taylor introms10 ppt 09 MEF

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Multicriteria Decision

Making

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■ Goal Programming

■ Graphical Interpretation of Goal Programming

■ Computer Solution of Goal Programming Problems with QM for Windows and Excel

■ The Analytical Hierarchy Process

■ Scoring Models

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■ Study of problems with several criteria, multiple criteria, instead of a single objective when making a decision.

■ Three techniques discussed: goal programming, the analytical hierarchy process and scoring models.

■ Goal programming is a variation of linear programming considering more than one objective (goals) in the objective function.

■ The analytical hierarchy process develops a score for each decision alternative based on comparisons of each under different criteria reflecting the decision makers preferences.

■ Scoring models are based on a relatively simple weighted scoring technique.

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■ Adding objectives (goals) in order of importance, the company: 1. Does not want to use fewer than 40 hours of labor per day.

2. Would like to achieve a satisfactory profit level of $1,600 per day.

3. Prefers not to keep more than 120 pounds of clay on hand each day.

4. Would like to minimize the amount of overtime.

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■ All goal constraints are equalities that include deviational

■ At least one or both deviational variables in a goal constraint must

equal zero.

■ The objective function seeks to minimize the deviation from the respective goals in the order of the goal priorities.

Goal Programming

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Labor goal:

x

₁

+ 2x

₂

+ d

₁-

- d

₁+

= 40 (hours/day)

Profit goal:

40x

₁

+ 50 x

₂

+ d

₂ -

- d

₂ +

= 1,600 ($/day)

Material goal:

4x

₁

+ 3x

₂

+ d

₃ -

_{- d}

3 +

= 120 (lbs of clay/day)

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1. Labor goals constraint

(priority 1 - less than 40 hours labor; priority 4 - minimum overtime):

 Minimize P₁d₁-_{, P}

4d1+

2. Add profit goal constraint

(priority 2 - achieve profit of $1,600):

 Minimize P₁d₁-, P₂d₂-, P₄d₁+ 3. Add material goal constraint

(priority 3 - avoid keeping more than 120 pounds of clay on hand):

 Minimize P₁d₁-_{, P}

2d2-, P3d3+, P4d1+

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■ Changing fourth-priority goal “limits overtime to 10 hours” instead of minimizing overtime:

 d₁+ + d₄- - d₄+ = 10

 minimize P₁d₁-, P₂d₂-, P₃d₃+, P₄d₄+

■ Addition of a fifth-priority goal- “important to achieve the goal for

mugs”:

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Goal Programming

Alternative Forms of Goal Constraints (2 of 2)

Complete Model with Added New Goals:

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Figure 9.1 Goal Constraints

Goal Programming

Graphical Interpretation (1 of 6)

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Minimize P₁d₁-_{, P}

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Figure 9.3 The Second-Priority Goal: Minimize d2-

Goal Programming

Graphical Interpretation (3 of 6)

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Goal Programming

Graphical Interpretation (4 of 6)

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Figure 9.5 The Fourth-Priority Goal: Minimize d1+

Goal Programming

Graphical Interpretation (5 of 6)

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Goal programming solutions do not always achieve all goals and they are not “optimal”, they achieve the best or most satisfactory solution possible.

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Exhibit 9.3

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Exhibit 9.5