It's very important that a cow comes on heat (returns to oestrus) soon after calving in New Zealand so she calves again close to the same time next year. If she misses one heat cycle, then she'll calve three weeks later the next year, and this has big negative management and economic implications.
Some cows will come on heat three weeks after calving, but this is too early to mate them, as their reproductive system needs time to settle down, involving massive changes and complex hormone interactions.
It's good to have a cow mated at her next heat which will be six weeks after calving. A healthy cow will be ready for breeding and become pregnant at this second heat.
Cows that don't cycle (are in anoestrus) are a great financial loss, so good managers have a "hit list" of cows which they expect to cause problems, and they'll have them lined up for veterinary inspection and appropriate treatment.
This hit list should include cows that have had a difficult calvings, and maybe have retained afterbirths and uterine infections into the bargain. Cows that are too thin at calving should be on this list, as should any cows that have had twins which are generally older. Cows that have had mastitis may have their oestrus delayed through a drop off in general health, and any cows that have been induced (aborted) may have hormonal upsets so they may not cycle early.
Some farmers argue that to save money, if they wait, these non-cycling cows will come on heat. This is a false policy and early veterinary treatment is the only wise move so their treatment will have a better chance of success.
Inducing (aborting) cows to calve early has now to be under strict veterinary control and there are strict rules about its use. Very old cows, heifers, and cows low in body condition should not be induced. Treated cows must have extra care and so do their calves. Don't keep induced calves and they should be humanely euthanased.