Practical development of transport routing model
Routing in transportation networks forms an important part of many logistics systems. Nowadays, transportation network information is typically obtained from a geographic information systems (GIS), in our case the complete road network of Slovenia maintained in Cadastral register of the economic public infrastructure (Zbirni kataster gospodarske javne infrastrukture). Traditionally, networks are modeled by graphs and optimizations are carried out by a wide range of network optimization algorithms addressing different types of routing problems. In this paper we focus on variants of Vehicle Routing Problem (VRP), which is a well-known computationally hard problem (NP-hard) in computer science. The problem consists of a set of goods that have to be delivered through the network to appropriate customers with minimal cost (cost is typically measured as total distance). The delivery can be made with multiple vehicles. In the classical VRP, the only constraint of the problem is the limited capacity of the vehicles. As even the classical version of VRP is known to be NP-hard, there are no practical algorithms for exact solutions; however, a number of algorithms produce good approximate solutions in reasonable time. In the process of the logistic system optimization in a large Slovene company with single central storage facility and delivery to locations all over Slovenia, we noticed the possibility of significant savings by optimization of routing of transport vehicles. However, compared to stock VRP there were many specifics. First, the fleet of vehicles is not homogenous (different types, capacities of trucks and vans with different transport costs). Second, due to practical limitations, the length of a daily route is limited to 8 hours per day, thus for far-away regions (Prekmurje) the route has to be broken into two days. Third, the company currently uses manual routing and has in place a system of regions, which are parts of Slovenia to which every route is limited (e.g. Dolenjska, Gorenjska, etc.). In our model we relax the regions thus increasing the space for potential optimizations. Another constraint that occasionally arises is that some customers require delivery at a certain hour of day. The last extension has been studied in theory and is known as VRP with time windows (VRPTW). In the paper we present a successful practical prototype implementation of an extended VRP model on the road network in Slovenia. We expect that as the system is further tested in practice, yet unforeseen constraints will emerge. Therefore the algorithm and its implementation must be structured in such a way that makes it easy to add new constraints. Algorithms based on the transformation of the problem to a different known problem would impose the complication of transforming the additional constraints. For these reasons we experimented with a number of local optimization algorithms, using the penalty method to incorporate constraints.