This Web site is designed and created for you. No one need be ashamed of what he or she does not know or how long it takes to master new information. Learning by the Web-enhanced material can be self-paced and non-judgmental. Using advantages of this technology to expand learning opportunities is especially crucial because we live in a time when learning is a necessity and no longer a luxury.
At one time, it was sufficient for a firm to produce a quality product. As competition grows in today's market, simply producing a quality product is not sufficient. Today, a firm must produce a quality product at less cost than its competitors and simultaneously manage inventory, warehouse space, procurement requirements, etc. In the future, still greater demands will be placed upon decision-makers.
A manager makes many decisions everyday. Some decisions are routine and inconsequential, while others may impact the operations of a firm. Some decisions cause a firm to lose or gain money or determine whether goals are reached. The field of Decision Science (DS), known also as Operations Research (OR), Management Science (MS), has helped managers develop the expertise and tools to understand decision problems, put them into mathematical terms and solve them.
Many tools and techniques help individuals and organization make better decisions. This site provides decision makers and analysts the tools that provide a logical structure to understand the mathematical techniques to solve formulated (i.e. modeled) problems. The primary tools are linear programming and decision analysis, which provide structure and value in helping define and under-stand a problem. On this site you will learn decision making methodologies to determine optimal strategic solutions to described problems. Personal Computers allow application of these techniques even in the small business environment. Finally, a clear understanding of a general approach to problem solving enables you to use other applied decision-making and planning techniques in this site.
Since the strategic solution to any problem involves assumptions, it is necessary to determine how much the strategic solution changes when the assumptions change. You learn this by performing "what-if" scenarios or sensitivity analysis.
Preparation for management, whether it is related to technology, business, production, or services, requires knowledge of tools, which aid in determining feasible and optimal policies. In addition to communication and qualitative reasoning skills, enterprises wishing to remain competitively viable in the future, need decision support systems to help them understand the complex interactions between all components of an organization's internal and external system. Such components are found in environmental design, transportation planning and control, facilities management, military mission planning and execution, disaster relief operations, investment management, and manufacturing operations.
An organization, like other organisms, must keep itself in a state of homeostasis--subsystems regulate one another so none of the parts is ahead or behind the system as a whole. This interaction is not trivial; mathematical modeling assists in understanding these fundamental relationships. OR/MS concepts focus on communication of results and recommended action. This helps build a consensus concerning the possible outcomes and recommended action. The decision-maker might incorporate other perspectives of the problem, such as culture, politics, psychology, etc., into the management scientist's recommendations. The creation of management science software is one of the most important events in decision-making. OR/MS/DS software systems are used to construct examples, to understand existing concepts, and to find new managerial concepts. New developments in decision-making often motivate developments in solution algorithms and revisions of software systems. OR/MS software systems rely on a cooperation of OR/MS practitioners, algorithms designers and software developers.
This site overview the major quantitative modeling tools successfully used to model the complex interactions described above. Although not exhaustive, this site provides framework for further study. The following tools will be studied: analytically based solutions to math models, linear programming, decision theory, integer programming and network models. Management Science encompasses many disciplines of study because decision-making is a central human activity.
Just like you, most of my readers are employed full time. They are engineers, doctors, lawyers, and other professionals. You and your classmates want to learn the business side of their professions. It is important to learn the language of the managers to overcome communication barriers. For example, engineers will learn how to translate "precision" into extra dollars in earning/saving.
Among my readers, there are some students who find it difficult to rethink and re-evaluate their pre-conceived ideas. In decision-making, one must have an open-mind to be able to think differently and to see from many perspectives. University classrooms provide the environment for debate and the exchange of ideas. Open-mindedness is the main requirement in achieving the ultimate goal of education, which is to be able to think for yourself. Change of opinion is often the progress of sound thought and growing knowledge. Upon completion of this course, you may find that it "validates" what you think about making good strategic decisions and causes a peace of mind. The contents of this site will help you to systematize what you already know from your own professional experience. Objective:
To provide an overview of this Web site and the foundations of management Science. What is Management Science? It is a rational, structured approach to problem solving. It is the study of developing procedures that can be used in the process of decision making and planning. To arrive at a sound decision, one must identify an objective measure of performance (to measure success). The objective must represent the goal the decision maker wants to accomplish.
