# Z94.1 - Analytical Techniques & Operations Research Terminology

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CAPABILITY. A measure of the ability of an item to achieve mission objectives given  the conditions during the mission. 

CAPACITATED TRANSPORTATION PROBLEM.  A bounded variable transportation problem (q.v.). 

CATASTROPHIC FAILURE. (See FAILURE, CATASTROPHIC.) 

CATERER PROBLEM.  A caterer requires for the next number of days rj fresh napkins on the jth day. j = 1,2,...n. Two types of laundry service are available. A slow service which requires p days and costs b cents per napkin; a fast service requiring q days q < p but costing c cents per napkin c > b. Beginning with no usable napkins on hand or in the laundry, the caterer meets the demands by purchasing napkins at a cents per napkin. How does the caterer purchase and launder napkins to meet requirements so as to minimize the total cost of n days? 

CHAIN (IN A GRAPH).  A sequence of arcs (i,i1), (i1,i2), (i2,i3)...(ik,j) connecting nodes i and j is called a chain. 

CHANCE CAUSES.  Factors, generally numerous and individually of relatively small importance, which contribute to variation, but which are not feasible to detect or identify.

CHANNELS, MULTIPLE.  A waiting line is said to have multiple channels when there is more than one station at which service is provided.

CHARACTERISTIC.  A property of items in a sample or population which, when measured, counted or otherwise observed, helps to distinguish between the items.

CHARACTERISTIC ROOT.  The characteristic root of a square matrix A is a value such that (l - lI) = 0 where I is the identity matrix.  For a p x p matrix there are, in  general, p such roots.  They are also known as Latent Roots and Eigenvalues.

The corresponding row-vectors u or column-vectors v for which

UA = lu or Av = lv

Are called characteristic vectors.

CHECKOUT.  Tests or observations of an item to determine its condition or status. 

CLUSTER SAMPLING.  A method of sampling in which the population is divided into mutually exclusive aggregates (or clusters) of sampling units related in a certain manner. A sample of these clusters if taken at random and all the sampling units which constitute them are included in the sample.

COEFFICIENT MATRIX.  The matrix of left-hand-side coefficients in a system of linear equations. It is to be distinguished from the matrix obtained by appending the right-hand side, which is called the “argumented matrix” of the system. [l9]

COEFFICIENT OF LOSS OF SERVICE.  The ratio of the average number of idle  service stations (servers) to the total number of service stations (servers).

COLUMN VECTOR.  One column of a matrix, or a matrix consisting of a single column. The elements of the column are interpreted as the components of the vector. 

COMPLEMENTARY SLACKNESS THEOREM.  For symmetric primal and dual linear programs (q.v.) the following theorem holds: Whenever inequality occurs in the ith relation of the primal (or dual) constraints for an optimizing solution, then the ith dual (or primal) variable of an optimizing solution vanishes. Conversely, if the ith variable of the dual (or primal) system is positive, then the ith relation of the primal (or dual) system is an equality. 

COMPOSITE ALGORITHMS. For linear programming, if neither the basic solution nor the dual solution generated by its simplex multipliers, remain feasible, the corresponding algorithm is called composite. 

CONE.  A set of vectors S is called a cone if for every vector X is S,  lX is in S for all

l ³ 0.

CONFIDENCE INTERVAL.  An interval calculated from sample data and distribution parameters with a specified probability or confidence.  To say that (a,b) is a 1-a confidence interval for the population parameter 0 means that the a priori probability that the random interval (A,B) will contain H is 1-a.  Another interpretation would be that (1-a)(100) percent of such intervals calculated by different random samples of the same size would contain 0 in the long run.

CONFIDENCE LEVEL. Probability that a particular value lies between an upper and a   lower bound, the confidence limits.

CONFIDENCE LIMIT. The bounds of an interval. A probability can be given for the likelihood that the interval will contain the true value.

CONSTANT ARRIVAL RATE DISTRIBUTION. (See ARRIVAL RATE DISTRIBUTION, CONSTANT.)

CONSTANT FAILURE PERIOD. That period during which the failures of units of a   particular item occurs at an approximately uniform rate. 

CONSTANT FAILURE RATE PERIOD.  That possible period during which the failures occur at an approximately uniform rate. 

CONSTANT VECTOR.  The right-hand side of a set of linear inequalities (equalities). By convention the linear relations of a linear programming problem are so arranged that all variables and their coefficients appear on the left, and the column of constants appears on the right. 

CONSTRAINT. An equation or inequality relating the variables in an optimization problem. 

CONSTRAINT MATRIX. In linear programming, the augmented matrix of the constraint equations. It is the matrix formed by the coefficient columns, or left hand sides, and the column of constants. 

CONSTRAINT QUALIFICATION.  This qualification places restrictions on the nature of the vicinity of a point satisfying certain conditions for optimality. These restrictions insure that the conditions are indeed, properly related to optimality.

A graphical method for evaluating whether a process is or is not in a "state of statistical control."

CONTROL CHART.  A graphical method for evaluating whether a process is or is not in a “state of statistical control.”

CONSUMER’S RISK.  b For a given sampling plan, the probability of acceptance of a lot the quality of which has a designated numerical value representing a level which it is seldom desired to accept.  Usually the designated value will be Limiting Quality Level (LQL).

CONVEX COMBINATION.  For the points X1, X2, . .., Xn a convex combination is a point

X = a1x1 + a2x2 + … = anxn

Where

ai  ³ 0  and SIai = 1.

CONVEX CONE.  A cone is convex if the positive sum of any two vectors in the cone is also in the cone.

CONVEX HULL. The convex  hull of a set of points S is the set of all convex         combinations of sets of points from S. 

CONVEX POLYHEDRAL CONE  A cone generated by a convex polyhedron. 

CONVEX POLYHEDRON.  The convex  hull of a finite number of points. [ 15]

CONVEX PROGRAMMING.  Optimization of a convex function over a convex region. Linear programming and quadratic programming are special cases of convex programming.

CONVEX SET. Geometrically, a set of points that contains all the points on the line segment joining any two points of the set; i.e., a set is convex if and only if each convex combination of any two points in the set is also in the set. 

CORRELATION. The linear relationship between two or several random variables within a distribution of two or more random variables.

COST COEFFICIENT.  The coefficient of a variable in the cost function of a linear        program. The elements of any objective function are sometimes referred to as cost coefficients. 

COST FUNCTION.  The objective function of a cost minimization program. 

COST RANGE. The range of values of a cost coefficient of a basic solution variable for which the current basis stays optimum. 

COST ROW. The row of objective function coefficients of a linear program matrix. 

COUPLING EQUATIONS.  When some of the constraints involve only the variables X and some others involve only the variables Y, the remaining equations involving both X and Y are called coupling equations. 

CUMULANTS.  These are values that are given by the coefficients in the expansion of a power series formed from the logarithms of the characteristic function of a random variable.

CUMULATIVE DISTRIBUTION FUNCTION, F(X)  A function giving, for every value x, the probability that the random variable X be less than or equal to x:  F(x) = P(X ≤ x)

CUT.  A partition of the nodes of a network into two sets such that the source node belongs to one set and the sink node to the other.

CUTTING PLANE.  The hyperplane boundary of an added linear inequality constraint in a programming problem. It may be thought of as “cutting off” part of the original convex region of feasible solutions in order to form a new convex region. 

CYCLING (LINEAR PROGRAMMING). The repeating of a basic feasible solution during application of the Simplex Algorithm (q.v.). 

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