# Z94.1 - Analytical Techniques & Operations Research Terminology

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BASIC FEASIBLE SOLUTION.  A basic solution to the m equations of the linear programming problem which also satisfies the non-negativity constraints. 

BASIC SOLUTION.  Given a system of m simultaneous linear equation in “n” unknowns, Ax = b(m < n) and with rank m. If an m x m nonsingular matrix is chosen from A, and if all the n-m variables associated with the remaining columns of this matrix are set equal to zero, the solution to the resulting system of equations is called a basic solution. 

BASIC VARIABLES.  The m variables not initially set equal to zero in a basic solution (q.v.). 

BASIS.  A basis in e-dimensional Euclidean space is a set of n linearly independent vectors. In linear programming, a basis is an (m x m) nonsingular matrix composed of activity vectors, i.e., a basis matrix. 

BASIS INVERSE.  The inverse of the basis matrix. 

BASIS MATRIX. (See BASIS) 

BASIS VECTOR.  A column of a basis matrix. 

BIAS.  A systematic error that contributes to the difference between a population mean of the measurements or test results and an accepted reference or true value.

BIDDING, COMPETITIVE.  Each firm seeking a particular contract must submit a sealed price and the firm which submits the lowest price is awarded the contract.

BIRTH-AND-DEATH PROCESS.  A stochastic process which attempts to describe the growth and decay of a population the members of which may die or generate new individuals. The types mainly studied have relatively simple laws of reproduction and mortality. [22:29, 5:91, 13:402, 25:265]

BLOCK BOX.  Describes a system (organism or mechanism) whose structure is unknown either because it cannot be observed or it is too complex to be understood.

BLEMISH.  An imperfection that occurs with a severity sufficient to cause awareness but that should not cause any real impairment with respect to intended normal, or reasonably foreseeable, usage requirements.

BLOCK PIVOT.  By introducing several columns at once into the basis, the notion of pivot element may be generalized to that of block pivot. 

BOUNDED VARIABLE.  A variable in a linear programming problem whose values are limited from above or below or both.

BOUNDED VARIABLE PROBLEM.   A linear programming problem in which all or most of the variables have bounds of the type 1j ≤  xj ≤ bj. 

BRANCH AND BOUND. A method for solving mathematical programming problems based on partitioning the solution set into smaller subsets (branching) and establishing bounds on the value of the objective function for the subsets (bounding). A subset is excluded from further consideration when it is established that it contains no feasible solution having a value equal to or better than the current best solution.

BRANCHING PROCESS.  A stochastic process describing the growth of a population in which the individual members may have offspring, the lines of descent “branching out” as new members are born. [22:32, 5:58, 13:272]

BURN-IN.  The operation of items prior to their ultimate application intended to stabilize  their characteristics and to identify early failures. 

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