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We propose a Fully Polynomial-Time Approximation Scheme (FPTAS) forstochastic dynamic programs with multidimensional action, scalar state, convexcosts and linear state transition function. The action spaces are polyhedraland described by parametric linear programs. This type of problems findsapplications in the area of optimal planning under uncertainty, and can bethought of as the problem of optimally managing a single non-discrete resourceover a finite time horizon. We show that under a value oracle model for thecost functions this result for one-dimensional state space is "best possible",because a similar dynamic programming model with two-dimensional state spacedoes not admit a PTAS.  The FPTAS relies on the solution of polynomial-sized linear programs torecursively compute an approximation of the value function at each stage. Ourpaper enlarges the class of dynamic programs that admit an FPTAS by showing,under suitable conditions, how to deal with multidimensional action spaces andwith vectors of continuous random variables with bounded support. These resultsbring us one step closer to overcoming the curse of dimensionality of dynamicprogramming.

Toward breaking the curse of dimensionality: an FPTAS for stochastic dynamic programs with multidimensional actions and scalar states