Spreadsheet Models & Decision Analysis
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Questions and Answers

Which guideline emphasizes the importance of organizing data before building the model?

  • Utilize text boxes for documentation
  • Do not embed numeric constraints in formulas
  • Organize the data, then build the model around the data (correct)
  • Use colors for better readability

What is a key limitation when solving linear programming problems graphically?

  • It is only feasible with two decision variables (correct)
  • It can only solve problems with one decision variable
  • It cannot address real-world problems
  • It is limited to linear equations only

Why should numeric constraints not be embedded in formulas according to spreadsheet design guidelines?

  • Formulas will perform better without them
  • It complicates the model and makes debugging difficult (correct)
  • They decrease the visual appeal of the spreadsheet
  • It is unnecessary if data is organized well

What best describes the importance of using color, shading, and borders in spreadsheets?

<p>They help distinguish changeable parameters from other model elements (C)</p> Signup and view all the answers

What relationship should be maintained according to the design guidelines?

<p>Logically related elements should be physically related (A)</p> Signup and view all the answers

Why should long and complex calculations be divided into several cells in a spreadsheet?

<p>It reduces errors and simplifies maintenance. (A)</p> Signup and view all the answers

What characterizes prescriptive spreadsheet models?

<p>They focus on maximizing or minimizing objectives. (C)</p> Signup and view all the answers

Which tool in Excel is used for optimization in prescriptive models?

<p>Solver (D)</p> Signup and view all the answers

Which of the following is NOT a feature of optimization problems?

<p>Descriptive functions (D)</p> Signup and view all the answers

What is the main purpose of using Monte Carlo simulation in spreadsheet modeling?

<p>To replace static inputs with random values. (D)</p> Signup and view all the answers

Which of the following describes decision variables in optimization models?

<p>They are the variable factors influenced by the decisions. (B)</p> Signup and view all the answers

In relaying choices for decision-making, what is a key benefit of what-if models?

<p>They help analyze multiple alternatives. (A)</p> Signup and view all the answers

Which aspect of decision-making do optimization problems generally involve?

<p>Maximizing or minimizing limited resources. (C)</p> Signup and view all the answers

Which component is essential in the structure of decisions made by a manager?

<p>An aim that the manager wants to achieve (B)</p> Signup and view all the answers

What describes decision making under risk?

<p>The decision maker knows the probabilities of the various outcomes (B)</p> Signup and view all the answers

What is the first step in the six steps of decision making?

<p>Clearly define the problem at hand (A)</p> Signup and view all the answers

Which criterion is categorized as an optimistic approach in decision making under uncertainty?

<p>Maximax (D)</p> Signup and view all the answers

In the decision-making process, what happens after an alternative is chosen?

<p>Events occur that are beyond the manager's control (C)</p> Signup and view all the answers

What is the primary focus of linear programming (LP) problems in resource allocation?

<p>Optimally allocating limited resources (D)</p> Signup and view all the answers

When faced with an order that cannot be completely filled by its own production capacity, what must a company decide?

<p>Which items to produce and which to subcontract (D)</p> Signup and view all the answers

What is the goal in an investment problem within finance?

<p>Maximizing return while adhering to cash flow and risk constraints (A)</p> Signup and view all the answers

In the transportation problem, what is the primary objective?

<p>Minimizing the cost of distribution (C)</p> Signup and view all the answers

What type of problems does the blending problem typically involve?

<p>Determining an optimal mix of ingredients or materials (D)</p> Signup and view all the answers

What is a characteristic of mixed integer-linear programming (MILP) in the context of blending problems?

<p>It involves blending several resources or materials (B)</p> Signup and view all the answers

What is a fundamental assumption of the transportation problem?

<p>Demand requirements and supply limitations must be considered (B)</p> Signup and view all the answers

Which of the following best describes the application of linear programming in logistics?

<p>It is used to effectively manage and allocate transport costs (C)</p> Signup and view all the answers

What is the primary objective of the transportation problem?

