Management science PPT M1

• Linear programming

  -is a problem-solving approach developed to help managers make decisions.
• Scientific method:

  Observation

  Problem definition

  Model construction

  Solution

  Implementation
• Observation

  -identifying a problem in the system (organization)
• Observation

  -system must be continuously and closely observed to identify problems as soon as they occur or are anticipated
• Observation

  -problems are not always the result of a crisis that must be reacted to
• Problem definition

  -Goals of the organization must also be clearly defined because the presence of an issue means that the firm's objectives aren't being realized in some way.
• Problem definition

  -Clearly stated objective aids in

  concentrating attention on the issue at hand.
• Model construction

  -abstract representation of an existing problem situation
• Model construction

  -most frequently it consists of a set of mathematical relationships.
• Implementation

  -This is an important but sometimes disregarded step in the procedure.
• It is not always a given that a model or solution will be applied once it has been developed.
• Decision variables

  -are mathematical symbols that represent levels of activity
• Objective function

  -is a linear relationship that reflects the objective of an operation
• Model constraint

  -is a linear relationship that represents a restriction on decision-making.
• Nonnegativity constraints restrict the decision variables to zero or positive values.
• optimal solution is the best feasible solution
• Extreme points are corner points on the boundary of the feasible solution area.
• It has been proven

  mathematically that the optimal

  solution in a linear programming model will always occur at an extreme point.
• Sensitivity analysis

  -is used to analyze changes in model parameters
• Multiple optimal solution

  -can occur when the objective function is parallel to a constraint line
• Slack variable

  -is added to a ≤ constraint to convert it to an equation

  (=)
• Slack variable

  -represents unused resources
• Surplus variable

  -is subtracted from a ≥ constraint to convert it to an

  equation (=).
• Surplus variable

  -represents an excess above a constraint requirement level.
• Instead of adding a slack variable as we did with a constraint, we subtract a surplus variable
• slack variable is added and reflects unused resources
• surplus variable is subtracted and reflects the excess above a minimum resource requirement level.
• Like a slack variable, a surplus variable is represented symbolically by s1 and must be nonnegative
• Alternate optimal solution

  -are at the endpoints of the

  constraint line segment

  that the objective function parallels
• Multiple optimal solution

  -provide greater flexibility to the decision maker
• Unboundedness

  -the objective function can

  increase indefinitely without

  reaching a maximum value
• Unboundedness

  -when the maximization can have infinitely large values without violating the requirements of the constraints
• Infeasibility

  -every possible solution point

  violates one or more constraints
• Infeasibility

  -has no feasible solution area
• Redundancy

  -happens when there is a

  redundant constraint, such

  as the requirement or

  limitation, that will not

  affect the feasible region
• Feasible region can still be

  determined even if the

  redundant constraint is

  removed from the model
• Properties of linear programming model:

  Proportionality

  Additive

  Divisible

  Certainty
• Proportionality

  -means the slope of a constraint or objective function line is

  constant
• Properties of linear programming model:

  The terms in the objective function or constraints are additive
• Properties of linear programming model:

  The values of decision variables are continuous or divisible