  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 problem as 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.
