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Stack #104403
| Question | Answer |
|---|---|
| Two most common objectives of a business | Maximize profit or minimize cost |
| Linear Programming | A model that consists of linear relationships representing a firm's decision(s), given an objective and resource constraints. |
| Decision variables | mathematical symbols that represent levels of activity |
| Objective function | a linear relationship that reflects the objective of an operation |
| Constraint | a linear relationship that represents a restriction on decision making |
| Parameters | numerical values that are included in the obhjective functions and constraints |
| A linear programming model consists of 3 things: | decision variables, an objective function, and constraints |
| Nonnegativity constraints | restrict the decision variables to zero or positive values |
| feasible solution | does not violate any of the constraints |
| infeasible problem | violates at least one of the constraints |
| graphical solutions are limited to linear programming problems with | only two decision variables |
| The graphical method provides a picture of | how a solution is obtained for a linear programming problem |
| constraint lines are plotted as | equations |
| the feasible solution area is | an area on the graph that is bounded by the constraint equations |
| the optimal solution | the best feasible solution |
| the optimal solution point | the last point the objective function touches as it leaves the feasible solution area |
| extreme points | corner points on the boundary of the feasible solution area |
| the optimal solution in a linear programming model will always occur at | an extreme point |
| constraint equations are solved simultaneously at the optimal extreme point to determine | the variable solution values |
| sensitivity analysis | the analysis of the effect of parameter changes on the optimal solution |
| multiple optimal solutions | occur when the objective function is parallel to a constraint line |
| a slack variable is added to a <= constraint to convert it to | an equation (=) |
| slack variable | represents unused resources |
| a slack variable contributes nothing to | the objective function value- because they represent unused resources. |
| 3 types of linear programming constraints | >=, =, <= |
| the optimal solution of a minimization problem is | the extreme point closest to the origin |
| a surplus variable | is subtracted from a >= constraint to convert it to an equation (=) |
| a surplus variable represents | an excess above a constraint requirement level |
| alternate optimal solutions | the endpoints of a constraint line segment that parallels the objective function- it is understood that these points represent the endpoints of a range of optimal solutions |
| the benefit of multiple optimal solutions | greater flexibility to the decision maker |
| unbounded problem | the objective function can increase indefinitely without reaching a maximum value |
| proportionality | the slope of a constraint or objective function line is constant |
| the terms in the objective function or constraints are additive, meaning that | the function of the union or sum of two quantities is equal to the sum of the functional values of each quantity |
| the values of decision variables are | continuous/divisible (as opposed to discrete/integer values) |
| all model paramters are assumed to be | constant and known with certainty |
| simplex method | a procedure involving a set of mathematical steps to solve linear programming problems |
| fractional relationships between variables in constraints must be | eliminated. |
| the constraint quantity value is sometimes referred to as the | right-hand-side value |
| for using QM, constraints cannot contain | fractional values |
| marginal value | the dollar amount one would be willing to pay for one additional resource unit |
| the range of values over which the current optimal solution point will remain optimal is its | sensitivity range |
| sensitivity range for a right-hand-side value | the range of values over which the quantity values can change without changing hte solution variable mix, including slack variables |
| 3 forms of sensitivity analysis | change constraint parameter values, add new constraints, add new variables |
| shadow price/dual value | the marginal value of one additional unit of resource |
| the sensitivity range for a constraint quantity value is also the range over which | the shadow price is still valid |
| standard form requires | all variables on the left of the inequality, and numeric values to the right, no fractional variables |
| double-scripted variable | just another variable name, like Xij |
| "balanced" transportation model | supply equals demand such that all constraints are equalities |
| "unbalanced" transportation model | supply does not equal demand, and one set of constraints is <= |
| "Profit" is maximized in the objective function by | subtracting cost from revenue |
| computers are needed for 3 types of integer programming models | total, 0-1, and mixed integer models |
| total integer model | all decision variables have integer solution values |
| 0-1 integer model | solution values of the decision variables are zero or one |
| mixed integer model | some solution values for decision variables are integers and others can be nonintegers |
| the branch and bound method solves the problem of infeasible or suboptimal solutions obtained by | rounding noninteger solutions |
| transportation problem | items are allocated from sources to destinations at a minimum cost |
| a linear programming model for a transportation problem has | constraints for supply at each source, and demand at each destination |
| transshipment model | an extension of the transportation model that includes intermediate points between sources and destinations |
| assignment model | a transportation problem in which all supply and demand values equal one |
| transportation problems, transshipment problems, and assignment problems are part of a larger class of linear programming problems known as | network flow problems |
Created by:
sweetjezka