Chapter12 V2

Question 1

What is Operations Research?

Answer 1

Operations Research is model-based decision support.

Question 2

What are key competencies in Operations Research?

Answer 2

• Model design (‘Modeling’)
• Model solving (‘Mathematics of OR’)

Question 3

What are the most important quality characteristics of a good model?

Answer 3

• Relevance: Are the problems of interest to the decision maker?
• Validity: Can the results and their interpretation be trusted?

Question 4

What are the key elements in conceptualizing a model?

Answer 4

• Problem Identification and Diagnosis
• Describing the relevant system elements, attributes, and relationships
• Defining goals and decision criteria

Question 5

What are the types of models in Operations Research?

Answer 5

• Evaluation models: Evaluate each decision alternative’s consequences.
• Optimization models: Determine the best alternative based on a desired consequence.

Question 6

What is the mathematical structure of an optimization model?

Answer 6

Maximise f(x₁, …, x_n) such that constraints g_j(x₁, …, x_n) ≥ 0, j = 1, …, k.

Question 7

What are the assumptions of Linear Programming (LP)?

Answer 7

• Divisibility: Variables can take fractional values.
• Non-negativity: Variables cannot be negative.

Question 8

What is the canonical form of a Linear Program?

Answer 8

Maximise z = Σc_jx_j subject to Σa_ijx_j ≤ b_i, and x_j ≥ 0.

Question 9

What is the purpose of slack variables?

Answer 9

Slack variables represent the unused amount of a resource and help convert inequalities into equalities.

Question 10

What is sensitivity analysis?

Answer 10

Analyses how changes in parameters (e.g., right-hand-side constraints) affect the optimal solution.