© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-1 Chapter 4 Modeling and Analysis Turban, Aronson, and Liang Decision Support Systems and Intelligent Systems, Seventh Edition

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-2 MSS Mathematical Models Link decision variables, uncontrollable variables, and result variables together decision variables, uncontrollable variables are the parameters while result variables are the outcomes which considered as dependent variables.

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-3 MSS Mathematical Models –Decision variables describe alternative choices they could be people, time and schedules. –Uncontrollable variables are outside decision- maker’s control these factors con be fixed, in which case they are called parameters and they can vary. –Fixed factors are parameters. –Intermediate outcomes produce intermediate result variables. –Result variables are dependent on chosen solution and uncontrollable variables.

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-4 MSS Mathematical Models Non-quantitative models // like employee satisfaction (intermediate outcome), which in turn determines the productivity level (final result) –Symbolic relationship –Qualitative relationship –Results based upon Decision selected Factors beyond control of decision maker Relationships amongst variables

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-5

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-6

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-7 The structure of MSS Mathematical Models

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-8 Mathematical Programming optimization Tools for solving managerial problems Decision-maker must allocate resources amongst competing activities Optimization of specific goals Linear programming is the best known technique in a family of optimization tools called mathematical programming. –Consists of decision variables, objective function and coefficients, uncontrollable variables (constraints), capacities, input and output coefficients

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-9 Mathematical Programming optimization linear programming Mathematical programming is a family of tools designed to help solve the managerial problems in which the decision-maker must allocate scarce resources among competitive activities to optimize a measurable goal. Ex. The distribution of machine time (the resource) among various products (the activities) is a typical allocation problem. Linear programming (LP) allocation problems usually the following characteristics.

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-10 Mathematical Programming optimization linear programming LP Characteristics: A limited quantity of economic resources is available for allocation. The resources are used in the production of products or services. There are two or more ways in which the resources can be used. Each is called a solution or a program. Each activity (product or service) in which the resources are used yields a return in terms of the stated goal. The allocation is usually restricted by several limitations & requirements called constraints.

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-11 Mathematical Programming optimization linear programming LP allocation model is based on the following rational economic assumptions: Return from different allocation can be measured & compared. The return from any allocation is independent of other allocations. The total return is the sum of the returns yielded by the different activities. All data are known with certainty. The resources are to be used in the most economical manner.

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-12 Mathematical Programming optimization linear programming

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-13 Mathematical Programming optimization The most common optimization models can be solved by a variety of mathematical programming methods, they are:

End of Chapter 4 © 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-14