On a daily basis a manager has to make many decisions. Some of these decisions are routine and inconsequential, while others have drastic impacts on the operations of the firm for which he/she works. Some of these decisions could involve large sums of money being gained or lost, or could involve whether or not the firm accomplishes its mission and its goals. In our increasingly complex world, the tasks of decision-makers are becoming more challenging with each passing day. The decision-maker (i.e., the responsible manager) must respond quickly to events that seem to take place at an ever-increasing pace. In addition, a decision-maker must incorporate a sometimes-bewildering array of choices and consequences into his or her decision. Routine decisions are often made quickly, perhaps unconsciously without the need for a detailed process of consideration. However, for complex, critical or important managerial decisions it is necessary to take time to decide systematically. Being a manager means making critical decisions that cannot and must not be wrong or fail. One must trust one's judgement and accept responsibility. There is a tendency to look for scapegoats or to shift responsibility.
Decisions are at the heart of any organization. At times there are critical moments when these decisions can be difficult, perplexing and nerve-wracking. Making decisions can be hard for a variety of structural, emotional, and organizational reasons. Doubling the difficulties are factors such as uncertainties, having multiple objectives, interactive complexity, and anxiety.
Making good strategic decisions is learnable and teachable through an effective, efficient, and systematic process known as the decision-making process. This structured and well-focused approach to decision-making is achieved by the modeling process, which helps in reflecting on the decisions before taking any actions. Remember that: one must not only be conscious of his/her purposeful decisions, one must also find out the causes for which they are made. There is no such thing as "free-will". Those who believe in their free wills are in fact ignorant to the causes that impel them to their decisions. There is no such thing as arbitrary in any activity of man, least of all in his decision-making. Just as he has learned to be guided by objective criteria in making his physical tools, so he is guided by unconscious objective criteria in forming his decision in most cases.
A basic education in OR/MS/DS/SS for managers is essential. They are responsible for leading the business system and the lives in that system. The business system is dynamic in nature and will respond as such to disturbances internally and externally.
Nowadays, the OR/MS/DS/SS approach has been providing assistance to managers in developing the expertise and tools necessary to understand the decision problems, put them in analytical terms and then solve them. The OR/MS/DS/SS analysts are, e.g., "chiefs of staff for the president", "advisors", "R&D modelers" "systems analysts", etc. Applied Management Science is the science of solving business problems. The major reason that MS/OR has evolved as quickly as it has is due to the evolution in computing power.
Since some decision problems are so complicated and so important, the individuals who analyze the problem are not the same as the individuals who are responsible for making the final decision. Therefore, this site distingushes between a management scientist, someone who studies what decision to make, and a decision maker, someone responsible for making the decision.
This site is about how to make good decisions when confronted with decision problems. It means real problems, the effective handling of which can make a significant difference. Almost all decision problems have environments with similar components as follows:
After recognizing this no-nonsense classification of decision-making components, the OR/MS/DS/SS analyst performs the following sequence with some possible feedback loops between its steps:
Since the strategic solution to any problem involves making certain assumptions, it is necessary to determine the extent to which the strategic solution changes when the assumptions change. You will learn this by performing the "what-if" scenarios and the necessary sensitivity analysis. Ensure that both plan and dispositions are flexible, adaptable to circumstances. Your plan should foresee and provide for a next step in case of success or failure.
One must evaluate the various courses of actions within the controllable inputs, consider various scenarios for uncontrollable inputs, and then decide the best course of action. As you know, the whole process of managerial decision-making is synonymous with the practice of management. Decision-making is at the core of all managerial functions. Planning, for example, involves the following decisions: What should be done? When? How? Where? By whom? As shown in the following diagram:
As indicated in the above diagram, perceiving the need to face the decision problem is a point of departure and no more. As soon as you elaborate, it becomes transformed by thought process to a mental model. The decision-making process contains a few well-defined stages, including describing, prescribing, and controlling the problem, each of these stages requires a set of relevant questions to be asked. Moreover, this process is never ending since the problem keeps changing, therefore there is a always need for feedback to measure the effect of your decision. Moreover, each decision problem that you make successfully became a rule, which served afterwards to make other decisions. This happens when your are facing a sequential decision-making problem.
Preparation for management, whether it is related to technology, business, production, or services, requires knowledge of tools, which can aid in the determination of feasible, optimal policies. In addition to skills related to communication and qualitative reasoning, enterprises wishing to remain competitively viable in the future, need model-driven decision support systems to help them understand the complex interactions between all components of a given organization's system, both internal, and external situations. The strategic assessment at this stage must recognize both the internal analysis such as the strengths and weaknesses, and the external analysis such as threats and opportunities.
There are also situations where some may feel that the decision-maker should rely on simply "do the right thing" and damn the analytical strategic thinking . Whereas many agree that for defensible and responsible decisions one should at least know the balance of the analytical approach as well as the human-side of the decision which includes the ethical elements.
