Solving the conflict-free electric vehicle routing problem using SMT solvers

Paper in proceeding, 2021

The vehicle routing problem is a combinatorial optimization problem of computing routes to serve customers while minimizing a cost function, typically the traveled distance or the number of vehicles required. Industrial applications of the problem in manufacturing plants are the scheduling and routing of Automated Guided Vehicles (AGVs) to deliver material between storage areas and assembly stations. For in-plant transportation it is necessary to take the limited space of the plant floor into account during scheduling and routing in order to limit the number of AGVs that are at certain areas at a given time. In addition, AGVs are most often powered by batteries and therefore have limited operating range and non-negligible charging time that will also affect the scheduling and routing decisions. In this paper we provide a monolithic model formulation for the scheduling and routing of AGVs with given time-windows for delivering material, restricted by capacity constraints on the path network, and with the need for battery recharge. The problem is modelled and solved using optimizing Satisfiability Modulo Theory (SMT) solvers. The approach is evaluated on a set of generated problem instances, showing that the solver can handle medium size instances in a reasonable amount of time.