The Pickup and Delivery Problem with Split Loads
Nowak, Maciek A.
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This dissertation focuses on improvements in vehicle routing that can be gained by allowing multiple vehicles to service a common load. We explore how costs can be reduced through the elimination of the constraint that a load must be serviced by only one vehicle. Specifically, we look at the problem of routing vehicles to service loads that have distinct origins and destinations, with no constraint on the amount of a load that a vehicle may service. We call this the Pickup and Delivery Problem with Split Loads (PDPSL). We model this problem as a dynamic program and introduce structural results that can help practitioners implement the use of split loads, including the definition of an upper bound on the benefit of split loads. This bound indicates that the routing cost can be reduced by at most one half when split loads are allowed. Furthermore, the most benefit occurs when load sizes are just above one half of vehicle capacity. We develop a heuristic for the solution of large scale problems, and apply this heuristic to randomly generated data sets. Various load sizes are tested, with the experimental results supporting the finding that most benefit with split loads occurs for load sizes just above one half vehicle capacity. Also, the average benefit of split loads is found to range from 6 to 7% for most data sets. The heuristic was also tested on a real world example from the trucking industry. These tests reveal the benefit of both using split loads and allowing fleet sharing. The benefit for split loads is not as significant as with the random data, and the various business rules added for this case are tested to find those that have the most impact. It is found that an additional cost for every stop the vehicle makes strictly limits the potential for benefit from split loads. Finally, we present a simplified version of the PDPSL in which all origins are visited prior to any destination on a route, generalizing structural results from the Split Delivery Vehicle Routing Problem for this problem.