Simulation Modeling in Prior-Posterior Decision Theory- A Case Study of Farmers’ Decision Problem

Abstract

This study aims at applying Prior-Posterior decision theory based  models to analyze and  solve the farmers’ decision problem who are faced with decision of determining among alternatives crops [Sorghum, Rice, Wheat & Corn] the best crop to invest on, that will give a highest yield and profit under the prevailing state of nature on each of a 100 acres land  located  in Obudu LGA in Cross River State for each of the Farm Settler. However, the study has the following objectives (i) laying bare the usefulness of the theory, (ii) measuring the magnitude of the difference between alternative actions (iii) presenting experimental results for considering decision making under uncertainties, and (iv) evaluating the optimal policy or strategy or action  that  maximizes the expected yield of cereal crop within the study area. The methodology involves experiments and data were compared to United State Department of Agriculture (USDA). The analysis and presentation of results were based on Simulation of Prior-Posterior decision models, Policy iterations, and Pearson Product Moment Correlation as interaction, validity, reliability tests respectively. Consequently, from the results of prior probabilities of the state of nature  and the likelihood of the alternatives courses of action, and applying Prior-Posterior Decision Models to the uncertain system, the following decision were generated: (a)Posterior Probabilities of the States of Nature (b) Marginal Probability of the Course of Action, (c) Maximum Expected Monetary Value[EMV*] (d) Expected Profit in a Perfect Information[EPPI], (e) Expected Value of Perfect Information[EVPI], and (f) Expected Value of System Information[ EVSI]. The results gave a clear indication  that Rice has the [EMV*] value of $17,178.21 at 40^th model iteration, making it the most suitable crop for each of  the Farmer Settlers to invest on, for maximum yield. EMV* of rice was also observed to be optimized from the 1^st and 40^th model iteration at the value of $14,175.66 and $17,178.21 respectively. The results of the analyses attest to the fact that rice production in Obudu study area is currently the most yielding crop. The performance of Prior-Posterior decision  models on the farmers’ decision was evaluated which gave Pearson  Product  Moment Coefficient(r) of  = 1.0.  This shows applicability of Prior-Posterior Decision Model Excel Algorithms in River Basin Multi-projects/objectives Planning and Management.

Keywords: Prior-Posterior, Modeling, Farm- Settlers -Decision, investment, Optimization.

DOI: 10.7176/CER/11-2-07

Publication date:March 31^st 2019