<p>Minimize the cost of distributing a product (D)</p> Signup and view all the answers

In which type of problem does the amount of flow exiting an arc differ from the amount entering the arc?

<p>Generalized network flow problem (C)</p> Signup and view all the answers

What kind of problems do maximum flow problems typically address?

<p>Determining maximum capacity in a network (B)</p> Signup and view all the answers

Which statement accurately describes the minimal spanning tree problem?

<p>It minimizes the lengths of the edges of the tree. (C)</p> Signup and view all the answers

Integer linear programming problems result when decision variables are restricted to which type of values?

<p>Integer values only (C)</p> Signup and view all the answers

What does an integrality condition ensure in linear programming?

<p>Certain variables must be integer values (D)</p> Signup and view all the answers

Which of the following describes the objective of the maximal flow problem?

<p>To determine the maximum material flow in a network (B)</p> Signup and view all the answers

How is the minimal spanning tree problem generally solved?

<p>Through manual algorithms (D)</p> Signup and view all the answers

What distinguishes integer variables from continuous variables in a problem?

<p>Integer variables can only take whole numbers. (C)</p> Signup and view all the answers

What is the principal outcome when the integrality conditions are dropped in the LP relaxation of an ILP?

<p>The feasible region changes significantly. (A)</p> Signup and view all the answers

When comparing ILP and its LP relaxation solutions, which statement is true?

<p>The objective value for ILP can be worse than LP relaxation. (D)</p> Signup and view all the answers

Why is rounding not a reliable method for obtaining feasible solutions?

<p>The rounded solution may be feasible but suboptimal. (D)</p> Signup and view all the answers

What is the purpose of a suboptimality tolerance factor in ILP packages?

<p>To allow stopping once a sufficiently good integer solution is found. (C)</p> Signup and view all the answers

What process does the branch and bound algorithm follow to solve ILP problems?

<p>It requires solving multiple LP problems termed 'candidate problems'. (A)</p> Signup and view all the answers

What happens when the objective value for LP relaxation is $64,306 and an integer solution is found at $61,090?

<p>This integer solution is within acceptable tolerance of the optimal. (D)</p> Signup and view all the answers

When might integer solutions not be guaranteed from the LP relaxation of an ILP?

<p>When dropping integrality conditions. (D)</p> Signup and view all the answers

Flashcards

Linear Programming (LP) Constraints

Restrictions or limitations on decision variables in a linear programming model.

LP Decision Variables

Values that represent the choices to be made in a linear programming problem.

Spreadsheet LP Solving

Using spreadsheets to find solutions to linear programming problems.

Spreadsheet Design Guideline

Guidelines for creating spreadsheets to solve linear programming problems.

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Spreadsheet Data Organization

Organize data in spreadsheets logically and physically for a model.

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Spreadsheet formulas

Short, clear expressions in a spreadsheet to perform calculations.

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Descriptive spreadsheet models

Spreadsheet models that describe possible outcomes based on various inputs, but not predict them.

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Predictive spreadsheet models

Models that predict future outcomes using data analysis tools in spreadsheet software.

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Prescriptive spreadsheet models

Models that advise or suggest the best course of action based on data and constraints.

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Monte Carlo simulation

A method in a spreadsheet that automates 'what-if' analysis by using random values for uncertain inputs.

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Optimization models

Models with an objective function to maximize or minimize, along with constraints to consider.

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Objective function

A function that needs to be maximized or minimized in an optimization model.

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Decision Maker

The person responsible for making a choice among different alternatives to achieve a specified goal.

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Decision Making Under Certainty

A decision-making environment where the consequences of each alternative are known with absolute certainty.

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Decision Making Under Risk

A decision-making environment where the probabilities of different outcomes are known.

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Decision Making Under Uncertainty

A decision-making environment where the probabilities of different outcomes are unknown.

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Maximax Criterion

An optimistic approach to decision making under uncertainty, maximizing the maximum possible outcome.

