We reviews an approach applying a clustering algorithm to build a transport- ation plan. This study is an example of using an assignment model to solve a part of vehicle routing problem.
A multi-carrier transportation plan is to arrange carriers to distribute goods around the country [78]. The transportation plan should select what carrier to use for a given load where the plan should avoid backward mileage which is the case of a delivery point that is closer to the source than some of the previ- ous delivery points. Loads in this scenario are of three types: Full truck load, Less than a truck load and Groupage. Note that Groupage is smaller size ship- ments which can be delivered by using either a carrier in a transportation plan or a courier service. The hybrid heuristic method has five steps to produce a transportation plan:
1. Clustering shipments, 2. Create subgroup, 3. Build initial loads, 4. Carrier assignment, and 5. Improve loads.
Clustering Shipment
Shipments are clustered into big regions. The aim is to identify delivery regions across the country where shipments in a cluster are geographically compatible. The delivery region is built by adapted DBScan (Density-Based Spatial Clus- tering of Applications with Noise) which is one of the automated clustering methods [60]. The basic DBScan generates clusters by using two parameters: the neighbourhood threshold e and the minimum number of points to become a cluster minPts. The algorithm starts from an unvisited point p. Next, it seeks for neighbourhood points of p which are points where their distances from p are less than e. If p has neighbourhood points more than minPts, it forms a cluster which contains the point p and its neighbourhood points. The point p is also
known as the core point. This means a selected point p is in a dense area if the
number of neighbouring points is more than the minPts threshold. Next, the
algorithm selects one of the neighbours of p to find neighbours of the new point. A point might not become a member of any cluster if it is not a neighbour of any core points and its neighbour is less than minPts, called noise. Noises are basic- ally non-core points that also are not neighbours of any core points. Noises are not a member of any clusters. Although, the adaptive DBScan may allow noise points to be part of a cluster if they are within e distance to the nearest point in a cluster. Note that some of the noise points may not be absorbed. The adapt- ation is applied to control the size of clusters. Clusters that have more than 20 location points and are split by applying additional DBScan on them. Too small clusters are avoided by adjusting the minimum point threshold, minPts.
Create Subgroups
This part groups locations and considers a group of locations as a single deliv- ery point. In this case, locations within a subgroup should be very close to each other, i.e. 5 mile radius. A subgroup must also have a total load less than or equal to the vehicle capacity. Additionally, the delivery time must be compat- ible such that all shipments can be served by the same vehicle.
Build Initial Loads
Loads are built by having maximum shipments which are limited by vehicle capacity. The loads built in this part must cover at least all full truck loads and less than truck loads. Groupage may add to the load where there is capacity left from the two load types. The initial loads may violate delivery time which will be fixed later.
Carrier Assignment
At this point, the complex problem is reduced to an assignment problem which assigns loads to carrier companies. The objective function of the model is to find the cheapest transportation cost. The problem is formulated into an integer programming model and it is solved by mathematical solver.
Improve Loads
This stage moves shipments between loads to improve the quality of the plan. This also includes removing delivery time violations and reducing the overall cost, such as by addressing total driving distance and vehicle utilisation. There are four moves that apply in this method: Move shipments between loads in the same cluster, Move shipment between loads in different clusters, Re-sequence subgroup shipment and Re-sequence and adjust shipment in loads. Move ship- ment between loads in the same cluster basically swaps and reassigns shipments in the same cluster iteratively. The move swaps a shipment which has time violation. The swap is repeated until no delivery time violations remain or no further improvements can be made. Move shipment between loads in differ- ent clusters swaps two shipments between clusters where the distance between shipments is less than 70 miles. Again, this move is applied repeatedly until no delivery time violation remains or no further improvements can be made. Re- sequence subgroup shipments is sequencing the deliveries in the subgroup where delivery time violations can be removed. In addition, the re-sequencing pro- cess may improve operational cost. Re-sequence and adjust shipments in loads explore the shipments in a load and re-sequence those shipments in order to eliminate shipment delivery time violations. Adjustments are made by moving shipments from load mode to parcel mode. The adjustment is made only when the move reducing total operational cost.
Experiment, Result and Discussion
This approach tackled the real-world instances which had number of ship- ments up to 103. This approach builds loads where the number of loads ranged between 18-25% of total shipments [78]. Loads filled were 60-74% of the vehicle capacity with a small number of delivery time violations (2-6 violations). The delivery time violations were resolved during the improve loads stage which reduced time violation down to 0-1 violation. The total cost of this stage was 0.85-6% higher than the cost from planning in carrier assignment stage but the load capacity was decreasing by about 0.27-6.3%. More importantly, the plan showed improvement compared to the human planner.
From this work, the clustering algorithm with cluster size adjustment mech- anism and the use of MIP model as a part of the method are two main features that may help to develop methods to tackle the HHC problem. In Chapter 4, we have found that the geographical region partition made in the HHC instances can be unbalanced which results in some sub-problems are larger than other sub-problems and the larger sub-problems will require significantly longer solving time. Therefore, the mechanism to control the problem size, in- spired by this hybrid heuristic, can reduce the overall computation times.
We also have seen the use of assignment model as a part of algorithm to solve the transportation problem where the problem is normally been formu- lated as a balance flow model. This work has shown that the assignment model can be solved by an open source solver. Later in this thesis, in Chapter 7, we develop an assignment model to solve the HHC problem from which we have learnt from this work that the assignment model is much easier to solve by the MIP solver.