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

Abstract

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 shadowprice 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.

Combined strip and discharge delivery of containers in heterogeneous fleets with time windows

“…Based on the M-TSPTW model, they develop heuristics to obtain solutions for large size instances. Following the assignment models as proposed in [40,39] and [31], [46] investigates the inland transportation of loaded heterogeneous containers.…”

“…Discharge Type of Containers Methodology [42] x homogenous Exact & Heuristic [13] x homogenous Exact & Heuristic [19,18] x homogenous Exact & Heuristic [38] x heterogeneous Heuristic [16] homogenous Exact [7] x heterogeneous Exact [17] x homogenous Exact & Heuristic [10] x homogenous Exact & Heuristic [43] x heterogeneous Exact & Heuristic [26] x homogenous Heuristic [48,49] x homogenous & heterogeneous Exact & Heuristic [51,50] x homogenous & heterogeneous Exact & Heuristic [4] x homogenous Heuristic [6] heterogeneous Heuristic [20] x homogenous Exact [40,39] x heterogeneous Exact & Heuristic [2,3] x homogenous Exact & Heuristic [37] x homogenous Exact & Heuristic [22,21] x heterogeneous Exact & Heuristic [41] x homogenous Exact & Heuristic [27] x homogenous Exact & Heuristic [31] x heterogeneous Exact & Heuristic [47] homogenous Exact & Heuristic [45,44] x homogenous Exact & Heuristic [33] x homogenous Exact [11] homogenous Exact [36] x homogenous Exact [14] x homogenous Exact [35] x homogenous Exact & Heuristic [34] x homogenous Exact [46] x heterogeneous Exact & Heuristic [12] x heterogeneous Exact…”

“…For example, many of the aforementioned works (e.g. [42], [19], [7], [31], [46]) do not distinguish between loaded and empty containers but consider them in the same fashion as a movement request from one location to another. The approach proposed under this assumption cannot recognise the empty container and therefore ignores the possibility of reusing them.…”

“…The costs considered are travelling costs of the truck which reflect the mileage/fuel cost and the potential penalty for driving hours exceeding the maximum working time regulation. Note that when empty containers exist and can be reused, the number of possible route configurations becomes very large which prevents the usage or extension of the assignment formula, as is done in [40] and [46]. Therefore, we present a new formulation based on network flow, which extends [11] to include heterogeneous fleets and network flow constraints at inland depots.…”