This analytical approach is known by several different names: Operations Research (OR), Operational Research (a UK-ism), Decision Sciences (DS), Systems Science, Mathematical Modeling, Industrial Engineering, Critical Systems strategic thinking, Success Science(SS), and Systems Analysis and Design. Analytical methods are applied to planning and management problems in areas such as production and operations, inventory management, and scheduling. Techniques, often using powerful computer programs, are available to solve problems ranging from real-time control of specific business, industrial, agricultural, and administrative operations to long-term planning models for corporations and public sector agencies.
It is ironic that the idea of utilizing knowledge from a variety of disciplines was a central tenet of the early days in OR/MS. From the beginning, practical problems did not fit into neat disciplinary boundaries. OR/MS/DS/SS became established in organizations and interdisciplinary teams and positions included mathematicians, statistician, psychologists, economists, sociologists, etc. However, over the years the interdisciplinary teams were broken up and new recruits into OR/MS/DS/SS tended to come from applied mathematical and statistical backgrounds. Academically, OR/MS/DS/SS became increasingly focused on mathematical models and strategic solution algorithms. OR/MS/DS/SS was locked into a hard, technical shell. In recent years, however, this situation is changing with the arrival of "soft" methodologies and critical systems strategic thinking .
Systems modeling process depict a complex problem, with its many, interconnected variables, in a way that amplifies and clarifies our understanding of the decision problem. A good model does not solve the problem in itself, but allows us to experiment with different systems variables to come up with new ideas about how to tackle the decision problem.
The typical OR/MS/DS/SS approach is to build a model for the problem being studied. Such a model is often (but not always) mathematical. Practical problems are often unstructured and the definition and clarification of problems, as well as the building of models, is an important part of the OR/MS/DS/SS methodology. Most people discover that the understanding created by building a model is a very valuable part of an OR/MS/DS/SS project. Once a model is built, algorithms often have to be used to solve it. An algorithm is a series of steps that will accomplish a certain task. The study, understanding, and invention of such algorithms is also an important part of OR/MS/DS/SS modeling for decision-making. The decision maker might incorporate some other perspectives of the problem such as cultural, psychological, etc., into the management scientist's recommendations. Finally, communicative and political skills are needed in implementing the results of an OR/MS/DS/SS model in a real-life situation. OR/MS/DS/SS models are aimed at assisting the decision-maker in his/her decision-making process.
The idea that the rational decision-making process can be studied, learned, and taught makes the decision-making process a scientific approach that is based on logical principles. Therefore, there is no such thing as "someone who is born as a business person"; rather, one becomes a business person. If a successful business person is also a management scientist, then he/she can transfer management knowledge to another person. This is because ideas are communicated using analytical language. If an approach is used where no conscious thought (i.e., knowing what you know) was present, then the rationale of the strategic solution cannot be explained nor defended to another person. Unfortunately, the evidence on rational decision-making is largely negative evidence, evidence of what people do not do.
You may ask, "Why must we learn the decision-making process?" Here are a few motivating reasons:
The field of OR/MS/DS/SS is always changing. Its changes are driven by the technology it uses and that it extends, and the applications that it affects.
Communication, which is a basic human activity, is not always accomplished successfully. Effective communication requires clarity of mind, clarity of purposeful signals, and a meeting of the minds. It is common that people are looking for hidden meaning! How often we have heard somebody saying, "That's not quite what I meant"?
Specialists in model building are often tempted to study a problem, and then go off in isolation to develop an elaborate mathematical model for use by the manager (i.e., the decision-maker). Unfortunately the manager may not understand this model and may either use it blindly or reject it entirely. The specialist may feel that the manager is too ignorant and unsophisticated to appreciate the model, while the manager may feel that the specialist lives in a dream world of unrealistic assumptions and irrelevant mathematical language.
The OR/MS/DS/SS modeling process is more than a set of analytical methods. OR/MS/DS/SS models are aimed at assisting the decision-maker in his/her decision-making process. A fundamental part of OR/MS/DS/SS modeling is the "systems approach" to problem solving. This approach indicates that the context of organizational problems is as important as the stated problem. Defining a problem, collecting data, consulting with people involved in the solution, and implementing change are all aspects of the OR/MS/DS/SS education and training. As it is easier to make plans than to carry them out, models that are not to be implemented are ones that were not drawn up correctly and taken seriously from the start.
The OR/MS/DS/SS modelling process helps to improve operations in business and government through the use of scientific methods and the development of specialized techniques. Operations Research is not "research"; it is the process cycle of re-searching for an optimal (or desirable) strategic solution to the existing decision problem/situation.
OR/MS/DS/SS modeling process provides systematic and general approaches to problem solving for decision-making, regardless of the nature of the system, product, or service. The approaches and tools used in OR/MS/DS/SS models are based on one or more of the following analytical methods, simulation, and qualitative or logical reasoning. Many of these tools and approaches depend on computer-based methodologies for implementation.
In summary, the OR/MS/DS/SS modeling process is the application of scientific methods to complex organizational decision problems/opportunities. The OR/MS/DS/SS models are aimed at assisting the decision-maker in his/her decision-making process. This modeling process is now widely used in the manufacturing industry, least cost distribution of goods, and finance functions as well as in service industries, and the health and education sectors. Improvement of an existing system and good designs for new systems are the aims of OR/MS.
The OR/MS/DS/SS modeling process is one of the greatest innovative decision-making tools of the twentieth century.
OR originated in Great Britain during World War II to bring mathematical or quantitative approaches to bear on military operations. Since then OR/MS/DS/SS has evolved to be applicable to the management of all aspects of a system, product, or service, and hence is often referred to as Systems Science or Management Science. It has now become recognized as an important input to decision-making in a wide variety of applications in business, industry, and government.
The term OR arose in the 1940's when research was carried out on the design and analysis of mathematical models for military operations. Since that time the scope of OR has expanded to include economics (known as econometrics), psychology (psychometrics), sociology (sociametrics), marketing (marketing research and marketing science), astrology (astronomy), and corporate planning problems. The growing complexity of management has necessitated the development of sophisticated mathematical techniques for planning and decision-making, and the OR/MS/DS/SS features prominently in this structured decision-making process cycle by providing a quantitative evaluation of alternative policies, plans, and decisions. The mathematical disciplines most widely used in OR/MS/DS/SS modeling process include mathematical programming, probability and statistics, and computer science. Some areas of OR, such as inventory control, production control, and scheduling theory, have grown into sub-disciplines of their own right and have become largely indispensable in the modern world.
Military organizations had gone through the same type of evolution as other businesses and industries. This organizational evolution took place in the twenty year gap between the end of World War I and the beginning of World War II when the military leadership had to turn to teams of scientists for aid. These teams of scientists were usually assigned to the executive in charge of operations; hence their work came to be known as Operational Research in the United Kingdom and by a variety of names in the United States: Operation Research, Decision Science, Operational Analysis, System analysis, Success Science, and Management Science. The name Operations Research is the most widely used.
The potential of computer and information systems as new tools for management forced the non-technically trained executives to begin to look for help in the utilization of the computer. The emerging search for assistance was accelerated by the outbreak of the Korean War. This vigorous growth of OR in the military continued to provide rapid applicability to other industries and sectors.
A scientific method of providing executive management with a quantitative base for decisions regarding operations under their control (Mores-Kimball 1943).
The application of the scientific method by inter-disciplinary teams to problems involving the control of organized (man-machine) systems so as to provide solutions which best serve the purpose of the organization as a whole (Ackoff- Sasieni 1968).
Optimal decision-making in, and modeling of, deterministic and probabilistic systems that originate from real life. These applications, which occur in government, business, engineering, economics, and the natural and social sciences, are largely characterized by the need to allocate limited resources. In these situations, considerable insight can be obtained from scientific analysis, such as that provided by OR/MS/DS/SS (Hiller-Lieberman 1974).
A branch of applied mathematics wherein the application is to the decision-making process (Gross 1979).
Comparing definitions given by More-Kimball and Gross, the divergence is notable after almost 40 years: in one case, OR/MS/DS/SS is defined as scientific method, while in the other it is seen as a branch of mathematics.
In examining these definitions, it should be noted that neither the old and well-established scientific discipline nor science itself has ever been defined in a way that is acceptable to most practitioners.
The Methodology of OR/MS
OR/MS/DS/SS is the scientific method of decision-making. In most discussions of the general scientific method you would find certain stages and essential processes, as depicted in the following flowchart:
Although these phases of an OR/MS/DS/SS project are normally initiated in the order listed, they usually do not terminate in this order. In fact, each stage usually continues until the project is completed and continuously interacts with the others.
