Operations Research Final Exam
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Questions and Answers

What decision would a pessimistic person make based on the payoff table?

  • Alternative 1 or 2
  • Alternative 2 (correct)
  • Alternative 3
  • Alternative 1

What is the minimum profit for Alternative 1?

  • $120
  • $170
  • $200
  • $100 (correct)

What is the maximum profit for Alternative 3?

  • $240 (correct)
  • $105
  • $110
  • $120

What is the maximum profit for Alternative 2?

<p>$140 (A)</p> Signup and view all the answers

What decision would be made using the criterion of realism with alpha = 0.4?

<p>Alternative 3 (D)</p> Signup and view all the answers

What is the minimum profit for Alternative 3?

<p>$105 (D)</p> Signup and view all the answers

What is the maximum profit for Alternative 1?

<p>$200 (B)</p> Signup and view all the answers

What is the condition of a linear programming problem in which there is a redundant constraint?

<p>There is a redundant constraint. (D)</p> Signup and view all the answers

In the simplex tableau, what does the quantity column represent?

<p>The right-hand side values of the constraints. (A)</p> Signup and view all the answers

What is the condition of a linear programming problem in which there are multiple optimal solutions?

<p>There are multiple optimal solutions. (B)</p> Signup and view all the answers

In the simplex tableau, what is the purpose of the pivot column?

<p>To identify the entering variable. (C)</p> Signup and view all the answers

What is the condition when the optimal solution of a transportation problem is not unique?

<p>Alternate optimal solutions (B)</p> Signup and view all the answers

What is the condition of a linear programming problem in which there is no feasible solution?

<p>There is no feasible solution. (B)</p> Signup and view all the answers

In the simplex tableau, what is the purpose of the pivot number?

<p>To calculate the ratio of the pivot column to the pivot number. (A)</p> Signup and view all the answers

What is the total transportation cost using the North-West Corner Method?

<p>4560 (A)</p> Signup and view all the answers

What is the improvement index for cell 1C using the North-West Corner Method as an initial solution?

<p>11 (C)</p> Signup and view all the answers

What does a Cj - Zj value of zero imply in the final optimal simplex tableau?

<p>Optimality. (C)</p> Signup and view all the answers

What is the purpose of the Zj column in the simplex tableau?

<p>To calculate the reduced costs. (A)</p> Signup and view all the answers

What is the improvement index for cell 3A using the North-West Corner Method as an initial solution?

<p>11 (A)</p> Signup and view all the answers

What is the improvement index for cell 2B after getting the first improved solution using the stepping stone method?

<p>1 (C)</p> Signup and view all the answers

What is the quantity shipped from cell 2C after getting the first improved solution using the stepping stone method?

<p>140 (C)</p> Signup and view all the answers

What is the purpose of the North-West Corner Method in a transportation problem?

<p>To find the initial basic feasible solution (B)</p> Signup and view all the answers

What is the use of the stepping stone method in a transportation problem?

<p>To find the next improved solution (C)</p> Signup and view all the answers

What is degeneracy in a transportation problem?

<p>When a basic variable is equal to zero (D)</p> Signup and view all the answers

What is the purpose of finding the improvement index in a transportation problem?

<p>To find the next improved solution (A)</p> Signup and view all the answers

Flashcards

Pessimistic Decision

Choosing the alternative with the lowest possible profit in a payoff table.

Alternative 1 Minimum Profit

$100

Alternative 3 Maximum Profit

$240

Alternative 2 Maximum Profit

$140

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Criterion of Realism (alpha=0.4)

Using a weighted average of the best and worst outcomes to make a decision.

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Alternative 3 Minimum Profit

$105

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Alternative 1 Maximum Profit

$200

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Redundant Constraint

A constraint that doesn't add any new information; it's implied by other constraints.

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Simplex Tableau Quantity Column

Represents the right-hand side values of constraints.

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Multiple Optimal Solutions

More than one solution that maximizes (or minimizes) the objective function.

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Simplex Tableau Pivot Column

The column used to determine the entering variable.

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Alternate Optimal Solution Transportation

More than one optimal solution for minimizing transportation cost.

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No Feasible Solution

No values satisfy all the constraints in a linear program.

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Simplex Tableau Pivot Number

The number used to calculate whether to add or subtract.

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North-West Corner Method

A method to obtain a basic feasible solution for transportation problem.

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Transportation Cost (NW Method)

$4560

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Improvement Index (Cell 1C)

11

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Cj-Zj = 0

Indicates optimality in the final simplex tableau.

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Zj Column

Calculate reduced cost.

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Improvement Index (Cell 3A)

11

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Improvement Index (Cell 2B)

1

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Quantity Shipped (Cell 2C)

140

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Stepping Stone Method

Used to find improved transportation solutions.

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Degeneracy (Transportation)

A basic variable equals zero in a transportation problem.

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Improvement Index Purpose

Identify routes to reduce overall transportation cost further.

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Study Notes

Operations Research

Decision Making Under Uncertainty

  • A pessimistic person would choose the alternative with the maximum minimum profit (maximin strategy).
  • The regret criterion is used to minimize the maximum regret (opposite of profit).
  • The criterion of realism is a weighted average of the pessimistic and optimistic attitudes.

Linear Programming

  • A special case of a linear programming problem can have no feasible solution, redundant constraints, multiple optimal solutions, or be unsolvable graphically.
  • The initial simplex tableau is used to find the optimal solution.

Transportation Problem

  • The North-West Corner Method is used to find an initial solution to the transportation problem.
  • The improvement index is used to improve the initial solution.
  • The stepping stone method is used to improve the solution further.
  • The transportation table shows the supply, demand, and transportation costs.

Key Concepts

  • Payoff table: a table showing profits for various situations.
  • States of nature: the possible outcomes of a decision.
  • Alternatives: the different choices available.
  • Criterion of realism: a weighted average of the pessimistic and optimistic attitudes.
  • Linear programming: a method to optimize a linear objective function subject to linear constraints.
  • Simplex method: a method to solve linear programming problems.
  • Transportation problem: a problem of finding the minimum cost of transporting goods from sources to destinations.
  • North-West Corner Method: a method to find an initial solution to the transportation problem.
  • Improvement index: a measure used to improve the initial solution.
  • Stepping stone method: a method to improve the solution further.

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Related Documents

OR Final make up_ 2-2017.docx

Description

This quiz assesses knowledge of operations research concepts, including payoff tables and decision-making under uncertainty. It covers various alternatives and states of nature, with a focus on profit maximization.

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