What are the factors to consider to help management decide to use Azure or an on-premise server/s to do data analytics and/or machine learning?
This is the main value prop of the cloud: if you run your analytics and ML in the cloud, you save a lot of engineering time spent on managing on-prem infrastructure. Current cloud offerings are mature enough that you can achieve quite a lot without having to write any code. One of the principles I outline in my book is "codeless infrastructure" and a focus on PaaS offerings. To name a few: Azure Data Factory provides cloud scale ETL, Azure Purview provides metadata management/governance, Azure Machine Learning handles all infrastructure concerns related to running ML. Most of these services are pay-per-use, and once you add up the cost of on-prem hardware, IT, + custom solutions built on top of that it should be clear that the cloud ends up being much cheaper. Not to mention the reliability aspect - better let Microsoft ensure infra is always up and running rather than spend engineering resources to do the same on-prem.