Chapter12 Flashcards
What is Operations Research?
Operations Research is model-based decision support.
What are the key competencies in Operations Research?
- Model design (Modeling)
- Model solving (Mathematics of OR)
What are models in Operations Research?
- Idealizations or abstractions of parts of reality
- Used to obtain information about consequences of actions
What are the most important characteristics of a good model?
- Relevance: Are the problems of interest to the decision maker?
- Validity: Can the results of the model and their interpretation be trusted?
What is an evaluation model?
A formal model that allows to evaluate each decision alternative with respect to its consequences.
What is an optimization model?
An optimization model determines the best alternatives based on a desired consequence (outcome).
What is the mathematical structure of an optimization model?
Maximize f(x₁, …, xn) subject to gj(x₁, …, xn) ≥ 0, where f is the objective function and g₁,…,gk are constraints.
What are the dimensions of optimization models?
- Few variables (<20) or many variables
- Continuous or integer variables
- Deterministic or probabilistic
- Linear or non-linear
- Static or dynamic
What are decision variables in Linear Programming?
The decision variables represent the amount of each activity to perform. For example: x₁ is the amount of coal A burnt per hour.
What is the objective function in Linear Programming?
The objective function in LP is the expression to maximize or minimize based on the activities, e.g., z = 24x₁ + 20x₂.
What is a feasible solution?
A solution that satisfies all constraints simultaneously, including non-negativity constraints.
What is the canonical form of a Linear Program?
Maximize z = Σcjxj subject to Σaijxj ≤ bi, where xj ≥ 0 and cj, aij, and bi are constants.
What is the purpose of slack variables in LP?
Slack variables convert inequalities into equalities and represent unused resources in a problem.
What is shadow price in sensitivity analysis?
The shadow price is the rate of change of the objective function concerning changes in the right-hand side of a constraint.
