  This paper extends the Arc Orienteering Problem (AOP) to large road networks
with time-dependent travel times and time-dependent value gain, termed Twofold
Time-Dependent AOP or 2TD-AOP for short. In its original definition, the
NP-hard Orienteering Problem (OP) asks to find a path from a source to a
destination maximizing the accumulated value while not exceeding a cost budget.
Variations of the OP and AOP have many practical applications such as mobile
crowdsourcing tasks (e.g., repairing and maintenance or dispatching field
workers), diverse logistics problems (e.g., crowd control or controlling
wildfires) as well as several tourist guidance problems (e.g., generating trip
recommendations or navigating through theme parks). In the proposed 2TD-AOP,
travel times and value functions are assumed to be time-dependent. The dynamic
values model, for instance, varying rewards in crowdsourcing tasks or varying
urgency levels in damage control tasks. We discuss this novel problem, prove
the benefit of time-dependence empirically and present an efficient
approximative solution, optimized for fast response systems. Our approach is
the first time-dependent variant of the AOP to be evaluated on a large scale,
fine-grained, real-world road network. We show that optimal solutions are
infeasible and solutions to the static problem are often invalid. We propose an
approximate dynamic programming solution which produces valid paths and is
orders of magnitude faster than any optimal solution.