What seems to make sense is, of course, tightly connected to such important factors as background beliefs, conceptual matrix, theory commitments, paradigms, and even worldviews. What seems to make sense is also notoriously dependent upon psychological circumstances, mental condition, levels of various substances in the brain, and so forth. Both batches of factors provide some potential for subjective, human intrusion into the process.
There is an internal phenomenal, experiential dimension to things appearing sense-making, and the presence of that feel, that seeming, that seeing, may be the most fundamental component of something's making sense to us. And we cannot get behind or underneath it to examine its credentials.
Things that make intense sense in dreams, or to the intoxicated, or to the mad, are often utterly indescribable in ordinary discourse. Not only is this "sense" faculty thus not infallible, but there is apparently no noncircular procedure for justifying reliance upon it. Any such case, to have any chance of being convincing, would have to employ resources and procedures and justification for employment of which would ultimately track back at least in part of the faculty itself. And there is, obviously, no hope whatever for an empirically based case of the required, noncircular sort.
Thus, one of the foundational aims of science may not even be definable in human-free terms. Ultimately, we are unable to avoid taking the deliverance of some human cognitive capacity or function as reliably given, and we simply go from there. There is no other alternative. And neither rigor, the empirical, nor formalisms will get us out of that. Something has to be fundamental in even the most rigid axiom system along with the given some notion of proof, rigor, etc. Even mere coherence still demands reliance on some ultimate identifying of coherence and upon some principle linking coherence to the relevant characteristics aimed at, upon some value assignment to that characteristic, etc. So the whole idea of understanding rests upon an involuntary endorsement of the objective legitimacy of specific human inner phenomenal experiences associated with particular things having a genuinely sense-making appearance.
Explanation of something is to help us in experiencing what is known as "making-sense." Something makes sense when we see how and why it occurs, or why it is as it is, what meaning (if any) it has, what role it plays in some contextual setting, and so forth. But not only is that "seeing" itself mediated by its embedding conceptual context, the relevant sense of seeing something is deeply experientially psychological, involving hard-to-define cognitive connections that may simply be causal results of our human cognitive structure. And the conditions of that experience seem nearly unmanageably rich. We have only the spottiest ideas of what go into it, which may be why our references in this whole area are almost always metaphorical - "see," "light," "grasp," and so on.
Like other scientists, OR/MS/DS/SS thinkers formulate theories and models, usually in mathematical terms. "Realism" in its philosophical sense is the tendency to identify concepts and quantities in those theories and models with real features of the external world.
This broad range of potential applications and wide variety of OR/MS/DS/SS modeling process techniques, which can be selected and combined for a multi-disciplinary approach, work together to make the profession a dynamic and exciting one.
Manufacturing, Insurance, Planning, Systems analysis, Marketing, Budgeting, Finance, Program evaluation, Banking, Services (non-profit).
The OR/MS/DS/SS profession should be particularly considered by persons who are attracted to the use of mathematics, statistics, and other branches of science, in general, for solving decision-making problems of practical significance.
Some individuals believe that OR/MS/DS/SS is viewed as a "young person's" profession. Given the fact that analytical modeling is at the heart of OR/MS/DS/SS activity, such an assertion might be relevant. This belief originally came from the mathematical community. Some mathematicians believe that mathematics is a mind game, therefore like any other game, young persons engage in them more fully. However, youth is not a time of life -- it is a state of mind. Therefore, as long as your mind is active, you are young and indeed well-suited for the excitement of the OR/MS/DS/SS profession. No one is too old if they have a passion to learn. To absorb new ideas is to live anew and to see the world with fresh eyes. Henry Ford said "Anyone who stops learning is old, whether at twenty or eighty. Anyone who keeps learning stays young. The greatest thing in life is to keep your mind young."
The growing trends in interventional managerial decision-making increasingly utilize applications of more than one technique and involve individuals from other disciplines. Moreover, they involve a blend of "hard" and "soft" as well as a mixing of different "hard" or "soft" techniques with the increasing use of multiple methods within one piece of analysis. A creative thinking must look in detail at how those from disciplines outside of OR/MS/DS/SS can come to work in the organizations on multi-disciplinary studies. Those who have come from such backgrounds, clearly share their perspectives and experiences.
OR/MS/DS/SS as Systems Sciences
Today the word "Engineering" has a broader meaning and scope than merely dealing with physical engines. The word engineering in phrases such as re-engineering business activities has a much wider scope.
For example, economists like to think of themselves as something like 'engineers' trying to keep the 'train' of state on track. Building upon foundations in mathematics, statistics, operations research, and economics, Systems Engineering involves the design, control, and management of complex systems arising in manufacturing, transportation, telecommunications, and the environment. By considering the system as a whole, rather than as individual components, Systems Sciences provide direction as to the optimal design of the business systems, as well as their on-going operations and maintenance.
Systems engineering exists as a discipline because the complexity of large scale systems tends to defy effective design of the whole. The core of the discipline focuses on certain areas of mathematics and methodology, rather than on particular physical sciences, as is typical of other engineering specialties. Systems engineers learn to model, simulate, optimize, integrate, and evaluate systems. They participate in group projects in such systems application areas as environmental control, telecommunications, transportation, project/construction management, and manufacturing.
OR/MS/DS/SS as Industrial Engineering
Industrial Engineers design systems that enable people and society to improve productivity, efficiency, effectiveness, and quality of the work environment. All engineers work at planning, designing, implementing, and controlling the systems that represent the way people use technology. The systems that are the subject of Industrial Engineering design are broad and are characterized by a need to integrate both the physical and decision-making capabilities of humans together with all other aspects of the system design. The following show the range of problems:
- the design of a work method and work station;
- the design of a factory layout and methods of controlling the flow of materials on the factory floor;
- the design of an overall corporate plan involving materials procurement, production, inventory and distribution.
The idea of a factory is also extended to include health care systems, municipal systems, and transportation systems; in fact, all of the systems that are essential to the functioning of modern society are included. Systems that facilitate effective decision-making and implementation in areas such as scheduling, inventory, and quality control are typical of industrial engineering.
Human behavior and capabilities are key elements in the systems with which Industrial Engineers work.
In designing the layout of a production line for an automobile manufacturer, the checkout counter for a supermarket, the organization of office work flow for a bank, a materials handling system, or a steel plant, the engineer must consider physical requirements, cost parameters, and the physiological and behavioral performance of the human operators. The Industrial Engineer has a dual role to extend human capability to operate, manage and control the overall production system and to ensure the safety and well being of those working in the system.
Design and development of these systems require the unique background of the Industrial
Engineer. The process of engineering always starts with measurement. Where other engineers
might measure temperatures, pressures, or wind loads, the Industrial Engineer measures the time of a work cycle, dollar values of expenditures, rates of machine failures, or demand processes for finished goods. Usually the mathematical analysis must take into account risk and uncertainty to a larger extent than in other engineering fields. Computer simulation and optimization are often required. The concepts and techniques found in Industrial Engineering are to assist you in developing the skills that meet the specific challenges of systems which involve managerial activities.
Also visit the following collection:
Decision Making Resources.
Further Reading:
Haviv M., and R. Hassin, To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems,
Kluwer Academic Publishers, 2003. Focuses on the practical viewpoint of customer behavior and its effect on the system performance measure.
OR/MS/DS/SS as Modern Manufacturing Systems
Rapid progress in the area of modern manufacturing is probably most evident through the developments in intelligent manufacturing systems. The same fast advancements have made the objective of achieving a balanced technical program a challenging task.
Modern manufacturing is the capability of surviving and prospering in a competitive environment of continuous and unpredictable change by reacting quickly and effectively to changing markets, driven by customer-designed products and services. Critical to successfully accomplishing in modern manufacturing systems are making quick but good decisions concerning the standard for the exchange of products, concurrent engineering, virtual manufacturing, component-based hierarchical shop floor control system, information and communication infrastructure.
Further Reading:
Gershwin S., (ed.), Analysis and Modeling of Manufacturing Systems, Kluwer Academic Publishers, 2003.
OR/MS/DS/SS as Management Information Systems
There is much overlap between the OR/MS/DS/SS and Information Systems fields. Many business operations require intensive knowledge of computing and information systems. Similarly, management of computing and information facilities often require a deep understanding of issues such as scheduling, replacement strategy, and policies on the development and adaptation of new technology.
The business world is becoming more computer and information intensive; therefore, specialists in OR/MS/DS/SS and Information Systems combine a background in OR/MS/DS/SS modeling process and a good knowledge of current computing technologies. They design and manage computerized systems that control the production and distribution of a firm's goods and services. Career opportunities exist in most industries and government organizations in the areas of systems analysis and design.
