TAXONOMY OF DECISION MODELING A. MODELS: 1. DETERMINISTIC vs PROBABILISTIC 2. LINEAR vs NONLINEAR 3. UNCONSTRAINED vs CONSTRAINED 4. CONTINUOUS vs DISCRETE 5. SINGLE OBJECTIVE vs MULTIPLE OBJECTIVES B. ANALYSIS: 1. SOLUTION vs SIMULATION SOLULTION METHODS: a. TOTAL ENUMERATION b. ALGEBRAIC c. CALCULUS d. ALGORITHM e. HEURISTIC C. RESULTS: 1. OPTIMIZATION vs DESCRIPTIVE 2. GENERAL CASE vs SPECIFIC CASE

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TAXONOMY OF DECISION MODELING (With Descriptions) A. MODELS: 1. DETERMINISTIC vs PROBABILISTIC Sometimes called “certainty” vs “uncertainty.” In deterministic models, parameter values are assumed to be known values, i.e., constants. In probabilistic models, parameter values are not known with certainty and are therefore represented by probability distributions. 2. LINEAR vs NONLINEAR Linear models are characterized by linear functional relationships, i.e., y = 2x “Linear” implies both “proportionality” and “Additivity.” Nonlinear models are characterized by nonlinear functional relationships, i.e., y = 3x2 or y = 5/x, or y = 7x1x2 3. UNCONSTRAINED vs CONSTRAINED Unconstrained models have no restrictions on the values of the solution variables. Constrained models have certain restrictions on the values of the solution variables, i.e., x ≤ 40, or x1 + 2x2 ≤ 300. 4. CONTINUOUS vs DISCRETE Sometimes referred to as “real” variables vs. “integer” variables. Continuous models contain continuous functional relationships and allow fractional solutions. Discrete models may require that the solution values be integer. 5. SINGLE vs MULTIPLE OBJECTIVES Many business decisions are made based on a single criteria such as profit or cost. However, in other situations, we may need to consider several criteria at once such as profit, cost, labor relations, pollution control, company image, etc. B. ANALYSIS: 1. SOLUTION vs SIMULATION Solution typically means “mathematical” manipulation of the model. A solution method is usually a mathematical manipulation that yields...

...Linear programming is a modeling technique that is used to help managers make logical and informed decisions. All date and input factors are known with certainty. Linear program models are developed in three different steps:
Formulation
Solution
Interpretation
The formulation step deals with displaying the problem in a mathematical form. Once that is developed the solution stage solves the problem and finds the variable values. During the interpretation stage the sensitivity analysis gives managers the opportunity to answer hypothetical questions regarding the solutions that are generated.
There are four basic assumptions of linear programming and they are as follows:
Certainty
Proportionality
Additivity
Divisibility
Linear programming is the development of modeling and solution procedures which employ mathematical techniques to optimize the goals and objectives of the decision-maker. Programming problems determine the optimal allocation of scarce resources to meet certain objectives. Linear Programming Problems are mathematical programming problems where all of the relationships amongst the variables are linear.
Components of a LP Formulation are as follows:
Decision Variables
Objective Function
Constraints
Non-negativity Conditions
Decision variables represent unknown quantities. The solutions for these terms are what we would like...

