Right before my shift was supposed to start, the company changed the schedule for their own reasons.
To suit their own needs, the company suddenly changed my shift as it was about to start.
The company had some problem, so they suddenly changed my shift at the last minute.
「会社の都合で」の英訳としては「Due to the company's circumstances」は合っていますが、あまり言わないと思います。「for their own reasons」「to suit their own needs」はもっと自然です。
上記の3番目は一番会話的な言い方です。「had some problem」は「いくつか問題があった」ではなく、「何かの問題があった」という意味です。