OR/MS/DS/SS as Production and Operations Management
Operations Management is the functional area of business that is concerned with the production of goods and services. In conjunction with other functional areas, it also deals with the management of resources (inputs) and the distribution of finished goods and services to customers (outputs).
Operations refers to the production of goods and services -- the set of value-added activities that transforms inputs into outputs.
Operations Management is concerned with management of the production and distribution of the goods and services of a firm or government organization. Issues in the management of operations include: forecasting of the demand for the organization's products and/or services; development of efficient manufacturing processes; Inventory planning and control; work force scheduling; and design and management of distribution and transportation networks.
The study of Operations Management embraces the disciplines of OR/MS/DS/SS, Statistics, and Computing and Information Systems. This field is a blend of field studies and the use of
computerized models to analyze and simulate the operation of real systems.
Operations are at the heart of most organizations, and opportunities are found in the area of forecasting,
inventory management, the design of production facilities, work force scheduling, and the location
and layout of distribution networks. Specialization in Operations Management is particularly useful when combined with the study of another functional area of business such as marketing, finance, or management information systems.
For more information, visit the following collection:
Decision Making Resources.
OR/MS/DS/SS as System Dynamics, and System Design Engineering
The general purpose of System Dynamics (SD) is enabling a correct choice of policy or strategy in a complex setting; while the purpose of System Design Engineering (SDE), is coming up with a workable architecture and overall design for a complex device, or physical system, or man-made system, such as am airport. For example, any air traffic control system would have SDE early in the design process.
Their similarities are that both tend to use models at a higher level of aggregation, and deliberately scope the system boundaries widely. Both are likely to start out conceptual and end
up mathematical model, and indeed sometimes both have well articulated modeling processes.
Their differences depend on their different application and purposes. SD tends to be doing just one OR/MS/DS/SS model at a time, and always the continuous time. SDE may well use many models, each in a different form and drawing on different disciplines for different parts of the system to be designed. In terms of who does it and what they know, in SDE technical engineering knowledge is the main focus, and knowledge of the client situation is an input to the process. In SD, the OR/MS/DS/SS model developer is
expected to be extremely familiar with all the moving pieces in the client's world. That is because a major task of the SD model developer is to represent that world. The SDE model developer task is to only to design something that will work as specified within that world.
The above comparison is useful to a point, just to know what goes on in other fields and perhaps extract isolated learning points as part of some other endeavor.
Introduction and Summary
What processes allow us to make a good decision? At what point does the thought process begin? Is there any structure in making a decision? This is where Applied Management Science and more specifically multi-perspective structured decision-making processes create their mark.
One needs to understand that reality is paramount to our logical reasoning process in making a model. One might ask what is a model? Models are different things to different people. Ask the kitchen chef what is a model and he might respond, why the recipe, of course. Here is a structured way to prepare that delicious dish or sumptuous dinner.
Models are categorized according to their distinctiveness such as kind, evolution in time, as well as accessibility of records. Models can be static in nature (Iconic), or act like reality but often not appear like reality (Analog). Mathematical and computer models are known as symbolic models. Here we see algebraic, numerical, and logical modeling. These mathematical models are designed to offer understanding to some aspect of said reality. Simulation models can be classified as computerized duplications of real systems. The computer performs these mathematical functions with precision and speed. Dynamic modeling in organizations is the collective ability to understand the implications of change over time. This skill lies at the heart of successful strategic decision process. The availability of effective visual modeling and simulation enables the analyst and the decision-maker to boost their dynamic decision by rehearsing strategy to avoid hidden pitfalls.
No human inquiry can be called science unless it pursues its path through mathematical exposition and demonstration, which is mathematical modeling. In creating a mathematical model, first is a mental model. Second, when written down to add clarity and dimension. And third, when you translate it into the language of science, that is mathematical model. Other managerial functions, such as organizing, implementing, and controlling, rely heavily on decision-making.
Reporting or communicating one's conclusions to the decision-maker is a vital aspect of the modeling process. After you have investigated and reasoned through the problem at hand, your results could prove disastrous if you were unable to relate your findings to the proper individual(s). It is therefore necessary to make every effort to create reports and provide information that is understandable for all parties involved.
The analytical decision-making process is an assessment based on the choice of alternatives. That is, choosing the alternative that fits the need of the person or organization. In order to provide solutions through modeling one must obtain the facts, eliminate things that are not relative to understand the real decision problem/opportunity.
There is a three-stage structure to the systems analysis, design, and control process. The prescription of a solution stage allows for the identification of a strategic solution in the implementation stage. These solutions depend upon budgets, time, and other considerations. For every managerial decision there are several possible solutions. Good decisions are based on considering all the solutions and choosing the one that fits the operation. Utilizing software to solve complex business problems in today's world has become commonplace. Analysis of this data can often be challenging. As the OR/MS/DS/SS person assigned to the problem, it is your job to provide solution information to the decision-maker. These Managerial Interpretations must be presented in a manner to which the decision-maker is accustomed. Presenting technical data to one that is not familiar with the "language" will render your report useless. Post-prescription monitoring activities include updating the strategic solution in order to control the problem. Change is ever present. The information to solve today's problems must remain current. Therefore, in order to maintain relevancy models must contain the latest information. This in turn provides the decision-maker with the best possible analysis to make quality decisions.
Validation is the process of comparing the model's output with the behavior of the phenomenon. This is to say that confirmation of the model's behavior is essential. How else can one determine if the proper model has been built. Then there is always the question of cost. Modeling can be very expensive. The more complicated the model, the greater the cost. Inputs and constraints added to existing problems create extra costs. Plus, there is the matter of timely decisions.
A Multi-perspective structured decision modeling process consists of reflections before action. According to Sun Tzu "Victory is achieved before, not during, battle."
Much of the analysis of OR/MS/DS/SS is through system models that are synthetic representations of physical/operational systems. A system model relates those variables which affect the performance of the system to a measure (or indicators) of systems performance in a logical manner. By experimenting with the model, the effects of various management decisions can be explored.
The analytical results obtained from a model must always be tempered with experienced judgment, since there usually exist factors that cannot be accounted for in the model. However, an analysis of the system through the use of a reasonable model usually provides valuable input to managerial decisions. While a system model may take many forms, it usually includes the logical relationships between the variables affecting system performance and some measure (or indicators) of system performance. These relationships are frequently expressed in a mathematical form. By altering values of the values of the variables in these relationships, the manager or analyst can determine the effect of the variety of the conditions on the operational effectiveness of the system described by the model.
The OR/MS/DS/SS approach to the decision-making process is mostly through mathematical models. The use of mathematical modeling spreads to the public and private sector and has grown rapidly since the availability of PC. By definition the mathematical modeling process of reality is the mathematization of reality as we perceive it. Mathematizing could be in the forms of quantifying, graphical visualizing, tabular coordinating and/or symbols notation systems to develop mathematical descriptions and explanations that make heavy demands on modelers' reality representational capabilities.
Practitioners in OR/MS/DS/SS have long held fast to the tenet that the system under study, and its operational characteristics, should dictate the modeling approach, and not that the modeling familiarity of the analyst should dictate his/her description of the system. This is an easy thing to state but quite another to accomplish, regardless of how true it may be. It is our belief that a conceptually oriented, interpretive perspective is of definite utility to the analyst in the quest for a model that, as accurately as possible, describes the system under study. In the modeling process one must consider the following facts:
- You must see, but that is not enough; you must then take time to observe.
- You must think, but that is not enough; you must then take time to reason.
- You must realize what needs to be done, but that is not enough; you must then take time to understand "how and why" and the consequences.
- You must also plan well your actions, but that is not enough; you must then take time to implement, and perhaps adapt, your plans.
- You must now communicate with the decision maker what you have done, but that is not enough; you must then take time to interpret what you have accomplished, its meaning and consequences so that others may also see.
There are essentially two polar points of view regarding analytical modeling process in OR/MS:
- If used properly methods will give the one "correct" answer to a decision problem and will prescribe the course of action for an executive to take; or
- The methods are native and essentially useless, the proverbial "will o' the wisp," and therefore "practical" people should not waste time studying them.
The truth lies somewhere between these two extreme opinions. Quantitative Methods can be useful if their proper place in the analysis of decision problems is clearly seen.
Since, abstraction is the most powerful tool that we have in strategic thinking about decision problems. Parts of this Web site are "philosophical" because a model is an abstraction of reality that we hope to use to understand reality: it must delicately weigh and balance the feature of reality that is important in a decision situation. Oversimplifying can lead to poor decisions. Making a model too complex can lead to untimely decisions as well as decision recommendations that are really not understood by anyone. A well-balanced model can provide important and useful information at low cost. Models do not simply appear; they are built and required extensive work.