...1. StillWater Mining Company
a)
Interest Rate 12%
Price per ounce $ 1,500.00
Cost per ounce $ 400.00
Total ounces a year 10,000
Profit per ounce $ 1,100
Revenue per year $ 15,000,000.00
Cost per year $ 4,000,000.00
Profit per year $ 11,000,000.00
Every year for the next 10 years, the firm earns a profit of $11 Million. The cash flow (in $ Million) is shown below:
Year T T+1 T+2 T+3 T+4 T+5 T+6 T+7 T+8 T+9
Profit 11 11 11 11 11 11 11 11 11 11
Using NPV formula, we find NPV=$62,152,453.31
b) The NPVs (in $ Million) for variations in profit per ounce and interest rate are shown in table below:
8% 9% 10% 11% 12% 13% 14% 15%
$500 33.55 32.09 30.72 29.45 28.25 27.13 26.08 25.09
$600 40.26 38.51 36.86 35.34 33.9 32.56 31.3 30.11
$700 46.97 44.92 43.01 41.22 39.55 37.98 36.51 35.13
$800 53.68 51.34 49.16 47.11 45.2 43.41 41.73 40.15
$900 60.39 57.76 55.3 53 50.85 48.84 46.95 45.17
$1000 67.1 64.18 61.45 58.89 56.5 54.26 52.16 50.19
$1100 73.81 70.59 67.59 64.78 62.15 59.69 57.38 55.21
$1200 80.52 77.01 73.74 70.67 67.8 65.12 62.59 60.23
$1300 87.23 83.43 79.88 76.56 73.45 70.54 67.81 65.24
$1400 93.94 89.85 86.02 82.45 79.1 75.97 73.03 70.26
$1500 100.65 96.27 92.17 88.34 84.75 81.39 78.24 75.28
2. Savings for Future Expenditures
Interest Rate 8%
Current College Tuition $ 40,000
Annual growth rate of tuition 5%
Time of first college payment (yrs) 6
Time of last college payment (yrs) 9
Annual growth rate of investment 6%
Time of last...

...St. Thomas University
School of Business
BUS 533 Quantitative Methods forBusiness
Dr. Maria Dolores Espino
Office: O’Mailia Hall Rm. 118
Tel: (305) 628-6791
E-mail: Mespino@stu.edu
Text :
Nagraj Balkrishnan ,Barry Render, and Ralph M. Stair Jr., Managerial DecisionModeling with Spreadsheets Prentice Hall, 2007.
Course Overview :
Quantitative methods are used in business to aid managers and leaders in making decisions. The purpose of this course is to provide students with a comprehensive working knowledge of the quantitative methods, techniques and skills necessary for the application of concepts in learned in other MBA courses. During this course student will focus on, forecasting techniques, linear regression, project scheduling, queuing theory and linear programming. Students will learn to solve realistic problems using EXCEL and other computer- aided tools.
.Course Objectives:
• To provide students with a foundation in quantitative methods and techniques commonly used in business decision-making.
• To provide students with the ability to analyze data and models, and present results in charts, graphs, and other numerical methods.
• To introduce students to computer-aided tools which enhance and facilitate the quantitative analysis process and provide them with the skills to solve quantitative problems using Microsoft Excel and other software.
Method of...

...Modeling, decision making, and optimization
In practical life, we have to continually make decisions. Making decisions are required for solving problems so that we can increase our opportunities and make life much easier and beneficial. There are many alternatives for making decisions, but making a rightful decision is a harder task. Evaluating these alternatives and choosing the best course of action represents the main essence of decision analysis.
For analyzing various decision alternatives, we have to make models.
Model
Physical
Mathematical
Visual
Mental
A model is an abstract, physical, or visual simplified replica with all features of a real object or situation.
A mathematical model is a model, which uses mathematical relationships to describe or represent an object or decision problem.
Benefits of modeling
Models are beneficial, because it is a simplified version of real object or situation, and useful to understand the real object or situation as long as it is valid. A valid model is that model, which represents the accurately the necessary characteristics of the object or problems being studied.
Models help to gain understanding about the real object or a situation, and thus help in decision-making....

...Term | Definition |
Systematic Biology / Systematics | * Study of the biodiversity * Quatitative science that uses the characteristics of living and fossil organisms(traits) to infer relationships between organisms over time |
Taxonomy | * Branch of systematic biology * Process of identifying, naming and organising biodiversity into related categories |
Taxon | General name for a group containing an organisms or groups of organisms that exhibit a set of shared traits |
Classification | Process of naming and assigning organisms or groups of organisms to a taxon |
Taxonomists | Scientists that study taxonomy |
Aristotle’s sorting | * Sort organisms into groups based on shared traits * Horses, birds, and oaks * Relied on physical traits to classify organisms * Proved to be problematic * Similar features are caused by convergent evolution, not from the common ancestor |
Natural Groups | * Grouping of organisms that represent a shared evolutionary history * Classified by: 1. Using a set of traits to construct a phylogeny 2. Evolutionary ‘famliy tree’ |
Carolus Linnaean | * Father of modern taxonomy * Develop binomial nomenclature * Each species received two-part Latin name * The first word is the genus, the second word is the specific epithet * In italics |
Reasons having scientific name | * A common name varies from country to country due to language difference *...

