Using The Excel Solver To Solve Mathematical Programs

Using The Excel Solver To Solve Mathematical Programs summarize the file "Chapter 8: Using The Excel Solver To Solve Mathematical Programs." Give pictures,animations in each slide for written language, pictures and slid. Chapter Overview 8.1 Introduction 8.2 Formulating Mathematical Programs 8.2.1 Parts of the Mathematical Program 8.2.2 Linear, Integer, and Nonlinear Programming 8.3 The Excel Solver 8.3.1 The Solver Steps 8.3.1.1 Standard Solver 8.3.1.2 Premium Solver 8.3.2 A Solver Example 8.3.2.1 Product Mix 8.3.2.2 Infeasibility 8.3.2.3 Unboundedness 8.3.3 Understanding Solver Reports 8.4 Applications of the Solver 8.4.1 Transportation Problem 8.4.2 Workforce Scheduling 8.4.3 Capital Budgeting 8.4.4 Warehouse Location 8.5 Limitations and Manipulations of the Solver 8.6 Summary 8.7 Exercises Chapter 8 Using The Excel Solver To Solve Mathematical Programs Chapter 8: Using The Excel Solver To Solve Mathematical Programs 2 8.1 Introduction This chapter illustrates how to use the Excel Solver as a tool to solve mathematical programs. We review the basic parts of formulating a mathematical program and present several examples of how the Solver interprets these parts of the program from the spreadsheet. We give examples of linear, integer, and non-linear programming problems to show how the Solver can be used to solve a variety of mathematical programs. We also give an overview of the Premium Solver and its benefits. This chapter is important for the reader to understand as many DSS applications involve solving optimization problems, which are mathematical programs. The reader should be comfortable with preparing the spreadsheet for use with the Solver. In Chapter 19, we revisit the Solver using VBA commands. We have several examples of DSS applications which use the Solver to solve optimization problems, su ch as Portfolio Management and Optimization. 8.2 Formulating Mathematical Programs The Excel spreadsheet is unique because it is capable of working with complex mathematical models. Mathematical models transform a word problem into a set of equations that clearly define the values that we are seeking, given the limitations of the problem. Mathematical models are employed in many fields, including all disciplines of engineering. In order to solve a mathemat ical model, we develop a mathematical program which can numerically be solved and re translated into a qualitative solution to the mathematical model. 8.2.1 Parts of the Mathematical Program A mathematical program consists of three main parts. The first is the decision variables . Decision variables are assigned to a quantity or response that we must determine in a problem. For example, if a toy manufacturer wants to determine how many toy boats and toy cars to produce, we assign a variable to represent the quantity of toy boats produced, x 1 , and the quantity of toy cars produced, x 2 . Decision variables are defined as negative , non-negative, or unrestricted . An unrestricted variable can be either negative or non-negative. These variables represent all other relationships in a mathematical program, including the objective, the limitations, and the requirements. The second part of the math program, called the objective function , is an equation that states the goal, or objective, of the model. In the same example of the toy manufacturer, we want to know the quantities of toy boats and toy cars to produce. However, the goal of the manufacturing plant’s production may be to increase profit. If we know that we can profit $5 for every toy boat and $4 for every toy car, then our objective function is: Maximize 5x 1 + 4x 2 In other words, we want profit to drive us in determining the quantity of boats and cars to produce. Objective functions are either maximized or minimized ; most applications involve maximizing profit or minimizing cost. The third part of the math progam, the constraints , are the limitations of the problem. That is, if we want to maximize our profit, as in the toy manufacturer example, we could produce as many toys as possible if we di d not have any limits. However, in most

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