Further Readings
Evans J., and D. Olson, Introduction to Simulation and Risk Analysis, Prentice Hall, 2002.
Harrington J. , and K. Tumay, Simulation Modeling Methods: To Reduce Risks and Increase Performance, McGraw-Hill, 2000. CD-ROM included.
Jennings D., and S. Wattam, Decision Making: An Integrated Approach, Pitman Pub., 1998
Kaplan M., Decision Theory as Philosophy, Cambridge University Press, 1996.
Klein G., et al., (Ed.), Decision Making in Action: Models and Methods, Ablex Pub., 1993
Lesh R., and H. Doerr, Symbolizing, Communicating, and Mathematizing: Key Concepts of Models and Modeling, in P. Cobb, E. Yackel, and K. McClain (Eds.), Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design, Lawrence Erlbaum Associates, N.J., 361-383, 2000.
Petroski H., Invention by Design: How Engineers Get from Thought to Thing, Harvard University Press, 1998.
Ross Sh., Simulation, Academic Press, 2001
Ross Sh., Introduction to Probability Models, Academic Press, 2002.
Ross Sh., An Elementary Introduction to Mathematical Finance: Options and other Topics, Cambridge University Press, 2002. It presents the Black-Scholes theory of options as well as introducing such topics in finance as the time value of money, mean variance analysis, optimal portfolio selection, and the capital assets pricing model.
Ross Sh., Stochastic Processes, Wiley, 1995.
Tomlinson R., and I. Kiss, (eds.), Rethinking the Process of Operational Research and Systems Analysis, Pergamon Press, 1984.
Walker W., S. Rahman, J. Cave, Adaptive policies, policy analysis, and policy-making, European Journal of Operational Research, 128, 282-289, 2001.
Multi-perspective Modeling Process
The modeling process is a well-focused strategic thinking while following some logical sequences. Therefore, in this sense, strategic thinking has to be learned in the way dancing has to be learned. One can dance with logic.
The most widely used models are spoken languages. Consciousness and language are closely related. We report our conscious experiences using language, and these verbal reports are the central model for human consciousness. We consciously experience linguistic stimuli such as words and sentences, and also process them unconsciously. Our language helps to structure our conscious experience, by shaping their mental model. Language is a model consisting of a sequence of metaphors to convey our feelings, desires, passions, etc. to other persons. Language is a system of encoding thoughts, moreover we think because we have words and the more words we have, the better able we are to think conceptually.
It is the impossible attempt to step outside our human condition - the ordinary language and its linguistic rules in particular its grammar, within which we do our strategic thinking , put limitations on our strategic thinking and its communication to others. We think in "words" and moreover the "grammar" is a major barrier for our strategic thinking . Consider the statement "nothing" does exist. It seems a meaningless statememt, however 3 - 3 = 0. As another example, we hear in the evening news that "Nobody was hurt in that car crash" is it necessary to state it? Grammar too puts limitations on our strategic thinking . For example every verb must have a subject. When we say, "It thunder," we know well that there is no such "it." One must rather say "Thunder is going on." Our false strategic thinking is incorporated in our whole language; we cannot reason without, so to speak, reasoning wrongly. We overlook the fact that speaking, no matter of what, is itself a model.
Because of all the above limitations is our spoken language, in many historical instances the scientists have to create new kinds of mathematics and logic to enable them to express and therefore communicate effectively their ideas. Mathematical development, being the language of science is an ever evolving and expanding process.
Why are fashion models called models? The answer is that they try to represent a reality of how you will look, for example, in the same clothes.
The external world presents itself to us through our sense perceptions collectively are only a set of interfaces mediums to our brains. By analyzing these raw data, we are in fact engaged in constructing of a mental model of the reality, however we see only what the mind is prepared to comprehend. Models are re-presentations of reality which may or may not represent reality accurately. Essentially all models are inexact, however some are more useful than the others are. For example, we make models about people inside our head. When we act, we find out if the model is accurate! Many people make the mistake of assuming their model is reality; they blame others and say "something is wrong." A "validated" model is the one which re-presents reality.
Anyone can perceive the outside world. A thinker can not only see the outside world, a thinker can re-present those perceptions as models, as depicted in the following figure:
The above figure represents the following steps:
- One perceives the outside world through his/her physical sense of perceptions.
- The thinker in the above figure processes and analyzes the information through mental activities to form an interpretation.
- The thinker re-presents the interpretation (now called understanding) back "as if" it is indeed the reality itself.
- The outside world appearances to the mind are of four kinds. Things either are what they appear to be; or they neither are, nor appear to be; or they are, and do not appear to be; or they are not, and yet appear to be. Rightly to aim in all these cases is the thinkers task.
You may ask "How does understanding come to a thinker?" The answer is, we understand the world in this way through knowledge. We become a little piece of the world by becoming conscious of it. However, we might be overconfident about our understanding and think we are better at guessing or estimating than we actually are. This happens because we perceive the world through 'our' senses and interpret what we perceive based on our experiences and trained ways of strategic thinking. The point is that there are many traps that we humans fall into when making important decisions.
Doing something does not imply understanding what we are doing or being conscious of how we are doing it. Talking, remembering, and making decisions are examples of activities in which we continuously engage in blissful ignorance of the process and procedures involved.
Unlike mathematics which requires only the consistency, mathematical models need interfaces between symbolic representation and the representations of external reality. Those interfaces are provided by observation and/or experiments. But what is observation? The word corresponds to the Latin verb "observe" which means to attend to in practice (e.g., to observe a custom), and also to watch attentively. Here we are interested in the second meaning i. e., watching attentively, deliberately, and explicitly.
To understand what we observe, we may perform some experiment on it. An n-order experiment is an experiment where the experimenter is permitted to change n conditions or parameters of the system under study. A set of observation is a zero-order experiment. While in the ordinary sensitivity analysis in optimization decision problems is 1-order experimentation.
The external world is conceived as actual because it exists in relation to a certain time and space. Understanding the external world is achieved by a chain of explanation that is logical in form and therefore free from the time's dominion. Understanding gives you a clear conception of what you think. Moreover it makes you the cause of what you think. The ideas become yours. These in turn, secure the joy, independence and serenity that we call "freedom". The grand aim of all science, including management science, is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses.
A model is a representation of reality from the modeler's perspective. Therefore, you must develop a multi-perspective model of the problem on hand to understand the problem. Friedrich Nietzsche's theory of knowledge comes to mind: "There is only a perspective seeing, only a perspective knowing, and the more affects we allow to think about one thing, the more complete will our concept of this thing, our objectivity, be." You must look at the problem from many angles and consider how the pieces fit together, to see the "whole" of the decision problem. Immanuel Kant and Arthur Schopenhauer, among others, called this model "the World as a representation" of our understanding through Time, Space, and Causality.
The representation of external world is a perspective modeling, which is a complex process involving combinations and interactions among perception, motivation, memory, learning and development, emotions, consciousness, language, rationality, sociality, personality, and psychopathology.
Scientific research is based on the idea that everything that takes place is determined by laws of nature, and it is a useful tool to explain the physical world. This this holds also for the action of people as Spinoza introduced the concept of Motivation to explain humans' actions, and stated that "there is no more dangerous error than that of mistaking the effect for the cause: I call it the real corruption of reason." Moreover, one must affirm differences by "ethics of letting be" and a "delight in differences" while committing to our own perspective.
The process of observing the system is a learning activity. Therefore, this is a tripartite concept, namely, Thinker-and-Learning-and-System. There are a variety of orders in which the three concepts could be arranged. For example, "systems for learning" which is mainly our educational institutions.
Modeling is the science of making an optimal judgment that requires a combination of many disciplines. Decision-making is a central human activity. Thus, we are all decision makers, and a "good" decision-making process encompasses many disciplines of study. Appreciation of decision making is wonderful: it makes what is excellent in this strategic thinking belongs to you as well. OR/MS/DS/SS modeling approach to decision-making is aimed at understanding the decision problem (or opportunity) and assisting the decision-maker in his/her decision-making process. Models explain the problems and provide solutions. As Ludwig Wittgenstein said, "the riddle does not exist. If a question can be put at all, then it can also be answered."
Why is the OR/MS/DS/SS a science? What is science? Science is the subject of thought. Thought itself is a sequence of internal symbolic activities that leads to novel, productive ideas or conclusions about a decision problem.
However, strategic thinking is performed on a version of the external world called a " mental model". Therefore, modeling is the process that occurs in the neural networks of your brain, i.e., chains of thought when starting the structured consecutive-focused-strategic thinking. Modeling includes perceiving, formulating our experience, processing, and re-presenting information from the external world. The result of these structured processes is called a model. Managerial problem solving requires mental modeling, which is a process of resolving stress (i.e., competition of forces) until our experience of the problem is formulated.