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LP for Resource Allocation

Linear Programming (LP) is ideal for problems where limited resources must be used effectively. It helps find the best way to allocate these resources.

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LP in Production Scheduling

LP can be used to determine the optimal way to assign tasks to machines in order to minimize completion time.

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LP in Supply Chain

Companies use LP to decide what to produce internally and what to outsource when facing production capacity constraints.

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Investment Optimization

Financial problems often involve maximizing investment returns while managing risk and cash flow requirements.

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Transportation Problem

A type of LP problem where the goal is to minimize the cost of transporting goods from multiple sources to multiple destinations.

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Network Flow Problems

Problems involving the movement of goods or resources through a network of nodes and links.

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Blending Problem

Finding the optimal mix of ingredients to create a product while meeting specific requirements.

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MILP in Blending

Blending problems often involve mixed integer-linear programming (MILP), which allows for both continuous and discrete decision variables.

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Generalized Network Flow

A network flow problem where the amount of flow entering and exiting an arc can differ, allowing for gains or losses in flow due to factors like production or consumption.

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Maximum Flow Problem

Finding the maximum amount of material that can be transported through a network, given constraints on flow capacity for each path.

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Minimal Spanning Tree

A type of network problem where the goal is to find a tree (connected network without cycles) with the minimum total edge length, connecting all nodes.

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Integer Linear Programming (ILP)

A type of linear programming problem where some or all decision variables must be integers, meaning they can only take on whole number values.

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Integrality Conditions

Restrictions in ILP that require certain decision variables to be integers, ensuring realistic solutions based on discrete quantities.

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What makes ILP different from LP?

ILP restricts some or all variables to integer values, while LP allows continuous values. This creates a discrete optimization problem, making solutions more practical for real-world scenarios.

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Example of an ILP problem

A company producing furniture needs to decide how many chairs and tables to make, considering limited resources like wood and labor, while ensuring they produce whole units of furniture.

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Integer Variable

A variable that can only take on whole number values in a mathematical model.

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Continuous Variable

A variable that can take on any value within a specific range, including fractions and decimals.

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LP Relaxation

A technique where integer constraints are removed from an Integer Linear Programming (ILP) problem to create a simpler Linear Programming (LP) problem.

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Optimal Solution to LP Relaxation

The best possible solution to the simplified LP problem, which may not always be a valid solution for the original ILP problem.

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Rounding Technique

A method of estimating the solution to an ILP problem by rounding the solution to the LP relaxation.

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Branch and Bound Algorithm

A method for solving ILP problems by systematically exploring possible integer solutions using a series of LP relaxations.

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Candidate Problem

A simplified LP problem created during the Branch and Bound algorithm, used to explore specific integer possibilities.

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Suboptimality Tolerance

A setting in ILP software that allows stopping the search for the optimal solution once a solution within a specified percentage of the optimal is found.

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Study Notes

Spreadsheet Models

  • Spreadsheet models are mathematical and logical models
  • Often referred to as "what-if" models
  • Frequently used business analytics tools
  • Easy-to-use sophisticated mathematical and logical functions
  • Allow for instantaneous recalculation of outputs after input changes
  • Less expensive than specialized software packages
  • Often pre-installed on computers
  • Considered reasonable and user-friendly

Make-versus-Buy Decision

  • Total manufacturing cost is the sum of fixed and variable costs
  • Fixed costs remain constant regardless of production quantity
  • Variable costs depend on and change with production quantity
  • Make-versus-buy decisions compare in-house manufacturing costs with outsourcing costs

Influence Diagram for Nowlin Plastics

  • Visual representation of the influence relationships in a model
  • Arrows connect nodes to illustrate influence between them
  • Right diagram depicts manufacturing versus outsourcing costs for bowling plastics
  • Modular approach simplifies modeling

General Principles of Spreadsheet Model Design and Construction

  • Separate parameters from the model—update parameters without disrupting formulas
  • Document the model with clear labels and formatting
  • Use simple, easily maintained formulas

