The Multi-period Multi-trip Container Drayage Problem with Release and Due Dates

The Container Drayage Problem (CDP) aims at routing a fleet of trucks, based at a common terminal, to serve customers while minimizing the total travel distance. Each trip starts from and ends at the terminal, and handles a subset of customers. Each customer requires either that a container is picked up or delivered. We introduce a more realistic variant, i.e., the Multi-trip Multi-period CDP with Release and Due Dates (MM-CDP-RDD), in which the planning horizon is composed of several periods (days). On each day, each truck may perform more than one trip respecting the Release and Due Dates (RDD) associated with customer services, corresponding to the first and the last day on which the service can be carried out, respectively. Drivers’ contracts impose limitations on the maximum driving time allowed on each day, on two consecutive days and on the whole weekly planning horizon. To model the MM-CDP-RDD, we propose both an Arc-based Integer Linear Programming (ILP) formulation and a Trip-based ILP formulation that receives as input all the feasible non-dominated trips. To efficiently address medium/large-sized instances of the problem, we also design six Combinatorial Benders’ Cuts approaches. All the methods are compared on a rich set of instances generated for this new problem.