Chapter 9

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Questions and Answers

What is the primary goal of the pottery company in terms of profit?

To reduce profit to zero

To maximize profit

To achieve a minimum profit of $1,600 (correct)

To minimize profit to $1,600

Why is the objective function in a goal programming model different from a standard linear programming model?

Because it uses deviational variables with different units of measure (correct)

Because it maximizes profit

Because it uses a single objective function

Because it minimizes cost

What does the term P3 in P3d3+ represent?

The company's third priority (correct)

The company's fourth priority

The company's second priority

The company's first priority

What is the primary difference between a goal programming model and a standard linear programming model?

The objective function terms are not summed to equal a total value (C) Signup and view all the answers

What is the primary difference between linear programming and goal programming?

The presence of multiple objectives (C) Signup and view all the answers

What is the outcome of using the analytical hierarchy process and scoring models?

A score for each alternative to rank their preferability (C) Signup and view all the answers

Which of the following is NOT a technique used to solve problems with multiple objectives?

Linear programming (B) Signup and view all the answers

What is the general format of goal programming models?

Similar to linear programming models (C) Signup and view all the answers

What is the purpose of using goal programming?

To consider multiple objectives in decision-making (D) Signup and view all the answers

What is the primary difference between goal programming and the analytical hierarchy process?

The format of the model (B) Signup and view all the answers

What is the result of using scoring models?

A ranking of alternatives in terms of preferability (D) Signup and view all the answers

What is the purpose of the goal constraint developed to limit overtime to 10 hours?

To limit overtime to 10 hours (D) Signup and view all the answers

What is the purpose of the weights in the objective function?

To prioritize the goals based on profit (A) Signup and view all the answers

What is the primary purpose of a pairwise comparison in AHP?

To compare two alternatives according to one criterion (B) Signup and view all the answers

What is the purpose of the pairwise comparison matrix?

To summarize the pairwise comparison ratings for each of the decision alternatives (D) Signup and view all the answers

What is the purpose of using a preference scale in AHP?

To quantify the decision maker's preference (A) Signup and view all the answers

Study Notes

Multi-Criteria Decision Making

In linear programming models, a single objective is either maximized or minimized.
In real-life scenarios, companies often have multiple objectives, also known as criteria, to consider when making decisions.

Goal Programming

Goal programming is a variation of linear programming that considers multiple objectives (goals) in the objective function.
Goal programming models have an objective function, decision variables, and constraints, similar to linear programming models.
Goal programming models can be solved graphically and using QM for Windows and Excel.
The objective function in a goal programming model specifies that the deviations from the goals represented in the objective function be minimized individually, in order of their priority.

Goal Constraints

Goal constraints can be formulated in different ways, depending on the specific goal.
For example, a goal constraint to minimize overtime can be represented as:
Alternative forms of goal constraints can be used, such as limiting overtime to 10 hours instead of minimizing overtime.

Multi-Criteria Decision Making Techniques

Three techniques can be used to solve problems with multiple objectives: goal programming, the analytical hierarchy process, and scoring models.
The analytical hierarchy process is a method that compares decision alternatives for different criteria, reflecting the decision maker's preferences.
Scoring models are based on a comparison of decision alternatives for different criteria, resulting in a mathematical score for each alternative that helps the decision maker rank the alternatives in terms of preferability.

The Analytical Hierarchy Process (AHP)

AHP is a method that involves pairwise comparisons of decision alternatives according to one criterion.
The decision maker compares two alternatives according to one criterion and indicates a preference using a preference scale.
The standard preference scale used for AHP has nine levels, ranging from "equally preferred" to "extremely preferred".
The preference values are used to create a pairwise comparison matrix, which is a rectangular array of numbers.
The pairwise comparison matrix shows the relative preferences of each decision alternative for each criterion.

Important Concepts

Deviational variables: variables that represent the amount of deviation from a goal or target.
Priority levels: goals are ranked in order of importance, with the most important goal being prioritized first.
Weights: coefficients that reflect the relative importance of each goal in the objective function.
Goal constraints: equations that represent the goals or objectives of the decision maker.
Objective function: a mathematical expression that represents the overall goal of the decision maker.

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