The study was executed in the context of a PhD research project, making up part of the Heijendaal Living lab project. It focuses on finding an effective solution method to solve a complex inventory-routing problem. A summary of the first results and their practical implications are reported in this paper.
There is an increasing interest in managing the last-mile logistics using intermediate facilities, often called hubs. Such supply chains are referred to as two-echelon distribution systems, where the first-echelon concerns the distribution network between the suppliers of products and the hubs, and the second-echelon concerns the distribution network between the hubs and the customers for the products. We discuss the optimization of those two-echelon distribution networks and provide practical insights in these distribution systems.
Figure 1 shows an example of a simple two-echelon supply chain consisting of one supplier with a central depot, two hubs and many customers with storage capacity.
Figure 1 Example of a Two-Echelon Supply Chain
Consider a supplier serving many customers from one or multiple central depots through a few hubs. Two separate, limited vehicle fleets are available for the delivery of goods in the first and the second echelon. It is allowed to store goods at the hubs’ and the customers’ locations. What are the optimal inventory and routing decisions to meet the demand of the customers over several time periods at the lowest cost? The routing decisions concern the order and the timing of the visits to the customers and to the hubs. The inventory decisions concern the inventory levels and the quantities to be delivered to each customer and each hub during each time period. This type of problem is referred to as a two-echelon inventory-routing problem.
We modeled the problem on-hand as a mathematical model. A few assumptions are made. The demand is considered deterministic. Moreover, the production capacity at the supplier’s central depots is considered unlimited. The transportation costs are linearly proportional to the distances travelled. All customers must be delivered via a hub.
The problem on-hand is solved exactly. We developed a branch-and-price algorithm and tested it on 400 newly generated instances with different settings and parameter values (including the number of second-echelon vehicles, number of suppliers, hubs, and customers, and inventory costs).
(Near) optimal results have been obtained for different sets of parameter values. We notice that for the instances for which an optimal solution was found, the first-echelon routes are typically back-and-forth routes, i.e. the first-echelon routings include only one hub, regardless of the number of hubs. This observation seems to imply that for small to medium cities, using a single hub in a strategic location may not be far from optimal.
GeneralThe algorithm has been developed for quite a general situation, allowing much flexibility for the supplier with respect to the use of hubs, partial deliveries, and moments/quantities of deliveries. However, this method may cause some inconvenience for the customers due to more or partial deliveries. The algorithm indicates whether delivery requirements can be fulfilled for a given situation. The algorithm also allows getting insight into what more storage space at the hubs, customers, and more/less, larger/smaller trucks could mean.
SustainabilityIn this context, only CO2 emissions have been considered. There is a general assumption that CO2 emissions are linearly proportional to the distance travelled. Then optimizing the distance travelled is equivalent to minimizing the CO2 emissions. However, this assumption is not always accurate as the emissions depend on the fuel used, which is linked to, among others, the speed of the truck, the vehicle’s characteristics, the road, and the drivers’ behavior. Hence, the optimization of the travelled distance only can be limiting if accurate values of the CO2 emissions are to be calculated. However, if using electric vehicles in the second echelon, then using a hub will reduce the CO2 emissions as the distance travelled by first-echelon trucks is significantly reduced.
LivabilityAlthough not the focus of this research project on using hubs, a few observations can be made. The use of hubs keeps larger trucks outside urban areas and reduces the related noise. However, the capacity of the first-echelon trucks initially used for the complete transport to the customers is larger than that of the second-echelon trucks. Hence, potentially a few more vehicles may have to be used in the second-echelon at different times depending on their capacity and the customers’ demand. In the context of the Heijendaal Living lab, this should rarely be the case because small deliveries are often made by different suppliers, which can be in turn consolidated in the hub before arriving to the customers. This will result in a decrease of the number of vehicles in the second-echelon.
CostsThe main aim of the algorithm is minimizing the total transportation and inventory cost for a supplier under a Vendor Managed Inventory setting. It can be stated that optimising only the transportation costs can already help significantly reduce the overall costs. However, optimising the transportation and the inventory costs can provide an extra reduction of the overall costs with the disadvantage of an increasing complexity of the solution method.
Service levelAll demand is delivered timely, where part of the demand may be delivered earlier than strictly required and has to be kept in stock, eventually requiring more handling by the customers (and the supplier) due to partial deliveries.
To make the model/solution method more useful, multiple products should be considered, making both the routing and inventory decisions more complex (many more options). Direct deliveries from the central depots of the supplier to customers could be allowed because it may be advantageous to visit customers that are nearby depots directly from the supplier. It could be interesting for a supplier to limit first-echelon trips to back-and-forth trips to a single hub depending on its proximity to the customers and the supplier. In practice, the actual transportation costs may be far more complex (among others, non-linear, dependent on the actual quantity transported in one vehicle). The model can easily be changed to include a fixed cost for each vehicle used.
There are many data issues. As clear from the case study with one supplier, it is not so easy to get the accurate distances, let alone the type of roads, speed limitations, etc., to determine fuel consumption, driver costs, time on the road, although they play an important role in the decision making of companies.
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Neem dan contact op met: Marco.Wolf@han.nl