Chapter 6 Supplement : Chapter 6 Supplement Linear Programming
Linear Programming : Linear programming (LP) techniques consist of a sequence of steps that will lead to an optimal solution to problems, in cases where an optimum exists Linear Programming
Linear Programming Model : Linear Programming Model Objective: the goal of an LP model is maximization or minimization
Decision variables: amounts of either inputs or outputs
Feasible solution space: the set of all feasible combinations of decision variables as defined by the constraints
Constraints: limitations that restrict the available alternatives
Parameters: numerical values
Linear Programming Assumptions : Linear Programming Assumptions Linearity: the impact of decision variables is linear in constraints and objective function
Divisibility: noninteger values of decision variables are acceptable
Certainty: values of parameters are known and constant
Nonnegativity: negative values of decision variables are unacceptable
Graphical Linear Programming : Graphical Linear Programming Set up objective function and constraints in mathematical format
Plot the constraints
Identify the feasible solution space
Plot the objective function
Determine the optimum solution
Linear Programming Example : Linear Programming Example
Linear Programming Example : Linear Programming Example
Linear Programming Example : Linear Programming Example
Slide 9: MS Excel worksheet for microcomputer problem
Slide 10: MS Excel worksheet solution
Constraints : Redundant constraint: a constraint that does not form a unique boundary of the feasible solution space
Binding constraint: a constraint that forms the optimal corner point of the feasible solution space Constraints
Slack and Surplus : Slack and Surplus Surplus: when the optimal values of decision variables are substituted into a greater than or equal to constraint and the resulting value exceeds the right side value
Slack: when the optimal values of decision variables are substituted into a less than or equal to constraint and the resulting value is less than the right side value
Simplex Method : Simplex Method Simplex: a linear-programming algorithm that can solve problems having more than two decision variables
Tableau: One in a series of solutions in tabular form, each corresponding to a corner point of the feasible solution space
Sensitivity Analysis : Sensitivity Analysis Range of optimality: the range of values for which the solution quantities of the decision variables remains the same
Range of feasibility: the range of values for the fight-hand side of a constraint over which the shadow price remains the same
Shadow prices: negative values indicating how much a one-unit decrease in the original amount of a constraint would decrease the final value of the objective function