You need to set the default options so that it applies to newly created date[time]pickers:
From the options page on how to set global defaults:
$.fn.datetimepicker.Constructor.Default = $.extend({}, $.fn.datetimepicker.Constructor.Default, {
viewMode: 'days',
format: 'MM/DD/YYYY',
});
Updated fiddle
Your issue was that this line
$('#monthDatetimepicker').datetimepicker({
format: 'MM/dd/YYYY'
doesn't get applied to anything as $('#monthDatetimepicker') === 0
at the time the code runs.
Moving that line to the end also does nothing as your newly created date inputs have id="monthDatetimepicker" + i
. Changing to a valid ID such as:
$('#monthDatetimepicker0').datetimepicker({
format: 'MM/dd/YYYY'
then only works for the first picker.
So you could do some hideous $("[id=^monthDatetimepicker]").datetimepicker...
or, easier, you could add a class into your html builder and use that as a selector. Or set it globally as above (which will affect other pickers unless they had a different format applied). (or use a datepicker instead...)