Flexible truckload pickup and delivery problem considering reserved orders and fuel consumption

Abstract

The orders of a transportation enterprise can be fulfilled by the private fleet or outsourced to a common carrier for a flexible transportation planning. In reality, some of the orders have to be reserved for the private fleet due to some constraints (such as trade secret), which can reduce the flexibility of transportation, thereby increasing the operational cost. To handle this problem, a flexible truckload pickup and delivery problem is proposed, where time widows, outsourcing, reserved orders, and fuel consumption of the private fleet are considered, and truck speed is taken as a decision variable instead of a parameter. Then, the proposed problem is described as a directed graph, and its attributes are analyzed to reduce the solution space; consequently, a mixed integer nonlinear programming model based on truck visiting time is established. After that, an updated time window partition based (UTWPB) method is developed, which is described by a sparse matrix to further reduce the solution space, and it can obtain a lower bound of the proposed problem by relaxing the constraints of the partitioned time windows. Numerical experiments demonstrate that the UTWPB method performs well compared with existing approximate methods, and it can offer reasonably accurate solutions for real-life scale instances. Additionally, sensitivity analysis is also conducted to confirm the effectiveness of the proposed model.