Actually I would say Alexander was primarily a tactician. To call him a strategist would be to misunderstand his character. He was not like the conventional picture of a strategist, manipulating military circumstance on a large scale to the advantage of his polity. He was a glory-hound, more like a viking going on a raid but on a gigantic scale. If he had been fighting for the interests of the Macedonian Empire then Carthage would have been his target after Persia, not India.