Re-arranging an array of payments to ensure no negative running balance

A company has a list of expected revenues and payments for the upcoming 
year in chronological order. The problem is that at some moments in time 
the sum of previous payments can be larger than the total previous revenue, 
which would put the company in debt. To avoid this problem the company 
takes a very simple approach: it reschedules some expenses to the end of 
the year.

You are given an array of integers, where positive numbers represent 
revenues and negative numbers represent expenses, all in chronological 
order. In one move you can relocate any expense (negative number) to the 
end of the array. What is the minimum number of such relocations to make 
sure that the company never falls into debt (in other words: you need to 
ensure that there is no consecutive sequence of elements starting from 
the beginning of the array, that sums up to a negative number)?