Firstly, I'd contest that it didn't have a writing system.
Khipus are increasingly coming to be known as systems of writing. There's fantastic works by people like Gary Urton, but Sabine Hyland managed to recover an interview of the child of one of the last Khipu makers about how they were used. Essentially they encoded labour obligations amongst ayllus (a concept that is both a village, "ethnic group", and social unit) and at public events people and groups would be shamed for not contributing. Some people think that it was merely a mnemomic but there's a lot of ethnographic literature about how they were used as letters and biographies. Unfortunately the Spanish burnt most of them.
Secondly, I'd contest how centralised it really was. I've written about this before on ask historians (https://old.reddit.com/r/AskHistorians/comments/8fblxr/the_inca_empire_is_famous_for_being_one_of_the/) but the Incan economy (and pre-incan) was incredibly regionalised. With historic ayllu groups continuing to fill the roles they had historically done, and engage in local trading. Stock houses and such were also localised, even if the administrators were sometimes from Cusco.
Essentially, the Incan Empire worked because it didn't centralise. It kept things regional. Part of the reason for this is it was never, ideologically that is, one empire. As they believed the corpses of former emperors were still living, inheritance wasn't a thing. So each emperor was forced to make their own palaces, and to expand in their own direction because the existing empire was owned by the dead former emperor.
Sources:
Hyland, S. Writing with Twisted Cords: The Inscriptive Capacity of Andean Khipus, Current Anthropology, 58:3, 412-419. 6
Hyland, S. 2016 How Khipus Indicated Labour Contributions in an Andean Village: An Explanation of Seriation, Colour Banding and Ethnocategories, Journal of Material Culture, 21:4, 490-509.
Urton, G. 2017 Inka History in Knots: Reading Khipus as Primary sources,
Demarest, A., and Conrad, G.W. 1984 Inca Imperialism: The Great Simplification and the Accident of Empire, in Ideology in PreColumbian Civilizations
I've seen this question pop up almost verbatim from time to time, while you wait for a more specific answer you might be interested on these responses on Incan accounting methods by /u/CommodoreCoCo :
And while I personally think responses on this one are kind of all over the place, and kind of dont follow this reddit's rules at all, they could help you get into the mindset necessary for the answer you're looking for: