Generic Models and Algorithms for Vehicle Routing and Scheduling

We present a framework for modeling and heuristic solving of large-scale real-world vehicle routing and scheduling problems (VRPSs). Real-world problems have in common that their size is usually large or very large (including thousands of requests) and that they include a number of side constraints that are not present in the abstract standard models that are usually considered in the Operations Research literature. Examples of such constraints include sorting capacities at locations, complex driver regulations, prescribed loading and unloading sequences etc. The purpose of our framework is to enable the design of a class of template heuristics that will be applicable to solving a large class of VRPSs without knowing all relevant constraints in advance. This approach is similar to the use of templates in object-oriented programming and has also been suggested, although with a different focus, in the Operations Research community. We know of two streams of research that have employed similar ideas. Firstly, researchers working on the solution of vehicle routing and crew scheduling problems by column generation [1] have suggested the use of resources that are propagated by shortest path algorithms in order to create partial solutions to the problems. Secondly, the use of constraint programming within vehicle routing, e.g. [2], also follows the idea that the main algorithms can be designed and implemented without knowing explicitly all relevant constraints in advance. The suggested framework has significant similarities with both these approaches, but also differs from them in several important aspects. It also uses the concept of resource variables and vectors as in [1], but allows for a more general update rule within routes and locations. Moreover, our focus is purely on heuristics, since the problem instances we consider cannot be solved to optimality with the algorithms available to us today. Using the concept of resource variables allows us to model the relevant constraints in a declarative way very similar to the constraint programming framework without the additional overhead