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The phrase "assignment is made" is correct and usable in written English.
It can be used in contexts where you are indicating that a task or duty has been assigned to someone.
Example: "Once the assignment is made, the team will begin working on the project immediately."
Alternatives: "task is assigned" or "duty is allocated".
Exact(20)
Many promising soldiers are being assigned to certain approved colleges for courses in engineering, and the assignment is made alphatetically, and that of 300 men….
Major Tim's assignment is made as British space activity is experiencing a big renaissance.
Actually, that score can be considered as an estimate of the degree of source separation carried out by the beamformers when a correct assignment is made.
In a first stage, referred to as naive scheme, a preliminary PRB assignment is made based on the open-loop power control algorithm.
The interpretation of a descriptive symbol is direct if and only if (i) it is given by an assignment of an extension or an intension, and (ii) this assignment is made by expressions of the metalanguage.
By means of the output of the meso-scale model, a dynamic multi-modal route assignment is made in a last step and detailed trips are generated in a micro-scale environment [45, 46].
Similar(40)
Instead, each assignment was made with something specific in mind, according to Mr. Bloomberg's statement.
This unenviable assignment was made even more onerous by his longstanding pessimism about the war.
A random assignment was made from 123 patients of the 149 initially recruited.
Appeals of pupil assignment were made directly to the governor.
The assignment was made based on his neutrality despite his inexperience officiating at the international level.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com