Successful OR/MS/DS/SS modeling approach to decision-making demands a proper attitude as well as an understanding of more technical matters. Although both the OR/MS/DS/SS analyst and decision-maker should understand problem identification, model building, and solution techniques, the attitudes of both are probably the most important elements of successful application. Although proper attitude is not sufficient for successful application, it is necessary. An analyst who focuses more on techniques for solution than on model formulation will not be successful. The analyst's main interest should be in providing assistance in decision-making and not in finding methods of solution that are more elegant or marginally faster than existing methods. A decision maker who thinks that she or he can turn the analyst loose without guidance and expect to get relevant information back that can be applied directly to the problem and then forgotten will not make the best use of quantitative inputs. Instead, the interaction between the decision-maker and OR/MS/DS/SS analyst must be open, interactive, and focused on the ultimate goal of the effort: to develop and make the best use of the quantitative input to a decision problem.
Today's business decisions are driven by data. In all aspects of our lives, and importantly in the business context, an amazing diversity of data is available for inspection and given insights. Moreover, business managers and decision makers are increasingly encouraged to justify decisions on the basis of data. Taking this course gives you an edge. Graduates with strong quantitative skills are in demand. This phenomenon will grow as the impetus for data-based decisions strengthens and the amount and availability of data increases. The quantitative toolkit can be developed and enhanced at all stages of your career.
The large system is the result of the application of scientific techniques to manufacturing and persists as a fundamental characteristic of modern industry. Today larger companies employ thousands of workers, deal in billions of dollars, manufacture hundreds of products, and service a multitude of markets. These service industries, including banks, hospitals, insurance companies, consulting firms, and governments, are faced with operational complexities similar to those noted for the manufacturing industry.
Due to the globalization of telecommunications markets, and to the general decline of monopolies, "other licenced operators" are starting to appear almost in every country. A new company entering a competitive market where a first, and even a second, operators already exist has to face several problems, and can analyze the opportunities the situation may offer. A problem is a chance for you to do your best.
The complexity of today's business operations, aggressive competition, and government controls have made the job of the manager increasingly difficult. It is no longer possible for one individual to be aware of the details of every characteristic of the firm or to make all decisions regarding its operation. Even within a manager's relatively small span of control the factors affecting his decisions are often so numerous and their effects so pervasive that "seat of the pants" decisions are no longer acceptable. As a result, effective decision-making often requires the availability of information analyzed and summarized in a timely fashion.
An effective and proven process has been developed over the last 70 years and is known as Operations Research/Management Science/Decision Science/Success Science (OR/MS/DS/SS).
In search of the genealogy of OR/MS, we might ask ourselves a more general question "What is OR/MS/DS/SS?" First let's find out what we mean by "Is" in general.
Management Science (MS) often takes an analytical view of a decision before making a decision. That is, reflection before action, as a Chinese proverb says, "To chop a tree quickly, spend twice the time sharpening the ax." Carpenters say, "Measure twice, cut once." It's no delay to stop to edge the tool.
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:
- Organizations are becoming more complex.
- Environments are changing so rapidly that past practices are no longer adequate.
- The costs of making bad decisions have increased.
You must also master the exact meanings of the Keywords and Phrases used in OR/MS/DS/SS professions because if your vocabulary is limited your thoughts are limited and vice versa. You have to know the business side of your profession. What is important for you is to learn the language of the managers. More management-oriented decision-makers are saying "your language seems so far removed from mine." These decision makers are simply left to sink or swim in an environment which seems to marginalize them simply through the use of OR/MS/DS/SS jargons. For example, industrial engineers (i.e., OR/MS/DS/SS practitioners in factories) must learn how to translate "precision" into extra dollars in terms of earnings/savings. This is the only language managers know.
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.
Overcoming the Communication Barriers: Knowledge is what we know. Information is the communication of knowledge. In every knowledge exchange, there is a sender and a
receiver. The sender makes common what is private, does the informing, the communicating. The receiver takes in the information turns it into knowledge. Depending on the audience of the report, the OR/MS/DS/SS model may or may not be included. It is the task of the management science team to write a report that is understandable by all that will read it. In short, without the ability to effectively translate the models and resulting calculations back into the real-world situation from which they were derived in an understandable way, the OR/MS/DS/SS professional is not able to accomplish his/her purpose. Communication is a chain of events in which the message serves as the basic link, as is depicted in the following flowchart, known as the Shannon's communication model. Feedback/acknowledgment provide assurance of consistency in the encoding and decoding processes.
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"?
Progressive Approach to Modeling: Modeling for decision making involves two distinct parties, one is the decision-maker and the other is the model-builder known as the analyst. The analyst is to assist the decision-maker in his/her decision-making process. Therefore, the analyst must be equipped with more than a set of analytical methods.
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.
Such miscommunication can be avoided if the manager works with the specialist to develop first a simple model that provides a crude but understandable analysis. After the manager has built up confidence in this model, additional detail and sophistication can be added, perhaps progressively only a bit at a time. This process requires an investment of time on the part of the manager and sincere interest on the part of the specialist in solving the manager's real problem, rather than in creating and trying to explain sophisticated models. This progressive model building is often referred to as the bootstrapping approach and is the most important factor in determining successful implementation of a decision model. Moreover the bootstrapping approach simplifies otherwise the difficult task of model validating and verification processes.
