管理科学09-多因子决策模型
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Minimize P1d1-, P2d2-, PFra Baidu bibliotekd1+ Add material goal constraint (3, avoid keeping more than 120 pounds of clay on hand):
Minimize P1d1-, P2d2-, P3d3+, P4d1+
5
Goal Programming Goal Constraint Requirements
All goal constraints are equalities that include deviational variables d- and d+.
A positive deviational variable (d+) is the amount by which a goal level is exceeded.
Chapter 9 - Multicriteria Decision Making
3
Goal Programming Model Formulation (1 of 2)
Beaver Creek Pottery Company Example:
Maximize Z = $40x1 + 50x2
subject to: 1x1 + 2x2 40 hours of labor 4x2 + 3x2 120 pounds of clay x1, x2 0
Introduction to Management Science 8th Edition by
Bernard W. Taylor III
Chapter 9 Multicriteria Decision Making
Chapter 9 - Multicriteria Decision Making
Chapter 9 - Multicriteria Decision Making
2
Overview
Study of problems with several criteria, multiple criteria, instead of a single objective when making a decision. Two techniques discussed: goal programming, and the analytical hierarchy process. 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.
A negative deviation variable (d-) is the amount by which a goal level is underachieved.
At least one or both deviational variables in a goal constraint must equal zero.
1
Chapter Topics
Goal Programming Graphical Interpretation of Goal Programming Computer Solution of Goal Programming Problems with QM for Windows and Excel The Analytical Hierarchy Process
Where: x1 = number of bowls produced x2 = number of mugs produced
Chapter 9 - Multicriteria Decision Making
4
Goal Programming Model Formulation (2 of 2)
6
Goal Programming Goal Constraints and Objective Function (1 of 2)
Labor goals constraint (1, less than 40 hours labor; 4, minimum overtime):
Minimize P1d1-, P4d1+ Add profit goal constraint (2, achieve profit of $1,600):
Adding objectives (goals) in order of importance, the company:
Does not want to use fewer than 40 hours of labor per day.
Would like to achieve a satisfactory profit level of $1,600 per day.
The objective function in a goal programming model seeks to minimize the deviation from goals in the order of the goal priorities.
Chapter 9 - Multicriteria Decision Making
Prefers not to keep more than 120 pounds of clay on hand each day.
Would like to minimize the amount of overtime.
Chapter 9 - Multicriteria Decision Making
Minimize P1d1-, P2d2-, P3d3+, P4d1+
5
Goal Programming Goal Constraint Requirements
All goal constraints are equalities that include deviational variables d- and d+.
A positive deviational variable (d+) is the amount by which a goal level is exceeded.
Chapter 9 - Multicriteria Decision Making
3
Goal Programming Model Formulation (1 of 2)
Beaver Creek Pottery Company Example:
Maximize Z = $40x1 + 50x2
subject to: 1x1 + 2x2 40 hours of labor 4x2 + 3x2 120 pounds of clay x1, x2 0
Introduction to Management Science 8th Edition by
Bernard W. Taylor III
Chapter 9 Multicriteria Decision Making
Chapter 9 - Multicriteria Decision Making
Chapter 9 - Multicriteria Decision Making
2
Overview
Study of problems with several criteria, multiple criteria, instead of a single objective when making a decision. Two techniques discussed: goal programming, and the analytical hierarchy process. 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.
A negative deviation variable (d-) is the amount by which a goal level is underachieved.
At least one or both deviational variables in a goal constraint must equal zero.
1
Chapter Topics
Goal Programming Graphical Interpretation of Goal Programming Computer Solution of Goal Programming Problems with QM for Windows and Excel The Analytical Hierarchy Process
Where: x1 = number of bowls produced x2 = number of mugs produced
Chapter 9 - Multicriteria Decision Making
4
Goal Programming Model Formulation (2 of 2)
6
Goal Programming Goal Constraints and Objective Function (1 of 2)
Labor goals constraint (1, less than 40 hours labor; 4, minimum overtime):
Minimize P1d1-, P4d1+ Add profit goal constraint (2, achieve profit of $1,600):
Adding objectives (goals) in order of importance, the company:
Does not want to use fewer than 40 hours of labor per day.
Would like to achieve a satisfactory profit level of $1,600 per day.
The objective function in a goal programming model seeks to minimize the deviation from goals in the order of the goal priorities.
Chapter 9 - Multicriteria Decision Making
Prefers not to keep more than 120 pounds of clay on hand each day.
Would like to minimize the amount of overtime.
Chapter 9 - Multicriteria Decision Making