Predict time of dispatch for marketing campaign
I might suggest a change to your theoretical setup:

It sounds like you are trying to maximize an equation f(t), where t is the time of dispatch, and f(t) is the risk adjusted chance of purchasing (as you note it can be 0-many).

In that case, it is likely better to use a setup like this:

===========================================================
  customer campaign    campaign_time       total_responses_within_1week   
-----------------------------------------------------------
1   100       a     2017-01-01 06:50:01       0
2   101       a     2017-01-01 06:50:01       3
3   101       a     2017-01-01 06:50:01       2
4   100       b     2017-01-07 06:30:21       1
5   101       b     2017-01-07 06:30:21       1
6   100       c     2017-01-14 06:43:55       1
7   101       d     2017-01-21 14:02:01       1
-----------------------------------------------------------


Unless you have specific internal data or journal research that directly indicates a relationship between speed of response and likelihood/number of purchases, I might avoid including it.

Now, if you need to estimate time of response for issues like labor or inventory, you could use a probabilistic model, but I'll avoid making specific recommendations there, as my relative strength is in regression models. You'd want the function to output a probabilistic curve over a given time period, and then sum all of those curves together (e.g. to estimate that during Weds morning, you will have 80-109 orders, so need 5 customer service reps).

If your goal is purely response frequency (within a relevant time), time of response doesn't need to be modeled, however.