If you want to find the index of the minimum element, you can use Enumerable#enum_forto get an array of pairs of index elements and find the minimum of them with Enumerable#min(which will also be minimal for the original array).
% irb
irb> require 'enumerator'
#=> true
irb> array = %w{ the quick brown fox jumped over the lazy dog }
#=> ["the", "quick", "brown", "fox", "jumped", "over", "the", "lazy", "dog"]
irb> array.enum_for(:each_with_index).min
#=> ["brown", 2]
If you want to associate it with specific array indices:
irb> start = 3
#=> 3
irb> stop = 7
#=> 7
irb> array[start..stop].enum_for(:each_with_index).min
#=> ["fox", 0]
irb> array[start..stop].enum_for(:each_with_index).min.last + start
#=> 3
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