A column generation-based decomposition and aggregation approach for combining orders in inland transportation of containers

A significant portion of the total cost of the intermodal transportation is generated from the inland transportation of containers. In this paper, we design a mixed integer linear programming (MILP) model for combining orders in the inland, haulage transportation of containers. The pickup and delivery process of both 20 and 40 foot containers from the terminals to the customer locations and vice versa are optimized using heterogeneous fleet consisting of both 20 ft and 40 ft trucks/chasses. Important operational constraints such as the time window at order receivers, the payload weight of containers and the regulation of the working hours are considered. Based on an assignment problem structure, this MILP solves efficiently to optimality for problems with up to 120 orders. To deal with larger instances, a decomposition and aggregation heuristic is designed. The basic idea of this approach is to decompose order locations geographically into fan-shaped subareas based on the angle of the order location to the port baseline, and solve the sub problems using the proposed MILP model. To balance the fleet size amongst all subgroups, column generation is used to iteratively adjust the number of allocated trucks according to the shadow-price of each truck type. Based on decomposed solutions, orders that are “fully” combined with others are removed and an aggregation phase follows to enable wider combination choices across subgroups. The decomposition and aggregation solution process is tested to be both efficient and cost-saving.