It could be possible that a company has more than one drop yard location available. In that case, a choice has to be made which drop yard to use in the tour of a vehicle. The vehicle serves all customers from that drop yard. In this section, we describe how this can be modeled. We also describe the situation that the depot is considered as one of the available drop yards. When the depot is chosen as the drop yard, the vehicle performs trailer tours directly from the depot. This
could be favorable when many customer locations are between the depot and the other drop yards. If, in that case, one of the other drop yards is used, the vehicle has to make a detour to visit that drop yard first and consequently the tour will be longer. Another advantage of using the depot as a drop yard is when the total amount of the load in a tour is less than or equal to the capacity of one trailer. Then it is not necessary to visit a drop yard to decouple trailers and it is much more efficient to do a single trailer tour directly from the depot.
5.1.1 Inclusion in the Model
In this model, we assume that when a vehicle uses a drop yard to decouple a trailer, it uses this drop yard also for the other trailer. In other words, a vehicle may not use a second drop yard in its tour. Before any decoupling of a trailer is done, there is a choice of where the first decouple takes place, thus a drop yard should be chosen for the tour. We describe two approaches to deal with this situation.
The first approach is to create a decouple node, switch node, and a couple node for every drop yard available. For each vehicle we create such a node set. We restrict ourselves to use not more than one drop yard in the vehicle tour, thus after the first decouple node of a drop yard is planned, the nodes of the other drop yards are not allowed in the solution anymore. The number of available nodes to plan can be reduced by not allowing the obsolete drop yard nodes to be planned after the moment that the decouple node is planned. The remainder of the DP algorithm is now the same as in the basic model, with only the switch node and a couple node for 1 drop yard that can be used. The DP algorithm is finished when all request nodes are planned and the tour is completed. The remaining drop yard nodes of the other drop yards stay unplanned. A consequence of this approach is that all options with all drop yards are investigated. This can lead to a high number of states that is investigated and increases the computation times. One way to deal with this problem is to limit the number of available drop yards to choose from. For example, one can preselect 2 or 3 drop yards, from a larger set, that can be used in the algorithm. This, however, causes that the algorithm does not necessarily leads to an optimal solution.
The second approach is to postpone the decision for which drop yard to use until the next request node is planned. As before, the decouple node is planned after the start node but this time no costs between these nodes are calculated and the drop yard node does not represent a specific drop yard yet. Instead, the costs for the route are calculated at the request node that is planned next. While adding the request nodes to the solution, the costs for the route are calculated including the decouple node. This is calculated for each possible location for the drop yard, which is given in the set of drop yards that can be used. The drop yard location that results in the lowest cost is stored in the current drop yard location for the decouple node. For each request node, switch node and couple node that is added, the best location for the drop yard is recalculated. Obviously, the location must be the same for each drop yard node, since we only allow the use of one drop yard in the vehicle tour. This approach results in fewer nodes for the drop yard: only 1 decouple node, 1 couple node, and 1 switch node are needed per drop yard. This also implies much fewer nodes in the DP algorithm that have to be planned and much fewer options that have to be investigated. Since the recalculation of the tours is quick the total calculation time will be shorter than in the first approach.
5.1.2 Use of the Depot as the Drop Yard
We can imagine that using the depot as a drop yard can be useful in some situations. For example, when many or all request nodes are located between the depot and the available drop yards. In that case, the vehicle must first pass all customers to decouple trailers at the drop yard, while it is shorter to go directly to the first customer to deliver the first load. To prevent the vehicle to use this long route and to allow the vehicle to deliver loads to customers directly from the depot with
a single trailer, we enable that the vehicle uses the depot as a drop yard. To accomplish that, we add the depot to the set of available drop yards to choose from. Thus we make a decouple node, a couple node, and switch nodes for this drop yard. In the cost matrix, the cost from other depot nodes to the drop yard nodes, representing the depot, are 0 and the costs from these drop yard nodes to the request nodes are the same as the other distances from the depot to the customers. If the amount of the loads from all customers together in a tour of a vehicle is at most the capacity of one trailer, it is not necessary to use two trailers and, consequently, it is unnecessary to visit a drop yard. In this case, all customers can be served with one trailer. This trailer can drive directly from the depot to the first customer, because no trailers have to be decoupled at the drop yard. In the basic model, we assume that the truck carries two trailers. This means that the second trailer can stay at the depot in this case, which saves travels from and to the drop yard with an empty trailer. In the solution of the DP algorithm calculations for this case, the switch node is directly followed by the couple node of the vehicle and the costs of travel between these nodes is 0.