  In this paper, we are interested in the synthesis of schedulers in
double-weighted Markov decision processes, which satisfy both a percentile
constraint over a weighted reachability condition, and a quantitative
constraint on the expected value of a random variable defined using a weighted
reachability condition. This problem is inspired by the modelization of an
electric-vehicle charging problem. We study the cartography of the problem,
when one parameter varies, and show how a partial cartography can be obtained
via two sequences of opimization problems. We discuss completeness and
feasability of the method.
