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