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# EGC 1 Anderson

### QuantMethodsBusinessCh5,7,8,10,11

Question | Answer |
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Dominated strategy | A strategy is dominated if another strategy is at least as good for every strategy that the opposing player may employ. A dominated strategy will never be selected by the player and as such, can be eliminated in order to reduce the size of the game. |

Expected Utility (EU) | The weighted average of the utilities associated with a decision alternative. The weights are the state-of-nature probabilities. |

Game Theory | The study of decision situations in which two or more players compete as adversaries. The combination of strategies chosen by the players determines the value of the game to each player. |

Lottery | A hypothetical investment alternative with a probability p of obtaining the best payoff and a probability of (1 – p) of obtaining the worst payoff. |

Mixed Strategy | GS; player randomly selects the strategy to play from among several strategies with positive probabilities. The solution to the mixed strategy game identifies the probabilities that each player should use to randomly select the strategy to play. |

Pure Strategy | A game solution that provides a single best strategy for each player. |

Risk Avoider | A decision maker who would choose a guaranteed payoff over a lottery with a better expected payoff. |

Risk Taker | A decision maker who would choose a lottery over a better guaranteed payoff. |

Risk Neutral Decision Maker | A decision maker who is neutral to risk. For this decision maker the decision alternative with the best expected monetary value is identical to the alternative with the highest expected utility. |

Saddle Point | A condition that exists when pure strategies are optimal for both players in a two-person, zero-sum game. The saddle point occurs at the intersection of the optimal strategies for the players, and the value of the saddle point is the value of the game. |

Two-Person, Zero-Sum Game | A game with two players in which the gain to one player is equal to the loss to the other player. |

Utility | A measure of the total worth of a consequence reflecting a decision maker’s attitude toward considerations such as profit, loss, and risk. |

Utility Function For Money | A curve that depicts the relationship between monetary value and utility. |

Alternative Optimal Solutions | The case in which more than one solution provides the optimal value for the objective function. |

Constraint | An equation or inequality that rules out certain combinations of decision variables as feasible solutions. |

Decision Variable | A controllable input for a linear programming model. |

Extreme Point | Graphically speaking, extreme points are the feasible solution points occurring at the vertices or “corners” of the feasible region. With two-variable problems, extreme points are determined by the intersection of the constraint lines. |

Feasible Region | The set of all feasible solutions. |

Feasible Solution | A solution that satisfies all the constraints simultaneously. |

Infeasibility | The situation in which no solution to the linear programming problem satisfies all the constraints. |

Linear Functions | Mathematical expressions in which the variables appear in separate terms and are raised to the first power. |

Linear Program | A mathematical model with a linear objective function, a set of linear constraints, and nonnegative variables. |

Mathematical Model | A representation of a problem where the objective and all constraint conditions are described by mathematical expressions. |

Nonnegativity Constraints | A set of constraints that requires all variables to be nonnegative. |

Objective Function | The expression that defines the quantity to be maximized or minimized in a linear programming model. |

Problem Formulation | The process of translating a verbal statement of a problem into a mathematical statement called the mathematical model. |

Redundant Constraint | A constraint that does not affect the feasible region. If a constraint is redundant, it can be removed from the problem without affecting the feasible region. |

Slack Variable | A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount of unused resource. |

Standard Form | A linear program in which all the constraints are written as equalities. The optimal solution of the standard form of a linear program is the same as the optimal solution of the original formulation of the linear program. |

Surplus Variable | A variable subtracted from the left-hand side of a greater-than-or-equal-to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount over and above some required minimum level. |

Unbounded | The situation in which the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints. |

100 Percent Rule | When simultaneous changes in two or more objective function coefficients will not cause a change in the optimal values for the decision variables. Also: indicate when two or more right-hand-side changes will not cause a change in any of the dual prices. |

Dual Price | The improvement in the value of the optimal solution per unit increase in the right-hand side of a constraint. |

Reduced Cost | Amt which an objective function coefficient would have to improve (increase for a maximization problem, decrease for a minimization problem) before it would be possible for the corresponding variable to assume a positive value in the optimal solution. |

Relevant Cost | A cost that depends upon the decision made. The amount of a relevant cost will vary depending on the values of the decision variables. |

Sensitivity Analysis | The study of how changes in the coefficients of a linear programming problem affect the optimal solution. |

Sunk Cost | A cost that is not affected by the decision made. It will be incurred no matter what values the decision variables assume. |

Arcs | The lines connecting the nodes in a network. |

Assignment Problem | A network flow problem that often involves the assignment of agents to tasks; it can be formulated as a linear program and is a special case of the transportation problem. |

Capicitated Transporation Problem | A variation of the basic transportation problem in which some or all of the arcs are subject to capacity restrictions. |

Capacitated Transshipment Problem | A variation of the transshipment problem in which some or all of the arcs are subject to capacity restrictions. |

Dummy Origin | An origin added to a transportation problem to make the total supply equal to the total demand. The supply assigned to the dummy origin is the difference between the total demand and the total supply. |

Network | A graphical representation of a problem consisting of numbered circles (nodes) interconnected by a series of lines (arcs); arrowheads on the arcs show the direction of flow. Transportation, assignment, and transshipment problems are network flow problems. |

Nodes | The intersection or junction points of a network. |

Transportation Problem | A network flow problem that often involves minimizing the cost of shipping goods from a set of origins to a set of destinations; it can be formulated and solved as a linear program by including a variable for each arc and a constraint for each node. |

Transshipment Problem | An extension of the transportation problem to distribution problems involving transfer points and possible shipments between any pair of nodes. |

Base-case Scenario | Determining the output given the most likely values for the probabilistic inputs of a model. |

Best-case Scenario | Determining the output given the best values that can be expected for the probabilistic inputs of a model. |

Controllable Input | Input to a simulation model that is selected by the decision maker. |

Discrete-event Simulation Model | A simulation model that describes how a system evolves over time by using events that occur at discrete points in time. |

Dynamic Simulation Model | A simulation model used in situations where the state of the system affects how the system changes or evolves over time. |

Event | An instantaneous occurrence that changes the state of the system in a simulation model. |

Numerical values that appear in the mathematical relationships of a model. are They are considered known and remain constant over all trials of a simulation. | |

Probabilistic Input | nput to a simulation model that is subject to uncertainty. Described by a probability distribution. |

Risk Analysis | The process of predicting the outcome of a decision in the face of uncertainty. |

Simulation | A method for learning about a real system by experimenting with a model that represents the system. |

Simulation Experiment | The generation of a sample of values for the probabilistic inputs of a simulation model and computing the resulting values of the model outputs. |

Static Simulation Model | A simulation model used in situations where the state of the system at one point in time does not affect the state of the system at future points in time. Each trial of the simulation is independent. |

Validation | The process of determining that a simulation model provides an accurate representation of a real system. |

Verification | The process of determining that a computer program implements a simulation model as it is intended. |

What-if Analysis | A trial-and-error approach to learning about the range of possible outputs for a model. Trial values are chosen for the model inputs (these are the what-ifs) and the value of the output(s) is computed. |

Worst-Case Scenario | Determining the output given the worst values that can be expected for the probabilistic inputs of a model. |

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