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Decision-Making Models

Utility A measure of the total worth of a consequence reflecting a decision maker’s attitude toward considerations such as profit, loss, and risk.
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.
Risk avoider Adecision maker who would choose a guaranteed payoff over a lottery with a better expected payoff.
Expected utility (EU) The weighted average of the utilities associated with a decision alternative. The weights are the state-of-nature probabilities.
Risk taker A decision maker who would choose a lottery over a better guaranteed payoff.
Utility function for money A curve that depicts the relationship between monetary value and utility.
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.
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.
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.
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.
Pure strategy A game solution that provides a single best strategy for each player.
Mixed strategy A game solution in which the player randomly selects the strategy to play from among several strategies with positive probab. The solution to the mixed strategygame identifies the probab.that each player should use to randomly select the strategy to play.
Dominated strategy A strategy is dominated if another strategy is at least as good for every strategy that the opposing player may employ. Adominated strategy will never be selected by the player and as such can be eliminated in order to reduce the size of the game.
Constraint An equation or inequality that rules out certain combinations of decision variables as feasible solutions.
Problem formulation The process of translating a verbal statement of a problem into a mathematical statement called the mathematical model.
Mathematical model A representation of a problem where the objective and all constraint conditions are described by mathematical expressions.
Decision variable A controllable input for a linear programming model.
Objective function The expression that defines the quantity to be maximized or minimized in a linear programming model.
Nonnegativity constraints A set of constraints that requires all variables to be nonnegative.
Linear program A mathematical model with a linear objective function, a set of linear constraints, and nonnegative variables.
Linear functions Mathematical expressions in which the variables appear in separate terms and are raised to the first power.
Feasible solution A solution that satisfies all the constraints simultaneously.
Feasible region The set of all feasible solutions.
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 Alinear 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.
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.
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.
Surplus variable Avariable 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.
Alternative optimal solutions The case in which more than one solution provides the optimal value for the objective function.
Infeasibility The situation in which no solution to the linear programming problem satisfies all the constraints.
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.
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.
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.
Arcs The lines connecting the nodes in a network.
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.
Capacitated transportation problem A variation of the basic transportation problem in which some or all of the arcs are subject to capacity restrictions.
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.
Transshipment problem An extension of the transportation problem to distribution problems involving transfer points and possible shipments between any pair of nodes.
Capacitated transshipment problem A variation of the transshipment problem in which some or all of the arcs are subject to capacity restrictions.
Shortest route Shortest path between two nodes in a network.
Maximal flow The maximum amount of flow that can enter and exit a network system during a given period of time.
Flow capacity The maximum flow for an arc of the network. The flow capacity in one direction may not equal the flow capacity in the reverse direction.
Queue A waiting line.
Queueing theory The body of knowledge dealing with waiting lines.
Operating characteristics The performance measures for a waiting line, including the probability that no units are in the system, the average number of units in the waiting line, the average waiting time, and so on.
Single-channel waiting line A waiting line with only one service facility.
Poisson probability distribution A probability distribution used to describe the arrival pattern for some waiting line models.
Arrival rate The mean number of customers or units arriving in a given period of time.
Exponential probability distribution A probability distribution used to describe the service time for some waiting line models.
Service rate The mean number of customers or units that can be served by one servicefacility in a given period of time.
First-come, first-served (FCFS) The queue discipline that serves waiting units on a first-come, first-served basis.
Transient period The start-up period for a waiting line, occurring before the waiting linereaches a normal or steady-state operation.
Steady-state operation The normal operation of the waiting line after it has gone through a start-up or transient period. The operating characteristics of waiting lines are computed for steady-state conditions.
Multiple-channel waiting line A waiting line with two or more parallel service facilities.
Blocked When arriving units cannot enter the waiting line because the system is full. Blocked units can occur when waiting lines are not allowed or when waiting lines have a finite capacity.
Infinite calling population The population of customers or units that may seek service has no specified upper limit.
Finite calling population The population of customers or units that may seek service has a fixed and finite value.
Created by: mmoreno12
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