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In this paper, we are interested in the synthesis of schedulers indouble-weighted Markov decision processes, which satisfy both a percentileconstraint over a weighted reachability condition, and a quantitativeconstraint on the expected value of a random variable defined using a weightedreachability condition. This problem is inspired by the modelization of anelectric-vehicle charging problem. We study the cartography of the problem,when one parameter varies, and show how a partial cartography can be obtainedvia two sequences of opimization problems. We discuss completeness andfeasability of the method.

Multi-weighted Markov Decision Processes with Reachability Objectives