Can I use machine learning to predict someone will buy something in a specific time?
Short answer:
Yes it can be done using machine learning if you have  features with sufficient information.
Long answer:
You can model this either as a multilabel problem (i.e Beer, chicken, pizza are multiple labels [non mutually exclusive] for the same data point) or as a multiclass problem (by creating a combination like &quot;Beer, chicken, pizza&quot;. In the multiclass case the labels would be mutually exclusive). You can use day of the week, name of person and some other attributes as features (aka predictors) for the model.
For a more detailed answer you'd need to tell us what you have already tried out so that the community can help you.
Also, see this   related question.