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.
The Cycle of Decision-Making
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.
Further Readings:
Gharajedaghi J., Systems Thinking - Managing Chaos and Complexity: A Platform for Designing Business Architecture, Butterworth-Heinemann, 1999.
Kauffman S., At Home in the Universe: The Search for Laws of Self-Organization and Complexity, Oxford Univ. Press, 1996.
Kim D., Introduction to Systems Thinking , Pegasus Communications, 1999. The author provides an interesting metaphor for strategic resources as water being contained in tank, flowing through pipes into and out of different parts of the business system and, most importantly, from and to competitors.
Mingers J., and A. Gill (editors), Multi-methodology: The Theory and Practice of Combining Management Science Methodologies, Wiley, 1997.
Historical Needs for OR/MS
Until the middle of the 19th century, most industrial enterprises only employed a few workers. However, as companies expanded, it became less and less feasible for one person to manage all of the new managerial functions of the business effectively. New scientific methodologies were developed to provide assistance to each new type of managerial function as it appeared. As more specialized forms of management emerged, more specialized subfunctions, such as statistical quality control, equipment maintenance, marketing research, and inventory control emerged. Whenever a managerial function is broken down into a set of different subfunctions, a new task, called the executive function of management, is created to integrate the diverse subfunctions so that they efficiently serve the interests of the business as a whole. The executive function evolved gradually with organizations themselves. However, increasing demands were made on the manager who, in turn, sought aid outside the organization. This gave rise to management consultants. What we call OR/MS/DS/SS today is, in fact, the use of scientific tools to aid the executive.
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.
The Nature and Meaning of OR/MS/DS/SS
Many definitions of OR/MS/DS/SS have been offered, as well as many arguments as to why it cannot be defined. The following definitions provide a useful basis for an initial understanding of the nature of OR/MS:
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).
Scientific approach to problem solving for executive management (Wagner 1969).
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.
Among key tasks of the scientific enterprise, perhaps none is more fundamental than that of making parts of the world understandable. Such understanding is typically seen as involving certain sorts of empirically supported explanations. That seemingly simple idea pitches us headlong into a variety of philosophical and historical thickets, but of present interest are apparent connections to human subjectivity, social structures, philosophical presuppositions, and other such matters.
Understanding something involves removal of at least some of its mystery. The process of coming to understand something involves a transition from mystery to sense making. It is a coming to see an answer to a particular sort of "Why?" question. Of course, what kinds of things strike us as mysterious, and why, involves all sorts of deep roots in, for example, human nature, cognition, specific context, and perspective. All those matters are structured in terms of human concepts, human experience, and the human condition generally.
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.
Explanations are what supply the materials that allow us to see. And a good explanation must supply the sort of materials that, in the complicated human cognitive context in question, will trigger that shift from mystery to sense. Different sorts of explanations may do that in different ways in different contexts. Very generally, explanations supply such materials by formally, narrative, or otherwise displaying a field of background causal webs, patterns, events, conditions, law, and/or historical developments within which the phenomena in question fit organically, so that the phenomena become integrated, constituent parts of some larger pattern or flow.
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.
Further Readings:
Engel A., Problem-Solving Strategies, Springer Verlag, 1998.
Proctor T., Creative Problem Solving for Managers, Routledge, London, 1999.
Starfield A., K. Smith, and A. Bleloch , How to Model It: Problem Solving for the Computer Age, Burgess Intl. Group, 1994.
The Prototype Applications
An important consequence of the application of OR/MS/DS/SS to a wide variety of problems is that a small set of problem types have been identified which account for most problems. Because of the frequent recurrence of these problems, prototype techniques have been developed for modeling them and for deriving solutions from these models. Prototype applications include:
Forecasting: Using time series analysis to answer typical questions such as: How big will demand for products be? What are the sales patterns? How will this affect profits?
Finance and Investment: How much capital do we need? Where can we get this? How much will it cost?
Manpower planning and Assignment: How many employees do we need? What skills should they have? How long will they stay with us?
Sequencing and Scheduling: What job is most important? In what order should we do jobs?
Location, Allocation, Distribution and Transportation: Where is the best location for an operation? How big should facilities be? What resources are needed? Are there shortages? How can we set priorities?
Reliability and Replacement Policy: How well is equipment working? How reliable is it? When should we replace it?
Inventory Control and Stockout: How much stock should we hold? When do we order more? How much should we order?
Project planning and control: How long will a project take? What activities are most important? How should resources be used?
Queuing and Congestion: How long are queues? How many servers should we use? What service level are we giving?
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.
Flexibility and Variety of Careers in OR/MS/DS/SS
Completion of OR/MS/DS/SS enables graduates to find employment as OR/MS/DS/SS analysts, academicians or managers. It is a fact that education and work in OR/MS/DS/SS can lead to the executive suite where decisions are made. Career opportunities in the following areas of business are excellent:
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."
Also visit the following collection:
Decision Making Resources
The Multidisciplinary and Interdisciplinary Nature OR/MS/DS/SS
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.
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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, w
