Planning with actions concurrency under resources and time uncertainty has been recognized as a challenging and interesting problem. Most current approaches rely on a discrete model to represent resources and time, which contributes to the combinatorial explosion of the search space when dealing with both actions concurrency and resources and time uncertainty. A recent alternative approach uses continuous random variables to represent the uncertainty on time, thus avoiding the state-space explosion caused by the discretization of timestamps. We generalize this approach to consider uncertainty on both resources and time. Our planner is based on a forward chaining search in a state-space where the state representation is characterized by a set of object and numeric state variables. Object state variables are associated with random variables tracking the time at which the state variables' current value has been assigned. The search algorithm dynamically generates a Bayesian network that models the dependency between time and numeric random variables. The planning algorithm queries the Bayesian network to estimate the probability that the resources (numerical state variables) remain in a valid state, the probability of success and the expected cost of the generated plans. Experiments were performed on a transport domain in which we introduced uncertainty on the duration of actions and on the fuel consumption of trucks.
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