Simulation Modeling In Markovian Decision Theory: A Case Study of The Gardener’s Problem

Abstract

This paper aims at studying simulation modeling in Markovian Decision theory considers its relationship to linear programming and adapts exhaustive enumeration method, policy iteration methods of certain stochastic systems of the finite and infinite stage models for solution of the gardener’s problems. The objective of the problem is to determine the optimal policy or strategy or action that maximizes the expected return (revenue) within the available limited fund over the planning period. Consequently, most of the problems are decision problems for the decision maker (the gardener) such as: (as” apply fertilizer or do not apply fertilizer” (b)”whether the gardening activity will continue for a limited number of years or indefinitely”. In the basic concept of Markovian Decision theory, the number of transitional probabilities and computational efforts required to solve a Markov chain grows exponentially with the number of states. The linear programming formulation in this paper is interesting, but it not as efficient computationally as the exhaustive enumeration method or the policy iteration algorithm methods of markovian decision problems, particularly for large values of stationary policies. In conclusion ,alternatively contingency and reliability tests were performed as a check which show no significant difference between the experimental and theoretical expected results and led to the acceptance of null hypothesis.