How to build cycle graphical model with inference

Hi Everyone
First, thank you very much for taking the time to help. Your help and time will surely be appreciated.
I have a question about of probabilistic graphical models. Please check this pdf file https://drive.google.com/file/d/1LytPwN0EHKSn8jJvLWfpIKpBZ63Liwo7/view?usp=sharing . It explains the model that I need to build. It also presents the inputs the model should process as well as the output required.  
Can you kindly have a look at this file, and suggest me the best way to build such a model?    
Thank you again.

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Asked:

on 28 Apr 2018

Edited:

on 30 Apr 2018

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