Local truckload pickup and delivery with hard time window constraints

This paper describes a solution method for a multiple traveling salesman problem with time window constraints (m-TSPTW). The method was developed for local truckload pickup and delivery problems such as those supporting rail or maritime intermodal operations but is suitable for application in other problems in which the number of tasks assigned to each server at any time is relatively small. We present a model and describe an iterative solution technique in which explicit time constraints are replaced by binary flow variables. At each iteration two versions of the problem, one over-constrained and the other under-constrained, are solved. The solution to the over-constrained problem provides a feasible solution, while the optimality gap provided by the two solutions informs the decision of whether to continue searching or to implement the best solution found so far. A specific time window partitioning scheme is used to ensure that the cost of solutions found is monotonically non-increasing. The method developed is suitable for real-time or quasi real-time implementation.