Soft time windows apply only to orders. They represent a preferred time of service (i.e. pickup or delivery). The optimiser may schedule pickups or deliveries outside of any soft time windows but will incur a penalty for doing so.
A soft time window penalty has two components: a fixed component that is incurred if the soft time window is missed and a variable component that is a per-minute rate based on the number of minutes from the nearest time window boundary. The soft time window penalty acts as an additional form of hidden cost.
Example Assume the time windows in Figure 1 are delivery soft time windows and we have 200 and 5 as the fixed and variable penalty components respectively. In this case the hard time window exists from 6:00-17:00. If the order was delivered at 12:20, then we would incur a fixed penalty of 200 and a variable penalty of 5 × 20 = 100 for a total penalty of 300.