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The standard DP (Dynamic Programming) algorithms are limited by the substantial computational demands they put on contemporary serial computers. In this work, the theory behind the solution to serial monadic dynamic programming problems highlights the theory and application of parallel dynamic programming on a general-purpose architecture (Cluster or Network Of Workstations). A simple and well-known technique, message passing, is considered. Several parallel serial monadic DP algorithms are proposed, based on the parallelization in the state variables and the parallelization in the decision variables. Algorithms with no interpolation are also proposed. It is demonstrated how constraints introduce load unbalance which affect scalability and how this problem is inherent to DP. [ABSTRACT FROM AUTHOR]