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Longman Dictionary of Contemporary English
line management
noun
EXAMPLES FROM CORPUS
▪ If you feel your workplace is causing you to suffer ill-health effects, then notify your line management.
▪ It also recognises that day-to-day business and executive authority is vested in line management.
▪ It is a process that forces line management to consider their operational priorities and also allows for decentralized decision-making.
▪ Meetings were held with the nursing officer and health visitor line management.
▪ Some say they were unaware of the full impact of the new line management structure when they met to discuss it.
▪ Staff in these Departments considering additional computers are at liberty to submit suggestions through line management in the usual way. 3.
▪ The rest were added to the hard-working ranks of our third organizational constituency: staff / line management.
▪ These were often displaced nurse managers who no longer had line management responsibilities at district level.
Wiktionary
line management

n. (context business English) A method of management in which instructions are passed to and from one's superior

WordNet
line management

n. administration of the line functions of an organization; administration of activities contributing directly to the organization's output

Wikipedia
Line management

Line management is a business term to describe the administration of activities that contribute directly to the output of products or services. In a corporate hierarchy, a line manager holds authority in a vertical (chain of command), and/or over a particular product line. He or she is charged with meeting corporate objectives in a specific functional area or line of business.

As an example, one type of line management at an automobile conglomerate might be the "light truck division", or even more specifically, the "light truck marketing line". Similarly, one type of line management at a financial services firm might be "retention marketing" or "state municipal bond funds".