...MS5313 Managerial DecisionModeling
Part I: Chapter 1 Describing Data with Graphical Methods
Exercises
Multiple Choice Questions:
Identify the letter of the choice that best completes the statement or answers the question.
1. Which of the following is most likely a population as opposed to a sample?
a) respondents to a newspaper survey.
b) the first 5 students completing an assignment.
c) every third person to arrive at the bank.
d) registered voters in a county.
D
2. Which of the following is most likely a parameter as opposed to a statistic?
a) The average score of the first five students completing an assignment.
b) The proportion of females registered to vote in a county.
c) The average height of people randomly selected from a database.
d) The proportion of trucks stopped yesterday that were cited for bad brakes.
D
3. To monitor campus security, the campus police office is taking a survey of the number of students in a parking lot each 30 minutes of a 24-hour period with the goal of determining when patrols of the lot would serve the most students. If X is the number of students in the lot each period of time, then X is an example of
a) a categorical random variable.
b) a discrete random variable.
c) a continuous random variable.
d) a statistic.
B
4. Researchers are concerned that the weight of the average American school child is increasing implying, among other things, that children’s clothing should be...

...Spreadsheet Modeling and Decision Analysis
Sensitivity Report A sensitivity report of the analysis described above was created and can be found in Appendix E. The solution is not degenerate because there are no zero values in the allowable increase or allowable decrease columns of the constraints in the Sensitivity Report. All of the constraints affect the optimal solution. The solution is unique because there are no zero values in the allowable increase or allowable decrease columns in the decision variables section of the Sensitivity Report. This shows that there are no other combinations of production levels that will optimize this solution.
Decrease the Price of Whole If MNC were to decrease the price of the Whole product by $0.25, the optimal solution would change. This decrease in price would cause Whole’s contribution margin to fall to $0.79 and the optimal profit to fall to $439.76, a $100.00 difference. These calculations can be found in Appendix G. The production levels, however, would not change. This is because, as can be seen in the Sensitivity Report, there is an allowable increase of $0.36 and an allowable decrease of $0.31 in the price of Whole. Because $0.25 falls within this range, this change in price would not affect the production levels of the optimal solution.
Appendix A
1
Appendix B
2
Appendix C Constraints X1= Whole Product X2= Cluster Product X3= Crunch Product X4= Roasted Product...

...Decision Sheet
Situation Analysis
Strengths of Nirmal Rayons
1.Duopoly in the market – only two major players
2.Unutilized capacity of 1200 tonnes - can be used in case of unexpectedly high demand
3. Capacity increase sanctioned by the government – can be used to service newer markets
4. Rising number of users for Cellulose film
Weaknesses of Nirmal Rayons
1. Increased supply – 2 existing firms and 3 new ones have been given letters of intent for increasing capacity
2. Substitutes – Cheaper alternatives like Cellophane like PVC have emerged in the market.
Problem Statement:
Nirmal Rayon’s MD needs to verify the accuracy of the consultant’s computations and to decide whether to install additional capacity or not.
Evaluation of the Consultants’ Estimation
The following issues were found with the consultants’ estimates:
Textiles: The consultant has assumed that the share of cellulose film within will reduce due to competition from PVC. However, because of the increased supply in the market, prices will be driven down and this will counter the effects of PVC. Thus, we can assume a constant share (74%) which leads us to a demand estimate of 2795 tonnes.
Confectionary: The computations for cellophane requirement are not consistent with the data provided in footnote in Exhibit A6 of the consultant’s report. Using the given conversion factor of 40kgs/tonne, we get a new estimated demand of 657 tonnes.
Revised Calculations
Textiles...

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