By analyzing (i.e., a structured consecutive-focused-strategic thinking) we process this information to under-stand reality (i.e., to see it beneath ourselves). The result is a "model." By describing a model of reality you become conscious of reality. Therefore, a model is a re-presentation of reality. To achieve an accurate model one must use a mathematical modeling process cycle.
Mathematics was invented by humans in an attempt to define life in their own terms. Mathematics has been used in all branches of physics. For example, on modeling our universe, Galileo Galilei said:
" this grand book -- I mean the universe -- which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics"
The essential fact is that all the pictures, which science now draws of nature, and which alone seem capable of according with observational facts, are mathematical models.
It would be wonderful to be able to learn such an awe-inspiring language and to master the underlying principles of mathematical modeling, even if you have never thought of yourself as mathematically inclined. Mathematical modeling (i.e., mathematical strategic thinking ) is the process of contemplating on the decision problem. In mathematical modeling, mathematics is used as a language to describe, and as a tool to prescribe, and control the decision-making process. Therefore mathematical models process aims at describing, prescribing, and controlling our decision-making process in all areas of human activities. The cardinal aim of mathematical modeling process is to make our world measurable, calculable, predictable, and thus more manageable.
Primarily the use of mathematics in decision making is that of language called mathematical modeling by which we discuss those parts of the decision problem which can be described by numbers or by similar relations of order. Mathematical models can describe complicated decision problems including the interactions among its components that are too complicated to be expressed everyday language. Therefore, mathematical modeling is the science of skillful operations with concepts and rules invented just for this purpose.
The decision-making process is contemplating on the elements of the decision. By definition of esthetics, the longer you contemplate on anything the more beautiful that thing is. With respect to beauty of the mathematical modeling process, we distinguish it from other mental manifestations; this process is the result of the perfect apprehension of relations formed by a complexity of elements of the model.
Our high school curriculum should put more emphasis on mathematical modeling rather than maths which in most cases are merely "puzzle solving" which has nothing to do with students lives. This will bring excitement in learning the math language and its applications.
In concluding this section, the main question for us is "how people make sense of each other and the world they live in?" Making sense is the activity of fitting decisions into a coherent pattern of mental representations that include concepts, beliefs, goals, and actions. Much of human strategic thinking can be understood in terms of coherence as constraint satisfaction, and many decision problems can be given coherence-based solutions. The main difficulty is how coherently can one integrate the strategic thinking with emotions. Emotions are bodily conditions by which our energy is increased or decreased, aided or restrained, and at the same time the idea of those conditions. Emotions which are under your control are good, because after all passions and compassions are related.
Further Readings:
Baron J., Thinking and Deciding, Cambridge University Press, 1994.
Churchman C., The Design of Inquiring Systems, Basic Books, New York, 1971. Early in the book he stated that knowledge can be considered as a collection of information, or as an activity, or as a potential. He also noted that knowledge resides in the user and not in the collection.
Jackson M., Critical systems thinking and practice, European Journal of Operational Research, 128, 233-244, 2001.
McCall M., and R. Kaplan, Whatever It Takes: The Realities of Managerial Decision Making, Prentice Hall, 2001.
Mingers J., and and A. Gill, (Eds.), Multi-methodology: The Theory and Practice of Integrating Management Science Methodologies, Wiley & Sons, 1997.
Newson M., and V. Cook, Chomsky's Universal Grammar: An Introduction, Blackwell Pub., 1996.
Pidd M., Tools for Thinking : Modelling in Management Science, Wiley, 1997.
Rowland G., A Tripartite Seed: The Future Creating Capacity of Designing, Learning, and Systems, Hampton Press, 1999.
Wittgenstein L., Philosophical Investigations, Prentice Hall, 1999.
From Mental Modeling to Analytical Modeling
Our interpretation of objects, events, and processes relationships in creating a mental model is partly learnt and partly the result of deeper cognitive-psychological responses.
Mental models shape the firms' actions because they affect what decision-makers see and pay attention to. In other words, mental models determine which information receives the attention of decision-makers and which is ignored. Decisions are the result of applying a decision rule or policy to information about the world, as we perceive it. The policies are themselves conditioned by institutional structures, organizational strategies, and cultural norms. Therefore, an appreciation of the hygiene of mental models is important for the decision-maker.
All mental models have a few key characteristics that the thinker must be aware of:
- Mental models include what a person thinks is true, not necessarily what is actually true.
- Mental models are similar, but not the same, in structure to the thing or concept they represent.
- Mental models are simpler than the reality they represent. They include only enough information that the thinker needs in making decision.
Reflecting on the Philosophy of Knowledge, there are two extreme schools of thought: Empirical and Theoretical. The Empirical (i.e., a Greek word for experience) approach to knowledge relies on experimentation, observations, and data analysis. Again, empirical knowledge is gathered from data from some area of experience and then conclusions are drawn from the data about the area of experience. Examples of empirical models are those you used to verify results in the physics labs by experimentation. Utilitarian schools of thought is based on the fact that: No man's knowledge can go beyond his experience. A fact in itself is nothing. It is valuable only for the idea attached to it, or for the proof which it furnishes.
The theoretical approach, on the other hand, relies on mental models and pure thoughts without any reference to the external world. Examples of theoretical models are the chemistry structure of molecules.
Theoretical-models are condensed, and abstract while applied-models are descriptive and concrete. The distinction between pure empirical and pure theoretical knowledge is expressed by Francis Bacon in the following analogies: "The men of experiment are like the ant, they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes the middle course; it gathers its material from the flowers of the garden and field, but transforms and digests it by a power of its own."
Modeling is at the core of OR/MS/DS/SS activity. It is situated between theory and experiment and utilizes both. OR/MS/DS/SS models are aimed at assisting the decision-maker in his/her decision-making process.
The OR/MS/DS/SS descriptive modeling process contains mostly "How" rather than "Why" questions. This is always the case in any scientific approach to problem solving, including OR/MS/DS/SS field of investigation with the views on underling relationships by the mean of causality (for physical entities) and motivation (for human actions). For example, Newton's theory of gravity says something very clear about how planets move, proposing a force that acting in a certain way, accounts very well for the observed phenomena. But why? To move from the how to the why you have to go from a theoretical entity (a force called gravity) to a real entity. If you ask 'why' the answer is 'because of gravity'.
The Critical Realism (CR) school of thought distinguishes between the empirical, the actual and the real. The first corresponds to sense data concerning events, the second to what happens whether we sense it or not, and the third to what causes the events to occur. CR argues that bodies or entities (people or material things or even abstract entities such as societies) have causal/motivational powers that exist whether they are brought into action or not. An event is caused as a result of the powers of various bodies acting in contingent ways. These causal powers are the things that we have to try to understand and model though they are not necessarily visible. The main fact is that in any modeling process one has to make assumptions about the world (ontology) and how we might find out about it (epistemology).
Pure scientific theories, in general, are judged on the basis of:
- how large their scope of validity and accuracy are in explaining observed phenomena
predicting unobserved ones;
- how simple and elegant they are;
- how well they fit in the prevailing structure of existing theories;
- how many and how plausible hypotheses they employ; and
- how flexible they are through their various admissible interpretations.
Scientific theories, the Simplex Method for optimization, as an example, may not be attainable by most branches of natural, life and social sciences, or any empirical methods. Theory construction in a particular scientific domain is constrained by the demands and possibilities imposed by the experiential data and the method of observing them. In some abstract sense, OR/MS/DS/SS scientists working in the 'non-exact' fields seek a compromise between the empirical basis of scientific knowledge, on one hand, and the systematic coherence and structure of scientific understanding, on the other. Fallible critique and self-correction is the nature of science. However, this is not the case in art, morality, and religion for example.
In scientific strategic-thinking process one must have an open-mind for new ideas, to be able to think differently, to see thing from many perspectives. The classroom universities and scientific journals are the environments for debates, and exchange of ideas. Open-mindedness is the main condition to achieve the ultimate aim of education: Being able to think for yourself.
In each class I teach, a few students enroll in the course, unfortunately with preconceiving ideas, and beliefs. That is why sometimes it is hard for them to rethink and re-evaluate those ideas.
Two Alternative Theories of Decision-Making: There are two basic theories of human decision-making. The first is called normative theory because it proposes to present guidelines and techniques for accomplishing predetermined goals. It tells you what decision you ought to make. The other is positive theory (or behavioral theory) and seeks only to describe and explain how decisions are made. The positive theory is based on: reproducibility, refutation, reductionism, and objectivity without any detachments.
