Chapter 8

• A basic assumption of linear programming that requires the contribution of each activity to the value of the objective function to be proportional to the level of that activity

  Proportionality Assumption of Linear Programming
• An activity has a nonproportional relationship with the overall measure of performance for a problem if the contribution of the activity to this measure is not proportional to the level of the activity
• An activity with a profit graph has decreasing marginal returns if the slope (steepness) of this profit graph never increases but sometimes decreases as the level of the activity increases
• A graph consists of a sequence of connected line segments

  Piecewise linear
• A spot in a graph where it is disconnected because it suddenly jumps up or down

  Discontinuity
• A method for using the known values in a profit or cost graph to find the equation for the graph that best fits these data

  Curve fitting method
• A solving method provided by Solver that is used to solve, or attempt to solve, some nonlinear programming problems

  Nonlinear Solver
• A special type of nonlinear programming where the objective function has both a quadratic form and decreasing marginal returns and all the constraints are linear

  Quadratic programming
• A powerful tool for solving certain kinds of prescriptive analytics problems, because it provides a choice of solving methods to best fit the problem under consideration

  Solver
• The highest point on an entire graph is called

  Global maximum
• A point at which a graph reaches its maximum within a local neighborhood of that point

  Local maximum
• A formula automatically becomes nonlinear if it ever multiplies or divides a changing cell by another changing cell or if it assigns an exponent (other than 1) to any changing cell
• T/F: At least one of the formulas that need to be entered into output cells is not linear; formula for the objective cell needs to be nonlinear

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• T/F: Nonlinear programming is used to model nonproportional relationships between activity levels and the overall measure of performance, whereas linear programming assumes a proportional relationship

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• T/F: Solving a nonlinear programming model is often much easier (if it is possible at all) than solving a linear programming model.

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• Nonlinear programming problems arise when any activity has a nonproportional relationship where the contribution of the activity to the measure of performance is not proportional to the level of the activity.
• Local maxima or local optima are the peaks of the graph because each one is a maximum
• Simplex LP (the Linear Solver) used to solve linear and BIP problems
• GRG Nonlinear (the Nonlinear Solver) used to solve nonlinear problems
• Quadratic (the Quadratic Solver) used to solve quadratic programming problems (only available with Analytic Solver)
• Evolutionary (the Evolutionary Solver) used to solve difficult nonlinear problems
• Evolutionary Solver has two significant advantages over the standard Solver for solving difficult nonlinear programming problems
• T/F: The complexity of the objective function does not matter. As long as the function can be evaluated for a given candidate solution (to determine the level of fitness), it does not matter if the function has kinks, discontinuities, or many local optima

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• T/F: Evolutionary Solver is a panacea

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• T/F: Evolutionary Solver does not perform well on models that have many constraints.

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• T/F: Evolutionary Solver is a random process. Running it again on the same model usually will not yield a different solution

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• T/F: By evaluating whole populations of candidate solutions, Evolutionary Solver keeps from getting trapped at a local optimum. Even if the whole population evolves toward a locally optimal solution, mutation allows the possibility of getting unstuck

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