# Z94.1 - Analytical Techniques & Operations Research Terminology

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LEFT-HAND SIDE. The mathematical expression to the left of the equality or inequality    sign in an equation or inequality. In linear programming, by convention, the left-hand side of each constraint is the complete linear function, while the right-hand side is the constant term. 

LEONTIEF SYSTEM. (See INTERINDUSTRY ANALYSIS.)

LEXICOGRAPHIC ORDERING. Dictionary ordering. 

LINEAR COMBINATION. An expression of the form a1x1 + a2x2 + ... + anxn where the ai are coefficients and the xi are variables or vectors. 

LINEAR CONSTRAINT. A constraint which contains variables which are related in terms of linear combinations. 

LINEARLY DEPENDENT. A set of vectors {X} is linearly dependent if a set of numbers aj, not all equal to zero, can be found such that  a1X1 + a2X2 + ... + akXk = 0. 

LINEAR EQUATION. An equation whose left-hand side and right-hand side are both linear functions of the variables. Such an equation can always be put in the form  f(x, y, z,) = c,  where f is a linear function and c is a constant. 

LINEAR ESTIMATOR. An estimator which is a linear function of the observations. 

LINEAR FUNCTION. A function of the form a0 + a1 x1 + a2X2 + ... + anxn, where the ai are coefficients, not all 0, and the x; are variables. The geometrical representation of a linear function is a straight line, plane, or hyperplane.

LINEAR INDEPENDENCE. A set of vectors (Xi)is linearly independent if the only set  of numbers ai for which alX1 + a2X2 + ... + akXk = 0 is al = a2 = ... = ak = 0. 

LINEAR INEQUALITY. An inequality whose left-hand side and right-hand side are both   linear functions of the variables. 

LINEAR MODEL. A model where each dependent variable is a linear function of independent variables.

LINEAR PROGRAMMING. The concept of expressing the interrelationship of activities of a system in terms of a set of linear constraints in nonnegative variables. A program, i.e., values of the variables, is selected which satisfies the constraints and optimizes a linear objective function in these variables. 

LINEAR PROGRAMMING PROBLEM. The problem of minimizing or maximizing a linear function in n variables subject to m linear constraints, with the variables restricted to be nonnegative. Mathematically, we have Min (max) cX subject to AX = b    X ≥ 0   with A an (mxn) matrix. The constraints AX = b can also be given in terms of inequalities, i.e., AX ≥ b, AX ≤ b or a combination of such constraints. 

LOCAL OPTIMUM. (See GLOBAL OPTIMUM.) 

LOOP (IN A GRAPH). A chain of arcs connecting node i to itself in a graph is called a loop (if the arcs are distinct, the loop is a simple loop). 

LOT TOLERANCE PERCENT DEFECTIVE (LTPD). Expressed in percent defective, the poorest quality in an individual lot that should be accepted.  Note: The LTPD is used as a basis for some inspection systems, and is commonly associated with a small       consumer’s risk. (See CONSUMER'S RISK.) 

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