Organization

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0 means "order of" and o means "of lower order than." If {un} and {vn} are two sequences such that lun1Vnl < K for every n greater than some fixed value U 0 , where K is a constant independent of n, we write Un = O(vn); for example, (2n - 1)/(n 2 + 1) = 0(11 n). The symbol 0 (colloquially called "big 0") is also extended to the case of functions of a continuous variable; for example, (x + 1) = O(x). We denote by 0(1) any function x which is defined for all values of x sufficiently large, and which either has a finite limit as x tends to infinity, or at least for all sufficiently large values of x remains less in absolute value than some fixed bound; for example, sin x = 0(1). If the limit of Un1Vn = 0, we write instead that Un = o(vn) (colloquially called "little o"). Thus, Un < Vn and Un = o(Vn) are two different ways of expressing the same relation; for example, sin x - x = o(x). The notation is also extended to functions of a continuous variable. Furthermore, Un = o(1) as n tends to infinity means that Un tends to 0 as n tends to infinity. In probability modeling (e.g., Markov chains and queueing theory), it is common to see o(L.'lt) used to represent functions going to 0 faster than the small increment of time ilt, so that the limllt-o[ o(ilt)/ ilt] = 0.

The ratio of mean service time to mean interarrival time; the rate at which work is brought to a queueing system. See Erland; Queueing theory.

OPEN NETWORK A queueing network in which all customers enter and eventually leave the network, that is, routing process contains no closed subsets of states for any type of customer. See Networks of queues; Queueing theory.

OPERATIONS EVALUATION GROUP (OEG) See Center for Naval Analyses.

OPERATIONS MANAGEMENT Mark A. Vonderembse and William G. Marchal The University of Toledo, Ohio Organizations exist to meet the needs of society that people working alone cannot. Operations are part of an organization and they are responsible for producing the tremendous array of products in the quantities consumed each day. Operations are the processes which transform inputs (labor, capital, materials, and energy) into outputs (services and goods) consumed by the public. Operations employ people, build facilities, purchase equipment in order to change materials into finished goods such as computer hardware and/or to provide services such as computer software development. Services are intangible products and goods are physical products. According to the classification scheme used by the U.S. Department of Commerce and Labor, services include transportation, utilities, lodging, entertainment, health care, legal services, education, communications, wholesale and retail trade, banking and finance, public administration, insurance, real estate, and other miscellaneous services. Goods are described as articles of trade, merchandise, or wares. Manufacturing is a specific term referring to the production of goods. In this descripINTRODUCTION:

OBJECTIVE FUNCTION The mathematical expression that is to be optimized (maximized or