known — that is, in terms of things whose objects, properties, and relationships have been established. The known is defined as a quantity whose value has been determined.
The existing state (the current system) may contain both knowns and unknowns; this means that the presence of unknowns need not prevent the system from functioning. The existing system is, by definition, logically constituted, but it may fail to satisfy a constraint. Thus, the mere functioning of a system is not the ultimate measure of its adequacy, since some systems may function perfectly well and yet fail to achieve their goals. Goals can only be defined in terms of system requirements. System requirements are established by means of a condition that specifies objects and properties in their proper relationships.
System requirements serve as a means of recording unambiguous statements that define the goal. Although system requirements are stated in terms of objects, properties, and relationships, goals may be expressed in terms of a desired state. For a given set of system requirements, the goals and the desired state may coincide entirely. If they differ, the requirements are said to represent the desired system. In general, goals are identified with the desired system.
The gap between the existing and desired systems constitutes the problem. The purpose of action is to minimize this gap. Maintaining or improving the operation of the system is understood in terms of this gap between the existing and the desired state. Maintaining the existing state means keeping the system's output within prescribed limits. Improving the system's state means obtaining output superior to, or beyond, what is produced under the existing state.
A solution determines how the gap between the existing and the desired state is to be bridged. A solution is therefore the means by which one state is transformed into the other. It describes the differences between the two states in terms of objects, properties, and relationships, and specifies how this bridging structure must be introduced to obtain the proposed state. The solution is implemented through feedback control consisting of an output model, a conformance check, and an action model.
Problem solving is carried out through a learning process. Learning is defined as a cognitive act resulting from stimuli. Cognition encompasses a broad range of intellectual activities, including the recognition of present or future patterns. Recognition is achieved by applying a criterion to the output. Cognition is one of the fundamental functions required to bridge the gap between the existing and the desired system. Other functions involved in learning include formulating the means by which one system state is transformed into another and the idea that indicates, a priori, how the desired state may be reached through changes to existing objects, properties, and relationships.
A successful formulation of the problem may amount to half its solution. For that reason, the systems analyst gives special attention to the earliest possible assessment of the problem's parameters, properties, and relationships. It is not always possible to introduce "ready-made" goals into a problem; goals proposed by someone else may prove insufficient. Moreover, the systems analyst can accept a proposed goal only after determining, through problem formulation, that it is free of redundancy and contradiction. A problem that is "half solved" through formulation is not a solved problem in the strict sense, but its formulation does mean that the main elements of the problem have been properly identified and related. For this reason, problem formulation may also be called problem definition.
The initial steps in formulating a problem aim at: 1) composing an initial problem statement; 2) interpreting this statement in relation to the various parts of the problem; 3) interpreting the facts pertaining to the problem; and 4) refining the initial problem statement. During the initial investigation, the analyst separates the known from the unknown in order to make the initial statement meaningful.
The counterpart of problem formulation is the development of a goal definition. The term "goal" describes the result to be achieved. A goal may take the form of a maximum (or minimum) whose magnitude has yet to be determined, or it may specify a range of values within which the solution must fall. In all cases, a goal is a desired outcome of activity.
The combination of goals that set the course of action and the constraining relationships that limit them forms the constraint framework within which the study of the problem begins. A constraint is the sum of rules, regulations, and guiding principles — whether self-imposed or externally imposed — that define the boundaries of the problem. Every problem must have a definable set of constraints. Compatibility between goals and constraining relationships is essential. Without agreement on constraints, agreement on solutions is highly unlikely. It is meaningless to speak of a "solution" if the interested parties cannot agree on the problem or on the constraints that define it.
When the systems analyst establishes the condition of the problem, he sets the limits of the investigation and, by extension, the boundaries of the constraint framework. In mathematical terms, conditions may be sufficient, redundant, or contradictory; they can take no other forms.
A condition is redundant if it contains unnecessary elements — elements that tend to cause waste. A condition may also contain a contradiction. A contradictory element is one so closely related to another that if one is true, the other must be false. The consequence of a contradictory condition is that parts of the problem are inconsistent with one another and therefore mutually opposed.
A sufficient condition is met when the constraints are compatible with the proposed goal and the goal is defined adequately with respect to the system requirements. Sufficiency implies exactness: it contains everything necessary to satisfy the requirement, without deficiency and without excess.
Problems with poorly defined structures are generally "solved" by accepting relative rather than absolute assessments without proof. Problems of very broad scope, problems whose solutions depend on things not yet developed, and problems involving hypotheses about combining systems that cannot yet be defined under existing circumstances — all these are problems with poorly defined structures.