Sensible decisions are always based on facts. Normative modeling is not about knowing the reality of the world, but rather having a sense of idealism of how the world should, or could, be. For example, an economist with positive views relies on facts to describe any slowdown in the economy while another economist with normative views sees it as an unavoidable cycle in economy, merely based on some ideologies; i.e., idols to worship. One of the well known myths of Normative economics is that there is always a recession in the US economy every 5 years. Here is another example of normative strategic thinking : Does history repeat itself, OR do historians repeat each other?
Further Readings:
Albach H. , and B. Bloch, Management as a science: Emerging trends in economic and managerial theory, Journal of Management History, 6(3), 138-158, 2000.
Archer M., et al. (Eds.), Critical Realism: Essential Readings, Routledge, 2000.
Badaracco, Jr., J., Defining Moments: When Managers Must Choose Right and Right, Harvard Business School Press, 1997.
Bailey M., Studies in Positive and Normative Economics, Edward Elgar Pub., 1992.
Bell D., H. Raiffa, and A. Tversky, (Ed.), Decision Making: Descriptive, Normative, and Prescriptive Interactions, Cambridge University Press, 1988.
Beroggi G., Decision Modeling in Policy Management: An Introduction to the Analytic Concepts, Boston, Kluwer Academic Publishers, 1999.
Buskrirk R., Modern Management & Machiavelli, New American Library, 1974.
Casti J., and A. Karlqvist, (eds.), Beyound Belief: Randomness, Prediction and Explanation in Science, CRC Press, 1991.
Christensen, C., The Innovator's Dilemma: When New Technologies Cause Great Firms to Fail, 1997, Harvard Business School Publishing.
Connolly T., H. Arkes, and K. Hammond (eds), Judgment and Decision Making: An Interdisciplinary Reader, Cambridge University Press, 2000.
Dawson R., The Confident Decision Maker: How to Make the Right Business and Personal Decisions Every Time, Morrow William & Co., 1995.
Findler N., Contributions to a Computer-Based Theory of Strategies, Springer-Verlag,
1990.
Gärdenfors P., and N-E. Sahlin, (Eds.), Decision, Probability and Utility, Cambridge Univ Pr., 1999. It covers the foundations of decision theory, the conceptualization of probability and utility, philosophical difficulties with the rules of rationality and with the assessment of probability, and causal decision theory.
Joyce J., The Foundations of Causal Decision Theory, Cambridge Univ Pr., 1999. It offers a ‘representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory.
Goldratt E., and J. Cox, Goal : A Process of Ongoing Improvement, 1988, North River.
Rivett P., The Craft of Decision Modelling, 1994, Wiley & Sons.
Sterman J., Business Dynamics: Systems Thinking and Modeling for a Complex World, Irwin Pub., 2000.
Sutherland S., Irrationality: Why We Don’t Think Straight!, Rutgers University Press, 1994.
Classifications of Models:
Mechanical, Mental/Verbal, Analytical, and Simulation Models
The decision analyst must identify which type of model best suits the decision problem. This is why we will discuss a classification of modeling the systems before getting into the process of model building. Although OR/MS/DS/SS mostly concentrates on mathematical models the other model types are also prevalent in practice.
What is a System: Systems are formed with parts put together in a particular manner in order to pursuit an objective. The relationship between the parts determines what the system does and how it functions as a whole. Therefore, the relationship in a system are often more important than the individual parts. In general, systems that are building blocks for other systems are called subsystems
The Dynamics of a System: A system that does not change is a static system. Many of the systems we are part of are dynamic systems, which are they change over time. We refer to the way a system changes over time as the system's behavior. And when the system's development follows a typical pattern we say the system has a behavior pattern. Whether a system is static or dynamic depends on which time horizon you choose and which variables you concentrate on. The time horizon is the time period within which you study the system. The variables are changeable values on the system.
Models can be classified according to their characteristics such as types, evolution in time, and availability of information, as shown in the following figure.
A Classification of Models
Iconic models are usually static in nature, such as a dollar bill. Analog models are physical, however they are designed to act like reality but usually do not look like reality. They are mostly mechanical models. However, business activities are dynamic processes. Business is a process that follows mathematical patterns. Therefore, it can be represented by symbolic (i.e. algebraic, numerical, logical) models. Symbolic models include a large class of models known as mathematical and computer simulation models.
Mechanical Models: A model that takes on the physical appearance of the object is called a physical model. This type of model is used to display or test the design of items ranging from new buildings to new products. In the aircraft industry, scale models of new aircraft are built and tested in wind tunnels to record the aerodynamics of design. An automobile-parts manufacturer may have a three-dimensional scale model of the plant floor, complete with miniature machines and equipment, so that a new layout of the plant can be analyzed. The machines in the model can be rearranged and new layouts studied in order to improve the material flow.
Mechanical models have the advantage of being usable for experimentation. In the aircraft example, the testing of a different design may mean that a completely new model must be built. In addition to offering the advantage of experimentation, mechanical models lucidly describe the problem or system under study; this is helpful in generating innovative design alternatives for solving the decision problem. Nevertheless, only a relatively small class of problems can be solved with mechanical models. Problems such as portfolio selection, media selection, and production scheduling are examples of problems that cannot be analyzed with a mechanical model. Basically, mechanical models are useful only in design problems and even some of these can be analyzed more efficiently and completely with mathematical models that can be computerized. Besides this, mechanical models do not contain explicit relationships between the decision alternatives and dependent variables or objectives and, trial-and-error methods of problem solving must be used. Although this in itself is not a major drawback, the trial-and-error process, coupled with a need to rebuild the model for each design change, can lead to a very time-consuming and costly process in some cases.
Mental/Verbal Models:A verbal model is a translation of the mental model. Therefore, a mental/verbal model expresses all of the functional relationships between the variables in a word passage. For example, consider the advertising manager of a company that manufactures breakfast cereal who makes the following statement concerning television commercials on Saturday morning: "a 20-second spot has much more impact on our target audience than a 15-second spot." In this example, the different time durations of the commercial are the decision alternatives; its "impact" which, we could infer, relates to the propensity of the viewers' parents to purchase the company's cereal, is the dependent variable. Thus, we have a relationship between decision alternatives and a dependent variable that relates to company objectives. Such models are used extensively in the business world and have the advantage of being easy to understand. Often they are an outcropping of many years of managerial experience and are useful for summarizing this experience in understandable language.
Mental/verbal models, however, have a number of shortcomings. The decision-maker cannot experiment with them, nor do they indicate specifically how the outcomes or measures (or indicators) of effectiveness change with the decision alternatives. In the preceding mental/verbal model, we do not know how much more impact a 20-second commercial has over a 15-second commercial. The other drawback is that it is not easy to show how the relationships change with the decision alternative. If we constructed a mental/verbal model that answered such questions for all possible commercial lengths, we would have a very lengthy mental/verbal model that would be difficult to understand and not useful for experimentation. Nevertheless, mental/verbal models can play an important role in the decision process. They can be used to verbalize decision strategies for more sophisticated models.
Analytical Models: Analytical models are mathematical models aimed at simplification, abstraction of real systems in order to provide insight, and understanding some interested aspect of the reality. However, modeling the reality by abstraction should be connected with real problems, domains, and practice by means of verification and or validation.
An abstraction may be looked at from one side as a compression of many instances into one generality or from the other side as a special purpose power tool that yields the solution for many problems. These types of models are applied mostly to the static and/or deterministic systems.
Compared with mechanical models, mathematical models facilitate experimentation because all dependent variables, independent variables, constants, and parameters are explicitly related through the language of mathematics. The decision-maker can test the effects of different decision alternatives, constants, and parameter values on the dependant variables much more easily than with any other type of model. Furthermore, mathematical models can represent many complex problems efficiently and concisely and, in many cases, provide the cheapest way to analyze these problems. It is for these reasons that we address the various mathematical models and solution techniques most often used in practice.
Solution procedures can be either single pass or iterative. A single-pass solution procedure is one in which the final values of all the decision variables are determined simultaneously according to some well-defined procedure. An iterative solution technique, on the other hand, is one in which a number of steps are required to arrive at a final solution and where partial or complete solutions are entertained at each step. Discrete or continuous variables are frequently necessary for a particular problem. Finally, an optimal solution is one that can be shown to be at least as good as any other given the assumptions of the model, whereas a satisfactory solution is one that is considered "good" with respect to the objectives and constraints, yet cannot be shown to be the best. Thus, if in our previous example of the normative-static-deterministic model the decision variables are continuous, the relationships linear, and an optimal solution is desired, the list of potential solution techniques for the model can be reduced to just one-linear programming. In this way, one or more viable alternatives for the solution methodology can be identified, and the formulation of the model can begin.