Descriptive and Predictive Spreadsheet Models

  • Decision-making is complex due to uncertainty and numerous options
  • Spreadsheet "what-if" models are descriptive models that help deal with uncertainty
  • Predictive models can be built from data in spreadsheets using Excel tools like regression and exponential smoothing

Prescriptive Spreadsheet Models

  • Simulation and optimization models are prescriptive
  • Monte Carlo simulations use a random value generation for uncertain inputs
  • Optimizing models aim to maximize or minimize an objective with constraints
  • Excel Solver optimizes models by maximizing or minimizing objectives with constraints

10 Optimization and Linear Programming

  • Decision-making involves optimization
  • Facing decisions with limited resources (e.g., class schedules, land use, worker availability)
  • Optimization models involve inputs, decision variables, objective functions, and constraints
  • Objective functions are maximized or minimized, subject to constraints

Linear Programming (LP) Problems

  • LP is a type of optimization problem
  • Involves linear functions and constraints
  • Excel spreadsheets can solve LP problems

Product Mix Problem

  • Multiple products compete for finite resources
  • Companies determine optimal product proportions to maximize revenue and profits

Spreadsheet Design Guidelines

  • Organize data; build model around data
  • Avoid embedding numeric constraints in formulas
  • Related items should be physically located together
  • Use easy-to-copy formulas
  • Left-to-right, top-to-bottom organization
  • Use visual aids like color, shading, borders, and protection to distinguish parameters.

Make-Versus-Buy Decision

  • Decisions about allocating scarce resources
  • Spreadsheet models are good for making decisions that maximize efficiency by optimally assigning tasks or resources.

Investment Problem

  • Manufacturing companies need to plan production and inventory for future periods.
  • Demand forecasts and resource constraints are taken into account to define optimal production and inventory levels for various time periods based on economic considerations.

Transportation Problem

  • Network flow problems minimize distribution costs
  • Distributing products from sources to destinations.

Blending Problem

  • Optimal mix of ingredients
  • Finding least costly mixtures of ingredients to produce a desired output (ex: Gasoline, Fertilizers)
  • Mixed Integer Linear Programming (MILP) blending problems

Production Planning Problem

  • Crucial for manufacturing companies to plan resource allocation (production and inventory).
  • Forecasting demand, considering resources, and determining production schedules.

11 Sensitivity Analysis

  • Evaluating how changes in input values affect optimal solutions of a model.
  • Understanding the impact of variability of input values on the model's optimal solution.
  • Useful for managing uncertainty in input values, by analyzing the robustness of the models results.

Network Modeling

  • Network flow problems: finding shortest paths, maximum flow, and other network-related problems.

12 Network Modeling

  • Network flow problems: finding shortest paths, maximum flow, etc.
  • Analyzing flows and related problems in networks.

13 Integer Linear Programming (ILP)

  • Linear programming where some or all variables must be whole numbers
  • Integrality conditions: integer constraints in LP models.

14 Aggregate Planning

  • Planning production and inventory over a specific time horizon.
  • Anticipating and meeting demand while balancing costs.

15 Simulation

  • Experimentally testing the behavior of real-world systems, typically on a computer
  • Testing strategies and understanding scenarios of variability.

16 Structuring Decisions

  • Types of decision-making in uncertain environments, including structured and unstructured, with specific examples to each case.

Decision Making in Uncertainty (Six Steps)

  • Define Problem
  • List Possible Alternatives
  • List possible outcomes or states of nature
  • List the payoff of each combination of alternatives and outcomes
  • Select a decision theory model
  • Apply the model and make the decision

Decision Making under Risk & Uncertainty

  • Decision-making considerations under both risk and uncertainty.
  • Applying models involving probabilities and outcomes in cases that involve uncertainty.

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Description

This quiz explores spreadsheet models, emphasizing their role as 'what-if' tools used in business analytics. Additionally, it covers the make-versus-buy decision process, comparing in-house versus outsourcing costs. Finally, influence diagrams specific to manufacturing contexts are discussed.

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