306 exam 1 cheatsheet

306 exam 1 cheatsheet - Linear programming model Both...

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Linear programming model : Both objective function and constraints are linear . Linear function : variables appear in separate terms with the first power and are multiplied by constants. Linear constraint : linear function (is restricted to be) “< ", “=", or “> " a constant. Binding constraints : a constraint is binding if the RHS of the constraint equals the LHS when evaluated for a solution. The slack or surplus of a binding constraint equals zero. Removal of a binding constraint will result in a change in the optimal solution and a new optimal solution and value will have to be determined. Boundary constraints : constraints that form a border of the feasible region. Removal of a boundary constraint will cause the feasible region to increase in size. Type of LPs Alternate optimal solutions : when the objective function line is Infeasible : no points satisfy all the constraints. Unbounded optimal solution : the feasible region is unbounded, and the objective function line can be moved in a direction in which the region is unbounded. Sensitivity analysis: post-optimality analysis *Many of the input parameters are only estimates and need to be refined if the model output is “sensitive” to small changes in these parameters. *Possible future changes in a dynamic problem environment need to be easily analyzed without resolving the model. *When certain parameters in the model represent managerial policy decisions, post-optimality analysis provides guidance to management about the impact of altering these policies. Sensitivity analysis is to determine how the optimal solution and optimal objective value are affected by changes in the model input data (parameters): we investigate possible change of objective function coefficient, RHS of constraint Changes of objective function coefficients *If an objective function coefficient changes, as long as the changed coefficient is not too far from the original coefficient, the optimal solution is still optimal for the changed model. *In other words, as long as the changed coefficient is located in some range (interval) that contains the original coefficient, the optimal solution remains optimal for the new model. *For each objective function coefficient, the range of numbers for the coefficient over which the optimal solution will remain optimal is called the range of optimality . Value = Z, solutions = X1 and X2… Adjustable cells Change within allowable, then optimal solution doesn’t change but value change Constraints Change within allowable, constraint = 0, both solution and value doesn’t change solution doesn’t change but value change Examples of nonlinear programming models
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