Simulation Models: The degree of abstraction in mathematical models is a definite impediment to the managerial acceptance of such models. It is not surprising to encounter resistance from managers who have not had sufficient training in and exposure to these models, and also from managers who have training but do not have the time to pay close attention to the model. Mathematical models use symbolic language of mathematics which has its own limitations. Analog models are also physical however they are designed to act like reality but usually do not look like reality. The models may be too complex (such as, an international airport) to solve efficiently, requiring gross oversimplifications of the real problem in order to get a good strategic solution. Under these circumstances, the problem that is "solved" no longer resembles the original problem, and, if the solution is implemented, disastrous organizational effects could result. Proper selection of model type and solution technique should minimize this type of mistake. The simulation models are the computerized duplications of real systems and are by far more realistic, especially for the modeling of dynamic and/or probabilistic systems such as an international airport. Dynamic modeling in organizations is the collective ability to understand the implications of change over time. This skill lies at the heart of successful strategic decision process. The availability of effective visual modeling and simulation enables the analyst and the decision-maker to boost their dynamic decision by rehearsing strategy to avoid hidden pitfalls.
All decision-making models can be classified as either Deterministic Models or Probabilistic Models. This depends largely on how influential the uncontrollable factors are in determining the outcome of a decision. Unlike deterministic models, the probabilistic models are viewed with the awareness of theory of games and expected outcome. The center of interest moves from the deterministic to stochastic using statistical estimations and predictions. Unlike deterministic models where a good decision is judged by its outcome alone, probabilistic models the decision maker is concerned with both the outcome value and the amount of risk each decision carries. We will cover both deterministic and probabilistic decision-making processes.
Further readings:
Chomsky N., On Language, New Press, 1998.
Harrington J. , and K. Tumay, Simulation Modeling Methods: To Reduce Risks and Increase Performance, McGraw-Hill, 2000. CD-ROM included.
Pidd M., Tools for Thinking : Modelling in Management Science, Wiley, 1997.
Decision-Maker's Environment
Since a model of a system is a re-presentation of the system that contains those elements that affect the objective of our decision, it is important to identify the most important elements and categorize them. The problem understanding requires criteria for grouping together entities of the decision model in a same category.
The desired output usually determines the controllable inputs, which includes your personal abilities and physical resources. The input into a system can be classified either as controllable or uncontrollable, as the figure below illustrates. Time-horizons for the modeling review must be selected that are short enough so that the uncontrollable inputs (or probabilistic knowledge of them) will not change significantly. Even for short time-horizons one might consider the time discounting factor for future periods. The output is often called performance measure (or indicators) for the system.
It is a fact that in any organization where performance is measured by some indicators, then performance improves. Moreover, when performance is measured and reported, the rate of improvement accelerates. In 1980, US Steel employed 120,000 people in steel making. Now (in 2001) it turns out the same tonnage with 20,000 workers.
The following Figure depicts the OR/MS/DS/SS structured decision-making process approach. Remember that, when structures and systems are aligned, they facilitate empowerment. When they are not, they work against it.
Structured Decision-Making Process and Its Components:
Analysis, Design, and Control
OR/MS/DS/SS models are aimed at assisting the decision-maker in his/her decision-making process. In the decision-making modeling process we investigate the effect of presenting different decisions retrospectively; that is, "as if" the decision has already been made under a different course of action. That is why the sequence of steps in the modeling process must be considered in reverse order. For example, the output (which is the result of our action) must be considered first.
It is helpful to understand the nature of the problem by asking "who?" "what?" "why? " "where? " "when?". Finally break them into three groups: Uncontrollable, Controllable, and Parameters (that defines the problem). As indicated in the above activity chart, the decision-making process has the following components:
- Performance measure (or indicators): Measuring business performance is at the top of the management decision making. The development of effective performance measurement (or indicator) is seen as increasingly important by many organizations. However, the challenges of achieving this in the public sector and for non-profit organizations are, arguably, considerable. Provides the desirable level of outcome (objective of your decision). Objective is important in identifying the problem. The major task for the decision-maker is the solution to the problem of "values" among different objectives, and the selection of a single objective that has the "highest value." Then if needed, all other objectives should be included in the set of constraints to be satisfied. The following table provides a few examples of performance measure (or indicator) for different levels of organizational:
|
Level
|
Performance
Measure
|
|
Strategic
|
Financial, Growth,
and Innovations |
|
Tactical
|
Cost, Quantity, and
Customer's satisfaction |
|
Operational
|
Target setting, and Conformance with standard |
For the chief executive officer, development of the organizational culture is the top responsibility, and creating balanced decision processes is a major aspect of culture building. Clearly, if you are seeking to improve a system's performance, an operational view is what you are after. Such a view gets at how a system really works - not simply what correlation its past output behaviors have generated. It is essential to understand how a system currently is working if you want to change how it will work in the future. Financial measures and indicators are often criticized for their narrow focus, because they often encourage short term decisions. Performance management is a cyclical process. It start with effective and efficient planning and end in compensation of individuals for their performance, as shown in the following process:
- Uncontrollable inputs: These come from the decision maker's environment. Uncontrollable inputs often create the problem and constrain the actions.
- Parameters: Parameters are the constant elements that do not change during the time horizon of the decision review. These are the factors partially defining the problem. Strategic decisions usually have longer time horizons than both the Tactical and the Operational decisions.
- Controllable Inputs: The collection of all possible courses of action you might take.
- Interactions Among These Components: These are logical, mathematical functions representing the cause-and-effect relationships among inputs, parameters, and outcome.
There are also a set of constraints which apply to each of these. Therefore, they do not need to be treated separately.
- Actions: Action is the ultimate decision and is the best course of strategy to achieve the desirable goal.
Decision-making involves the selection of a course of action (means) in the pursuit of one's objective (ends). The way that our action impact the outcome of a decision depends on how the inputs and parameter of the problem are interrelated and how they relate to the outcome.
Functionality is the most important type of relationship involved in the decision-making process interactions. When the outcome of a decision depends on our course of action, then we must consider all actions, one by one. This is to bring about a desirable change in some other aspect of our action. We succeed if we have knowledge about the interaction among the components of the problem.
"Oh, my mind, please grant me the serenity to know what input is controllable, and what is not. To choose the best of the first kind, and the ability to perform probability and statistical analysis to predict and then react to any change in the second kind, and the wisdom to know the difference!" Wisdom is the accurate application of accurate knowledge.
- Controlling the Problem: Few problems in life, once solved, stay that way. Changing conditions tends to un-solve problems that were previously solved, and their solutions create new problems. One must identify and anticipate these new problems.
The Difficulties of Objective Function Determination: It is not always an easy task to define a clear and measurable objective function in many organizations. This is a dilemma for almost all non-profit organizations. The term not-for-profit often brings to mind the idea of an altruistic organization serving society. The reality is that the not-for-profit is a far more complex organization that is responsible to diverse groups of stakeholders. Unlike for-profit organizations, not-for-profit organizations have to focus on dual, and often conflicting, goals
relating to fulfilling their overall mission while also generating enough revenue to maintain their operating structures. Therefore, one must analyze the effects of both the economic and
mission related orientations operationalized through the service encountered.
Remember: if you cannot control it, measure it in order to predict it.
For example in a marketing system, the inputs are shown in the following table:
|
-
Classification -
|
|
Type
of Input
|
Controllable
Input
|
Uncontrollable
input
|
|
Constant
|
Market
Area
|
Number
of Competitors
|
|
Parameter
|
Number
of Salesman
|
Season
of the year
|
|
Variable
|
Inventory
|
Total
Demand
|
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A Marketing System
Strategic Thinking: Successful strategies are usually developed as a result of strategic thinking, not as a result of formal planning processes. Why? Strategy is not about plans but about insights into how to create value; the process of developing insights should not be confused with planning, which is about turning insights into action. Often, companies fail to distinguish between the purpose of a business (why the business exists) and constraints (what the business must do in order to survive). For example, satisfying stakeholders is constraint, it is not the purpose or reason the business exists. The following are a sample of useful outcomes from an effective strategic-thinking process:
- Determines and reveals the organization's purpose in terms of its long-term objectives, action programs, and resource allocation priorities.
- Selects the businesses the organization is in or is considering entering.
- Attempts by responding properly to both the environmental opportunities and threats and the strengths and weaknesses of the organization.
- Engages all the hierarchical levels of the firm - corporate, business, and functional.
- Defines the nature of the economic and non-economic contributions the firm intends to make to its stakeholders.
- Provides a coherent, unifying, and integrative pattern of decisions a firm is making.
Further Readings:
Ashton R., and A. Ashton, Judgment and Decision-Making Research in Accounting and
Auditing, Cambridge Univ Pr., 1995. Important factors such as the pricing of products and services, evaluating corporate performance, granting credit to prospective borrowers, and investing in financial securities are considered.
