Sensitivity Analysis: An Applied Approach
In this chapter, we discuss how changes in an LPs parameters affect the optimal solution. This is called sensitivity analysis. We also explain how to use the LINDO output to answer questions of managerial interest

APPENDIX 2
Cases
Jeffrey B. Goldberg
UNIVERSITY OF ARIZONA
CASE
1 2 3 4 5 6 7 8 9 10 11
Help, Im Not Getting Any Younger! Solar Energy for Your Home
1351
1351
CASE
CASE
Golf-Sport: Managing Operations
1352 1355 1356
CASE
Vision Corporation: Production Pla

Nonlinear Programming
In previous chapters, we have studied linear programming problems. For an LP, our goal was to maximize or minimize a linear function subject to linear constraints. But in many interesting maximization and minimization problems, the o

Decision Making under Uncertainty
We have all had to make important decisions where we were uncertain about factors that were relevant to the decisions. In this chapter, we study situations in which decisions are made in an uncertain environment. The foll

Introduction to Linear Programming
Linear programming (LP) is a tool for solving optimization problems. In 1947, George Dantzig developed an efcient method, the simplex algorithm, for solving linear programming problems (also called LP). Since the develop

Probabilistic Dynamic Programming
Recall from our study of deterministic dynamic programming that many recursions were of the following form: ft (current state) min
all feasible decisions
(or max)cfw_costs during current stage
ft
1
(new state)
For all the

Transportation, Assignment, and Transshipment Problems
In this chapter, we discuss three special types of linear programming problems: transportation, assignment, and transshipment. Each of these can be solved by the simplex algorithm, but specialized alg

Integer Programming
Recall that we dened integer programming problems in our discussion of the Divisibility Assumption in Section 3.1. Simply stated, an integer programming problem (IP) is an LP in which some or all of the variables are required to be non

Markov Chains
Sometimes we are interested in how a random variable changes over time. For example, we may want to know how the price of a share of stock or a rms market share evolves. The study of how a random variable changes over time includes stochasti

Deterministic EOQ Inventory Models
In this chapter, we begin our formal study of inventory modeling. In earlier chapters, we described how linear programming can be used to solve certain inventory problems. Our study of inventory will continue in Chapters

Deterministic Dynamic Programming
Dynamic programming is a technique that can be used to solve many optimization problems. In most applications, dynamic programming obtains solutions by working backward from the end of a problem toward the beginning, thus

Results and Discussions: The emission spectra from various sources were determined. A partial energy level diagram was determined using wavelengths found from the hydrogen spectrum. Intensities are listed out of ten. Fluorescent Light Spectrum The fluores

Part A 1) Fluorescent Light Wavelength(nm) 550 610 430 440 580 585 403 Color Green Red Purple Blue Yellow Orange Could not see with eye sight In tensity 10 9 6 4 2 1
2) Incandescent light bulb shows continuous spectrum
3) Wavelength(nm) 710 and 670 580 54

Optical Spectroscopy by Erin Samplin Lab Instructor: Xiaoxiao Li October 23, 2007
Purpose Determine the composition of an unknown solution containing two or more ionic salts on the basis of its emission spectra. Create a partial energy-level diagram for h

Experiment #5: Optical Spectrometry
Purpose: The purpose of this experiment was to observe the emission spectra of various compounds by methods of spectrometry including the use of a spectrometer and a computer, to conceive and perform a procedure to iden

Optical Spectroscopy
Results and Discussion: This experiment was done to find the emission spectra of a variety of materials. The two main goals were: to determine the composition of a solution which contains two or more ionic salts, and to construct a pa

Optical Spectroscopy
By Yiliu (Peter) Wang Teaching Assistant: Josie Bodle October 26th, 2007
Results and Discussion:
The emission spectra from a variety of sources fluorescent light, incandescent light, helium, salt solutions, and hydrogen gas were exami

APPENDIX 1
@Risk Crib Sheet
@Risk Icons Once you are familiar with the function of the @Risk icons, you will nd @Risk easy to learn. Here is a description of the icons.
Opening an @Risk Simulation
This icon allows you to open up a saved @Risk simulation.

Simulation with Process Model
In Chapter 21, we learned how to build simulation models of many different situations. In this chapter, we will explain how the powerful, user-friendly simulation package Process Model can be used to simulate queuing systems.

Simulation
Simulation is a very powerful and widely used management science technique for the analysis and study of complex systems. In previous chapters, we were concerned with the formulation of models that could be solved analytically. In almost all of

Game Theory
In previous chapters, we have encountered many situations in which a single decision maker chooses an optimal decision without reference to the effect that the decision has on other decision makers (and without reference to the effect that the

Review of Calculus and Probability
We review in this chapter some basic topics in calculus and probability, which will be useful in later chapters.
12.1
Review of Integral Calculus
In our study of random variables, we often require a knowledge of the basi

Advanced Topics in Linear Programming
In this chapter, we discuss six advanced linear programming topics: the revised simplex method, the product form of the inverse, column generation, the DantzigWolfe decomposition algorithm, the simplex method for uppe

Network Models
Many important optimization problems can best be analyzed by means of a graphical or network representation. In this chapter, we consider four specic network modelsshortest-path problems, maximum-ow problems, CPMPERT project-scheduling mode

Sensitivity Analysis and Duality
Two of the most important topics in linear programming are sensitivity analysis and duality. After studying these important topics, the reader will have an appreciation of the beauty and logic of linear programming and be

Basic Linear Algebra
In this chapter, we study the topics in linear algebra that will be needed in the rest of the book. We begin by discussing the building blocks of linear algebra: matrices and vectors. Then we use our knowledge of matrices and vectors

An Introduction to Model Building
1.1
An Introduction to Modeling
Operations research (often referred to as management science) is simply a scientific approach to decision making that seeks to best design and operate a system, usually under conditions req