This objective serves as a starting point for developing a model for the decision problem. The context of modeling: What is a model, what is management science model? The process, including the feedback loop plus common principals underlying modeling. Limitations of modeling plus sources of error. A partial list of model-types: optimization models, decision analysis models.
Mathematical Modeling (Reflection before action. Think and plan before start doing). Problem Understanding and Formulation, Search for Solution, What-if Analysis
Deterministic and Stochastic Models: An example for deterministic modeling is linear programming as a successful modeling tool optimization, while decision analysis is a modeling tool for problems under uncertainty. Topic: Problem Formulation: Linear Programs Introduction: Mathematical Modeling & Classification of Models:
A Linear Programming model seeks to maximize or minimize a linear function, subject to a set of linear constraints. The linear model consists of the following components:
The Importance of Linear Programming:
Linear programming deals with that class of programming problems for which both the function to be optimized is linear and all relations among the variables corresponding to resources are linear. This problem was first formulated and solved in the late 1940's. Rarely has a new mathematical technique found such a wide range of practical business, commerce, and industrial applications and simultaneously received so thorough a theoretical development, in such a short period of time. Today, this theory is being successfully applied to problems of capital budgeting, design of diets, conservation of resources, games of strategy, economic growth prediction, and transportation systems. In very recent times, linear programming theory has also helped resolve and unify many outstanding applications.
It is important for the reader to appreciate at the outset that the "programming" in Linear Programming is of a different flavor than the "programming" in Computer Programming. In the former case, it means to plan and organize as in "Get with the program!” while in the latter case, it means to write instructions for performing calculations. Training in the one kind of programming has very little direct relevance to the other. In fact, the term "linear programming" was coined before the word "programming" became closely associated with computer software. This confusion is sometimes avoided by using the term linear optimization as a synonym for linear programming. Topic: Computer Applications and Sensitivity Analysis Introduction: Dealing With Uncertainties and Scenario Modeling: The business environment is often unpredictable and uncertain because of factors such as economic changes, government regulations, dependence on the subcontractors and venders etc. Managers often find themselves in a dynamic, unsettled environment where even short long range plans must be constantly reassessed and incrementally adjusted. All these require a change-oriented mentality to cope with uncertainties.
Human uses mathematical and computational constructs (models) for a variety of settings and purposes, often to gain insight into possible outcomes of one or more courses of action. This may concern financial investments, the choice on (whether/how much) to insure, industrial practices and environmental impacts. The use of models is flawed by the unavoidable presence of uncertainties, which arise at different stages, both in the construction and corroboration of the model itself, in its quality assurance, and especially in its use.
Every solution to a decision problem is based of certain parameters which are assumed to be fixed. Sensitivity analysis is a collection of post-solution activities to study and determine how sensitive the solution is to changes in the assumptions. Other names for such activities are stability analysis, what-if analysis, uncertainty analysis, computational and numerical instability, functional instability, tolerance analysis, post-optimality analysis, allowable increases and decreases, and many other similar phrases which reflect the importantness of this stage of the modeling process.
One may tackle uncertainties in a more "deterministic" manner. The approach comes under various names such as "scenario modeling", "deterministic modeling", and "sensitivity analysis", and "stability analysis". The idea is to subjectively come up with a ranked list of higher level uncertainties that might presumably have a bigger impact on the eventual mapping result, before zooming in on the details of any particular "scenario" or model. For example, the problem parameters, and the uncontrollable factors indicated in the above Figure for the Carpenter's problem, required a complete sensitivity analysis in order to enable the carpenter to be in control of his/her business. Objective: As you know by now, this site has three components: Key words & Phrases, How to work with mechanical tools (such as, any solution methodologies), and most of all what are the implications of all these to Business Decision Making. As I pointed out this site is not about say, linear programming (LP), we are using LP as an application and a tool. Since you have mastered, the Key words & Phrase, and Techniques, now we are able to concentrate on the Managerial Business Making Process, which deals with how you interpret the solution results produced by your computer package. An understanding of the influence of the above on the course of action suggested by the model. The following is condensed list of reasons why sensitivity analysis should be considered.
