# Z94.1 - Analytical Techniques & Operations Research Terminology

Defined in this section are a set of terms that are in current use in the practice of teaching Operations Research.  As with any such set of terms, the list is not exhaustive.  However, we believe that the terms defined are characteristic of current practice, and span a significant space of modern Operations Research.

The previous edition, (1989) Industrial Engineering Terminology, is the basis for most of the definitions of this section.  Many thanks to the 1989 committee for their work.  A few new terms have been added for this edition and several terms had their definitions adjusted to reflect current practice or understanding.

Michael R. Taaffe,
Department of Operations and Management Science
Graduate Faculty of Industrial Engineering
Graduate Faculty of Scientific Computation

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Bibliography

## DEFINITION

ABSOLUTE MAXIMUM (MINIMUM). The  function f(x) defined over a set D is said to take on its absolute maximum (minimum) over D at a point x* in D if     f(x) ≤ f(x*), (f(x) ≥ f(x*)), for every point x in D.

ACCELERATED TEST.  A test in which the applied stress level is chosen to exceed that stated in the reference conditions in order to shorten the time required to observe the stress response of the item, or magnify the response in a given time. To be valid, an accelerated test must not alter the basic modes and/or mechanisms of failure. [20]

ACCELERATION FACTOR.  The ratio between the times necessary to obtain a stated proportion of failures for two different sets of stress conditions involving the same failure modes and/or mechanisms. [20]

ACCEPTANCE SAMPLING.  Sampling inspection in which decisions are made to accept or not-accept product or service; also, the methodology that deals with the procedures by which decisions to accept or not-accept are based on the results of the inspection of samples. Note: In lot-by-lot sampling, acceptance and non-acceptance relate to individual lot. In continuous sampling, acceptance and non-acceptance relate to individual units, or to blocks of consecutive units, depending on the stated procedure.

ACCESS, RANDOM. When units in the waiting line of a queue are chosen for service by  a random choice rule, the procedure is one of random access to service—or service by random access.

ACCOUNTING PRICES. Internal prices assigned to company-owned resources as an aid to decision-making and control. In certain linear programming applications, the dual variables at optimality may be regarded as including a set of accounting prices for the various scarce resources. Accounting prices in the linear-programming format are called shadow prices (q.v.). [12]

ACCURACY.  Closeness of agreement between an observed value or test result and an accepted reference value. Note: The term accuracy, when applied to a set of observed values will be a combination of random components and a common systematic error or bias component.

ACTIVITY.   (1) A decision variable whose level is to be computed in a programming problem. (2) A job in a network of jobs such as in a PERT network. [19]

ACTIVITY ANALYSIS PROBLEM.  A linear programming problem whose constraints represent resource use and variables represent commodities to be manufactured. The i-th coefficient of an activity vector “j” represents the number of units of resources “i” required to produce a unit of commodity “j.” The right-hand side coefficients indicate the amount of each resource available, while the objective function coefficients represent the profit per unit of activity. [15]

ACTIVITY LEVEL. The value taken by a decision variable in an intermediate or final solution to a programming problem. [ 19]

ACTIVITY REDUNDANCY. (See REDUNDANCY, ACTIVE.) [20]

ACTIVITY VECTOR. A column of the constraint matrix (q.v.) associated with a decision variable in a programming problem.

ADJACENT EXTREME POINT METHODS.  Two extreme points of a convex set (q.v.) lying on the same boundary edge are called adjacent. All methods, such as the simplex method (q.v.) which move from one extreme point (q.v.) to an adjacent one are called extreme point methods. [9]

ADMISSIBLE BASIS.. A set of m linearly independent activity vectors associated with a basic feasible solution (q.v.). (See BASIS)(BASIS SOLUTION.) [15]

ALGORITHM.  An inductive and iterative mathematical technique for developing numerical solutions to certain classes of problems.

ALTERNATE OPTIMA.   Distinct solutions to the same optimization problem. [9]

ANALYSIS OF VARIANCE.  A technique which subdivides the total variation of a set of data into meaningful component parts associated with specific sources of variation for the purpose of testing some hypothesis on the parameters of the model or estimating variance components.

ARC.  In a connected network with more than two nodes, an arc is a line connecting two nodes. It is often designated by an ordered pair (ni,nj), where ni and n are the nodes of the network at the ends of the line.

ARITHMETIC AVERAGE.  The sum of a set of sample values divided by the number of values in the set.

ARITHMETIC MEAN.  The sum of a set of population values divided by the number of values in the set.

ARRIVAL RATE DISTRIBUTION, CONSTANT.  The term constant applied to rates and times implies that a given rate or given time varies throughout its history under study in accordance with one probability density function. [12]

ARRIVAL RATE, MEAN.  In a waiting line, is the expected number of arrivals  occurring in a specified time unit.

ARRIVAL TIME, CONSTANT. (See arrival rate distribution, constant) [12]

ARTIFICIAL BASIS.   A set of artificial vectors which may be used to initiate the  simplex method (q.v.). [15]

ARTIFICIAL VARIABLES.  Auxiliary variables introduced into the equality constraints, at the start of the simplex method of linear programming in order to provide an identity basis required to initiate the procedure. [12]

ARTIFICIAL VECTOR.  The column vector associated with an artificial variable. It is a unit vector, with + 1 in the row where the artificial variable occurs and zero elsewhere. [12]

ASSEMBLY LINE BALANCING PROBLEM.  An assembly line consists of a number of work stations. To assemble the product under consideration, a number of jobs must be performed subject to certain sequencing requirements concerning the order in which they are performed. Given the desired production rate of the product, management wishes to accomplish two objectives: assign jobs to balance the work among stations and minimize the total number of these stations. The times required to do each job are specified. The problem can be formulated as integer linear programming (q.v.). [18]

ASSIGNMENT PROBLEM.  The problem of placing n elements into n cells, one        element to a cell, at minimum cost, where the individual cost of putting element i in cell j is a given constant cij. The problem can be stated as a linear programming problem or a transportation problem. The problem is usually interpreted as one of assigning n persons to n jobs, such that the value of person i in job j is cij. The problem is then to determine the assignment with maximum total value. [19]

ATTRIBUTES INSPECTION.   A  term used to designate a method of inspection whereby units of product are examined to determine for each unit whether it does or does not conform to a requirement. Example: Go and Not- Go gaging of a dimension. Note: inspection by attributes may be either one of two kinds: inspection whereby either the unit of product is classified simply as conforming or nonconforming, or the number of nonconformities in the units of product is counted, with respect to a given requirement or set of requirements.

AUGMENTED MATRIX.  The coefficient matrix augmented by the column of right-hand-side constants; the same as the constraint matrix (q.v.). [19]

AVAILABILITY. The ability of an item to perform its designated function when  required for use.

AVERAGE. (See ARITMETIC AVERAGE.)

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