Mobility offer allocations in corporate settings

Corporate mobility is often based on a fixed assignment of vehicles to employees. Relaxing this fixation and including alternatives such as public transportation or taxis for business and private trips could increase fleet utilization and foster the use of battery electric vehicles. We introduce the mobility offer allocation problemas the core concept of a flexible booking system for corporate mobility. The problem is equivalent to interval scheduling on dedicated unrelated parallel machines. We show that the problem is NP-hard to approximate within any factor. We describe problem specific conflict graphs for representing and exploring the structure of feasible solutions. A characterization of all maximum cliques in these conflict graphs reveals symmetries which allow to formulate stronger integer linear programming models. We also present an adaptive large neighborhood search based approach which makes use of conflict graphs as well. In a computational study, the approaches are evaluated. It was found that greedy heuristics perform best if very tight run-time requirements are given, a solver for the integer linear programming model performs best on small and medium instances, and the adaptive large neighborhood search performs best on large instances.