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Trucking companies may try to schedule around congestion patterns, but must meet customer demands for on-time service in preferred time windows.

The Routing Problem is an important management problem in the field of physical distribution and logistics. In practice, the logistics system usually includes more than one depot, and the start of the service at each customer must be within a given time window.

The objective of the proposed time window is to minimize the total cost, which consists of the fixed cost for the vehicles, the routing cost, and the customer inconvenience cost, which is modeled as a penalty cost for violation of the time windows of each customer. Like other combinatorial problems, solving this pickup and delivery problem is time-consuming, and sometimes it is impossible to find an exact solution.

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