Think about some job i, i+1. The total time to complete job i+1 (in order of [1 ... i-1] [i] [i+1]) is

T + a_iT + b_i + a_i + 1(T + a_iT + b_i) + b_i + 1

 = (a_i + 1 + 1)((a_i + 1)T + b_i) + b_i + 1

when T =  total time took to complete till job i-1

now think that we process in order of [1 ... i-1] [i+1] [i], then the total time is

(a_i + 1)((a_i + 1 + 1)T + b_i + 1) + b_i

Say c_i = a_i + 1. now, if this inequality holds, it's better to swap job i and i+1.

c_i + 1c_iT + c_i + 1b_i + b_i + 1 > c_ic_i + 1T + c_ib_i + 1 + b_i

which is

c_i + 1b_i + b_i + 1 > c_ib_i + 1 + b_i

now replace c_i to a_i, we get :

a_i + 1b_i > b_i + 1a_i

So, if above equality holds, we should swap i and i+1. This is essentially angular sort.

code : http://ideone.com/c70x8s