In formulating (or stating) a problem, the systems analyst must accomplish the following tasks: first, describe how the problem was discovered; second, establish why it is considered a problem; third, distinguish it from a mere "symptom" of related problems; and fourth, provide operational definitions of the problem's undesirable consequences. The analyst will commit a serious error if, during problem formulation, he proposes solutions or assigns causes. Preparing a problem statement is, above all, aimed at bringing the problem into sharp focus. No demands are placed on hypotheses at the formulation stage. To maintain control over the problem, it is desirable to have logically connected, clearly identifiable facts at hand.
Investigating the historical aspects of a problem has its merits. The point in time at which the problem first became apparent can serve as valuable evidence, enabling it to be linked to preceding, identifiable actions. Sometimes it is important to determine the circumstances that gave rise to the problem.
The same phenomenon may not be perceived as a problem by everyone. It is therefore necessary to establish the rationale for treating a given phenomenon as a problem. Phenomena in business, government, and military institutions may be classified as problems if they tend to disrupt profit expectations or reduce operational effectiveness. However, certain non-obvious problems can be predicted only through analytical methods. In cases where problems are not apparent, disruption of the system's operation does not occur immediately but becomes a possibility.
In solving a problem, the first task is to determine the set of objects to be analyzed. This set of objects, taken as a whole, constitutes an alternative. Evaluating alternatives is a means of selecting solutions or goals. A given problem may be solved through many different alternative procedures. Alternatives may or may not have quantifiable aspects. For example, the number of people or pieces of equipment in an alternative is quantifiable, whereas the type of market, the degree of market influence, or the location of a market may be only partially quantifiable. The existence of alternatives implies the ability to choose between two or more acceptable solutions. The substance of alternatives defines the conditions under which a choice can be made.
Assumptions are statements about the believed state of an object, property, or relationship. Propositions are hypotheses or postulates. If the propositions are false, then the assumptions are false and the condition of the problem is contradictory. Assumptions are used to cope with difficult realities that tend to disrupt the problem-solving procedure. If the assumptions do not alter the level of risk or the cost-effectiveness ratio of a given alternative, they are a useful and essential part of the problem. Assumptions place on the systems analyst the burden of ensuring consistency.
An assumption permits the inference of a fact not known with certainty from the existence of other known facts.
A criterion is the means by which alternatives are measured or selected. A criterion compels the systems analyst to demonstrate logical reasoning in selecting preferences. A criterion indicates the relative performance of an alternative in terms of other measures, such as time, cost, or effectiveness. It is a standard by which a judgment can be rendered on the relative merit of a choice.
Risk is a measure of potential exposure to shortcomings. High risk may also be characterized by low statistical probability, although the precise measure of risk may not always be quantifiable. To describe risk in complex problems involving both quantitative and qualitative dimensions, the term "uncertainty" is used.
In this usage, "uncertainty" refers to the relative plausibility of an event that has actually occurred. Risk or uncertainty may manifest themselves throughout the entire problem-solving process. Risk increases if, for example, the criteria are inherently unsuited to measuring what they are supposed to measure. Risk also increases if assumptions accepted as true prove to be false. Risk may emerge as a dominant characteristic of an alternative that was chosen due to undetected feedback errors from output to input.
An alternative is one of two or more possibilities from which to choose. For an alternative to be considered, it must represent an acceptable potential solution to the stated problem. When alternatives are comparable, the distinction between them is established. When they are not comparable, the respects in which they differ are identified. In accordance with this definition, alternatives may differ in degree or in kind.
There are two general forms of alternatives: functionally different and operationally different. The functional form can be illustrated by a sailboat and a single-engine airplane, both of which may be considered alternative solutions to the same problem. The operational form can be illustrated by three variants of the same automobile, each designed to solve the same problem. Functional alternatives differ in how they solve problems. Operational alternatives differ in the ways objects, properties, and relationships are assembled into a system. Alternatives are evaluated by their total resource requirements and cost, and by the expected return. The aim in defining alternatives may be to maximize, minimize, or optimize system effectiveness.
In mathematics and statistics, there is a rule that only one measure can logically be maximized or minimized at any one time. This rule applies with equal force to mixed quantitative-qualitative problems. It is unlikely, for example, that both the time and cost of solving a problem could be minimized without degrading system effectiveness. One variable may be maximized while others are optimized — that is, they will closely approach, but not attain, their ideal states given the maximum of that one variable. Optimum means the best in the sense of "all things considered." It does not mean "the very best." It may mean the most favorable conditions for achieving a given goal. Optima may be perceived as so "favorable" that a specialist would describe them as "ideal," "excellent," or "the very best." However, this characterization is a posteriori, and it is not part of the logical construction of alternatives.
In most cases, the maximum and minimum of a problem's solution may be unknown; consequently, the optimum will also be unknown. These considerations show that it is possible to construct an alternative whose maximum or minimum is of little practical use. Even when the systems analyst lacks an understanding of the absolute value of each alternative, it is still possible to establish a set of estimates that allows the problem solution to be described.