Further comparisons of stochastic and deterministic models for the optimal control of Lanchester-type attrition processes.
Hannah, William Pickens.
Taylor, James G.
Howard, Gilbert T.
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The optimal fire distribution policy obtained using a stochastic combat attrition model is compared with that for a deterministic one. The same optimal control problem for a homogeneous force in combat against a heterogeneous force of two homogeneous types is considered using two different models for the attrition mechanism in a fight-to-the-finish the Lanchester-type differential equation formulation and its analagous stochastic version of a continuous parameter Markov chain with stationary transition probabilities. Considering dynamic programming methodology, a computer program was developed to numerically determine the optimal fire distribution policy (closed-loop or feedback) for the stochastic attrition process. Numerical values are generated for several parameter sets and compared with the optimal fire distribution policy for the corresponding deterministic attrition process. Results indicate that the optimal fire distribution policy for the stochastic model is more complex than the deterministic one.
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