The phrase "vast production" is correct and usable in written English.
You can use it to refer to a large amount of something that has been produced, such as a large amount of goods or services. For example, "The company has tripled its vast production of automobiles in the past five years."
Limited use was made of this hydrogenation technology in Europe; the greatest potential use for the process lay in the United States, where a vast production of cottonseed oil, a by-product of the Southern cotton industry, awaited developments that would permit its conversion to a plastic fat.
Every movie that's being made here is a vast production.
Models were used elsewhere in the vast production line.
Earthworms are important aggregate-forming managers in the soil owing to the vast production of casts.
One of the major environmental and health concerns is the vast production of acid mine drainage.
By 1915, Hollywood had become the epicenter of American filmmaking, with studio "dream factories" structuring its vast production.
A second 100,000-ton facility supplies a vast ethylene production plant outside of town.
Developing in an original way Augustinian and Thomistic doctrines, Giles's vast literary production includes Aristotelian and biblical commentaries and theological and political treatises.
The appointment of someone with vast radio production experience will please Radio 4's core audience who are famously resistant to change.
The place was so vast that production assistants scuttled back and forth on scooters and bicycles, and included an 800,000-gallon tank with wave and wind machines and what amounted to a giant, ceiling-mounted shower head.
"The vast programming, production and media resources of our two companies position us extremely well to serve audiences, advertisers and all constituents of these new channels," Armando Nuñez, the president of CBS Studios International, said in a statement.