Bond T., and Ch. Fox, Applying the Rasch Model: Fundamental Measurement in the Human Sciences, Lawrence Erlbaum Associates, Inc., 2001.
Jackson M., Systems Methodology for the Management Sciences, Kluwer Academic Publishers, 1992.
Joyce J., The Foundations of Causal Decision Theory, Cambridge Univ Pr., 1999.
It offers a ‘representation theorem' that shows that both causal decision theory and its main rival,
Richard Jeffrey's logic of decision, are both instances of a more general conditional decision
theory.
Gable C., Strategic Action Planning Now: A Guide for Setting and Meeting Your Goals, CRC Press, 1999.
Keys P., Operational Research and Systems: The Systemic Nature of the Operational Research, Kluwer Academic Publishers, 1991.
Monahan G., Management Decision Making, Cambridge Univ Pr., 2000. A spreadsheet-based introduction to the tools and techniques of modern managerial decision making.
Neely A., Measuring Business Performance, Economist Books, 2002.
Sloma R., How to Measure Managerial Performance, Beard Group, 1999.
Weinberg G., An Introduction to General Systems Thinking , Dorset House, 2001.
Modeling Is At the Heart of the Decision-Making Process
The structured modeling process is at the heart of OR/MS/DS/SS activities. The main question then becomes, "How close is the model to the real world?" Know that a model is not reality, but it does contain some parts of reality. The question is: "Does it contain the important parts relevant to the decision problem?"
Modeling and our reasoning reflect our desire to grasp reality. Modeling is a structured consecutive-focused-strategic thinking for understanding reality for utilitarian purposes. The connection between partitioning a circle into 360 degrees and a year into a number of days is an interesting example. This desire for a mathematical model of the universe and its processing difficulties is apparent. Some analogous ones existed in music, architecture, etc. These mathematical models to represent reality required fitting between small integer numbers (for ease of representation), and complex phenomena whose numerical parameters did not exactly fit in the integer-based scheme. It is credible that the 360-system and the 6-8-9-12 scheme in music were the results of this conflict; these examples are mathematically suitable models and semantically justified. As Bill Gates said, "If you're any good at math at all, you understand business. It's not its own deep, deep subject."
What is Mathematics? Mathematics is the science of patterns and orders, as well as the language of science. Mathematics is the only language shared by all human beings regardless of culture, religion, or gender. Moreover, no human investigation can be called real science if it cannot be demonstrated mathematically.
With mathematics as a language we can explain the mysteries of the universe or the secrets of DNA. We can understand the forces of planetary motion, or discover cures for catastrophic diseases. Mathematics is not just for calculus majors. It's for all of us. And it's not just about pondering imaginary numbers or calculating difficult equations. It's about making good strategic decisions.
Mathematics is part of human culture because it does not exist outside of the human mind. Symbolic reasoning and calculations with symbols are central to analytical (i.e. mathematical) modeling. Therefore, like any foreign language, you must develop an understanding of mathematics, which is the language of all sciences, including the OR/MS/DS/SS modeling process aimed at assisting the decision-maker. Here is an example of the usefulness of mathematical symbols: Suppose you wish to buy a shirt for $50 (tax included), the tax is 5%, what is to original price of your shirt? Let x and y be the amount of the tax and the original price respectively, therefore, the mathematical model is 50 = x + y, and x = 0.05y. This gives, 50 = 0.05y + y = 1.05y. Therefore, the original price is 50/1.05 = $47.62. How much is the tax? How do you generalize this result? You may ask, what is this x, in mathematics? Well, whatever we do not know we call it x (or any other letter from the end of alphabet series). X also has a political significance as in Malcom X.
A mental model is a representation of your thoughts about reality. Therefore, it is an objectification of reality, which in turn means the subjective begetting of the reality. Mathematical models employ symbols and notations, including numbers. Thus, there are three distinct concepts: the reality, the mental model, and the representation. In its many different forms, analytical modeling is a procedure that recognizes and verbalizes a problem and then quantifies it by turning the words into mathematical expressions. Modeling is a structured consecutive-focused-strategic thinking for understanding the decision problems, and actions.
In all high schools around the world mathematics is used to translate Word or Story Problems into symbolic representations (i.e., mathematical models). After solving, the results are translated back into the original language in which the problem was stated.
OR/MS/DS/SS is a systematic approach to problem solving in that it considers the context of the problem as important as the problem itself. It utilizes a team approach by capitalizing on the talent of an OR/MS/DS/SS analyst to assess, coordinate, and incorporate knowledge relevant to solving a certain decision problem from experts in other fields, (known also as think-tank approach). The difficulties in clear communication among the team members in any OR/MS/DS/SS project can increase with the size of the team. Span of management refers to the number of employees supervised by a single person. The term itself has nothing to do with a desired size of the span. In other words, whether the one supervises two employees or one hundred, span of management is the term applied to the number. In the three-person group (i.e., one supervisor and two employees), the six possible relationships or interactions may exist.
By applying a scientific approach, managers are also able to make accurate predictions for what is not under their control. OR/MS/DS/SS modeling process is a scientific approach in that it uses measurable and numerical scales to translate observed phenomena. If 'God geometrizes' as Plato says, man certainly arithmetizes. The world is qualitative. However, humans can understand, compare, and manipulate numbers only. Qualitative information may be characterized and processed by assigning numbers. Therefore, we use some measurable, numerical scales to quantify the world. This enables us to understand the world by finding any relationship, and using manipulation, comparison, calculation, etc. Then we use the same scale to qualify it back to the world. This is the essence of the "human understanding structured process." As Tom Peters, an international authority on business management says, "If you can't measure it, you can't manage it".
There has been recognition that some knowledge cannot be quantified and cannot be captured, codified or stored. However, the predominant approach to the decision making based on this knowledge is to try to convert it to a form that can be handled using the quantitative analysis.
Quantitative analysis tends to drive out qualitative analysis, even in the Liberal Arts areas of study, such as organization science, sociometrics, and psychometrics. The "fuzzy set theory" has even been developed to quantify qualitative terms that we use to express our feelings. However, it is questionable whether the internal world of one's own experience can also be subjected to analytical modeling, just like the external world. The following is a paraphrase of what Adam Smith said about the main difficulty in representation of feelings: "It is not an easy task to construct analytical models for feelings, because our senses will never inform us of what, e.g., somebody is in suffering as long as we ourselves are at our eases." However, in the medical professions it is common to be questioned, "on a scale of one to ten, one being the worst, how do you feel?" This elicits subjective answers from the patients.
Mathematical modeling can claim to be the most original creation of mankind.
The originality of modeling lies in the fact that in model building connections between things are exhibited which, apart from the agency of human reason, are extremely unobvious. Thus the ideas, now in the minds of modelers, lie very remote from any notions that can be immediately derived by perception through the senses; unless it is perception stimulated and guided by an antecedent modeling process.
Advantages of using the modeling approach to problem solving: A question for you: "When a management scientist goes to work, does he/she wait for problems to be assigned or does he/she go find problems?" Do not create problems for yourself and others. Wait for the problem to be assigned to you. The problem owner(s) and the management scientist consultant are two different parties.
Unfortunately, when you graduate from your MBA program and are equipped with many problem solving techniques, you may have a temptation to use these techniques by looking for any kind of problems. (Do you recall when you were young and first held a hammer? Didn't everything start to look like a nail?) This may create unnecessary difficulties for the organization you are supposed to help. Remember that Problems come first and then the solutions, not the other way around!
A management scientist provides aid and/or facts to the decision maker in order to make a better decision. The management scientist should not attempt to make these decisions or to influence the decisions. As such, the management scientist and the decision maker should not be the same person. The management scientist, therefore, is to serve as an objective voice to interpret a managerial decision problem that cannot be solved internally because of proximity or bias.
A mathematical (i.e., analytical) model is the one whose relationships are expressed in the rigorous language of mathematics. In this way, a mathematical model is abstract because one cannot visualize the system it is supposed to portray by merely looking at it.
Defining the system boundaries: Often, in modeling process the analysts do not model "systems" -- rather, they model specific problems that the decision makers (i.e., the managers) wish to understand. It is important and necessary to clearly define the boundaries of the system's decision problem under investigation. In this context a system is the restricted portion of the universe under consideration and its boundaries are the limits that separate the system from the remainder of the universe. Often it may turn out that the initial choice of boundaries is too restrictive. Therefore, to fully analyze a given system, it may be necessary to expand the system boundaries to include other subsystems that strongly affect the decision strategy. Suppose you are to study and make a descriptive model of an international airport, what are the boundaries for such a large system?