Decision making Process:
Managerial Interpretations: The decision problem is stated by the decision-maker often in some non-technical terms. When you think over the problem, and finding out what module of the software to use, you will use the software to get the solution. The solution should also be presented to the decision-maker in the same style of language, which is understandable, by the decision-maker. Therefore, just do not give me the printout of the software. You must also provide managerial interpretation of the solution in some non-technical terms.
Warning: Computer solutions for the network and integer problems are valid; however the produced sensitivity results may not be valid. This is due to the facts that, among other things, these problems are Integer-LPs. Moreover, in the case of network models anyone constraint in any of these models is always redundant. Therefore, simply ignore the sensitivity analysis of the printouts.
Topic: Decision Analysis - I Introduction:
Making Justifiable, Defendable Decisions: Decision analysis is the discipline of evaluating complex alternatives in terms of values (usually in $, this is what the managers care about) and uncertainty (what we do not know). Decision analysis provides insight into how the defined alternatives differ from one another, and generates suggestions for new and improved alternatives. We use numbers to quantify subjective values and uncertainties, which enables us to understand the decision situation. The numerical results must be translated back for generating qualitative insight.
Humans can understand, compare and manipulate numbers. Therefore, in order to create a decision analysis model, it is necessary to create the model structure and assign the probabilities and values to populate the model for computation. This includes the values for probabilities, the value functions for evaluating alternatives, the value weights for measuring the trade-offs amongst objectives and risk preference.
Once the structure and numbers are in place, the analysis can begin. Decision Analysis involves much more than computing the expected, weighted utility of each alternative. If we stopped there, decision makers would not get much insight. We have to examine the sensitivity of the expected, the weighted utility to key probabilities, and the weights and risk preference parameters. As part of the sensitivity analysis, we can calculate the value of perfect information for uncertainties that have been explicitly modeled.
Additional quantitative comparisons include the direct comparison of weighted utility for two alternatives on all of the objectives and the comparison of all of the alternatives on any two selected objectives showing the Pareto optimality for these two objectives.
Complexity in the modern world, along with Information quantity, Uncertainty and Risk, make it necessary to provide a rational decision making framework. The goals of decision analysis are: To give guidance, information, insight, and structure in the decision making process in order that better, more "rational" decisions can be made.
Know that a decision needs a decision maker who is responsible for making decisions. The decision maker has a number of alternatives, and must choose one of them. The objective of the decision maker is to choose the best alternative. When the decision has been made, events may have occurred over which the decision maker had no control. Each combination of an alternative chosen, followed by an event happening, leads to an outcome with some measurable value. Managers make decisions in complex situations. Decision tree and payoff matrices describe these situations and add structure to problems.
Objective: The field of decision analysis provides framework for making important decisions. Decision analysis allows us to select a decision from a set of possible decision alternatives when uncertainties regarding the future exist. The goal is to optimize the resulting payoff in terms of a decision criterion. Maximizing expected profit is a common criterion when probabilities can be assessed. When risk should be factored into the decision making process, Utility Theory provides a mechanism for analyzing decisions in light of risk.
Topic: Decision Analysis - II Introduction: Probabilistic Modeling: Considering the uncertain environment, the chance that "good decisions" are made increases with the availability of "good information." The chance that "good information" is available increases with the level of structuring the process of Knowledge Management. One may ask, "What is the use of decision analysis techniques without the best available information delivered by Knowledge Management?" The answer is: one must not make responsible decisions until one possess enough knowledge. However, for private decisions one may rely on, e.g., the psychological motivations, as discusses under "Decision-Making Under Pure Uncertainty" in this site. Moreover, Knowledge Management and Decision Analysis are indeed interrelated since one influences the other, both in time, and space.
As a cautious note, you may experience some difficulties in comprehending the decision analysis problems; this is true for everyone while translating the way the problems are worded and the type of questions that are asked. Therefore, the most difficult part of decision analysis is the translation of the problem. Here are my suggestions: Read the problem may time, slowly. I suggest also drawing a decision tree to start with, then read the problem few time to modify the tree. Remember that, the mathematical representation of a decision analysis problem is the decision tree.