The structure (monotonicity, convexity, multimodularity, directional convexity and K‐convexity) of optimal policies is used to reduce the exponential growth with respect to the size of a sequential decision process and to compare different control systems.
Monotonicity can be derived using Tattice programming techniques, sample path analysis or discrete events dynamic programming.
We cover the discrete and continuous‐time MDP and POMDP models with Borel, countable‐and finite‐state and action spaces, as well nonstationary ones.
Applications include admission/control of (networks of) queues, maintenance, inventory, production and innovation.
Recent research suggests that new product specifications evolve during its realization. In this paper, we introduce a nonstationary Markovian model that supports the dynamic achievement of the new product definition without precedence constraints, taking into account both market and technological uncertainty. We use lattice programming techniques to prove the existence of a nondecreasing monotonic optimal policy. Thus, we enable a more efficient computation of optimal policies of the Markov decision process. We also prove that the monotonic optimal paths are robust to tile variation of key-parameters as the solving rate of the design activities and the safety margin for achieving the new product at the deadline.
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