IJE Transactions A: Basics Vol. 23, Nos. 3 & 4, November 2010 - 215 MATHEMATICAL MODELING AND PERFORMANCE OPTIMIZATION FOR THE DIGESTING SYSTEM OF A PAPER PLANT R. Khanduja* Department of Mechanical Engineering, Yamuna Institute of Engineering and Technology, Village Gadholi, Yamuna Nagar -133103 Haryana, India rajiv_khanduja@rediffmail.com P.C. Tewari Department of Mechanical Engineering, National Institute of Technology, Kurukshetra-136119, Haryana, India D. Kumar Department of Mechanical & Industrial Engineering, Indian Institute of Technology, Roorkee, Uttranchal-247667, India * Corresponding Author (Received: December 6, 2009 – Accepted in Revised Form: July 15, 2010) Abstract This paper deals with the mathematical modeling and performance optimization for the Digesting system of a Paper Plant using Genetic Algorithm. The Digesting system of a Paper Plant has four main subsystems, arranged in series and parallel. Considering exponential distribution for the probable failures and repairs, the mathematical formulation of the problem is done using probabilistic approach and differential equations are developed based on Markov birth-death process. Then, these equations are solved using normalizing conditions to determine the steady state availability of the Digesting system. The performance of each subsystem of the Digesting system in a Paper Plant has also been optimized using Genetic Algorithm. Therefore, the findings of the present paper will be highly useful to the plant management for the timely execution of proper maintenance decisions and hence to enhance the system performance. Keywords: Performance Optimization, Digesting System, Genetic Algorithm ﭼﮑ ﻴ ﺪﻩ ﺍ ﻳ ﺳﺎﺯ ﻣﺪﻝ ﺑﺎ ﻣﻘﺎﻟﻪ ﻦ ﻱ ﺭ ﻳ ﺎﺿ ﻲ ﺑﻬ ﻭ ﻴ ﺳﺎﺯ ﻨﻪ ﻱ ﻋﻤﻠﮑﺮﺩ ﻱ ﺍﻟﮕﻮﺭ ﺍﺯ ﺍﺳﺘﻔﺎﺩﻩ ﺑﺎ ﻳ ﮊﻧﺘ ﺘﻢ ﻴ ﺑﺮﺍ ﮏ ﻱ ﺳ ﻴ ﺴﺘﻢ ﻫﻀﻢ ﻳ ﺩﺍﺭﺩ ﮐﺎﺭﺑﺮﺩ ﮐﺎﻏﺬ ﮐﺎﺭﺧﺎﻧﻪ ﮏ. ﺳ ﻴ ﻫﻀﻢ ﺴﺘﻢ ﻳ ﺩﺍﺭﺍ ﮐﺎﻏﺬ ﮐﺎﺭﺧﺎﻧﻪ ﮏ ﻱ ﺯ ﭼﻬﺎﺭ ﻳ ﺮﺳ ﻴ ﺍﺻﻠ ﺴﺘﻢ ﻲ ﺑﻪ ﮐﻪ ﺍﺳﺖ ﺳﺮ ﺻﻮﺭﺕ ﻱ ﻣﻮﺍﺯ ﻭ ﻱ ﺍﻧﺪ ﺷﺪﻩ ﻣﺮﺗﺐ. ﺗﻮﺯ ﻳ ﺗﻮﺍﻧ ﻊ ﻲ ﺑﺮﺍ ﺷﺪﻩ ﮔﺮﻓﺘﻪ ﺩﺭﻧﻈﺮ ﻱ ﻧﻘ ﺎ ﻳ ﺗﻌﻤ ﻭ ﺺ ﻴ ﺍﺣﺘﻤﺎﻟ ﺮﺍﺕ ﻲ، ﻓﺮﻣﻮﻻﺳ ﻴ ﺭ ﻮﻥ ﻳ ﺎﺿ ﻲ ﺩ ﻣﻌﺎﺩﻻﺕ ﺍﺯ ﺍﺳﺘﻔﺎﺩﻩ ﺑﺎ ﻣﺴﺌﻠﻪ ﻳ ﻔﺮﺍﻧﺴ ﻴ ﻠ ﻲ ﭘﺬ ﺍﺣﺘﻤﺎﻝ ﺭﻭﺵ ﻭ ﻳ ﺮ ﻱ ﭘﺎ ﺑﺮ ﻳ ﻓﺮﺍ ﻪ ﻳ ﺗﻮﻟﺪ ﻨﺪ- ﻣﺮﮒ ﻣﺎﺭﮐﻮﻭ(Markov) ﺗﻮﺳﻌﻪ ﻳ ﺍﺳﺖ ﺎﻓﺘﻪ. ﺍ ﺳﭙﺲ، ﻳ ﺷﺮﺍ ﺍﺯ ﺍﺳﺘﻔﺎﺩﻩ ﺑﺎ ﻣﻌﺎﺩﻻﺕ ﻦ ﻳ ﺳﺎﺯ ﻧﺮﻣﺎﻝ ﻂ ﻱ ﺑﺮﺍ ﻱ ﺗﻌ ﻴﻴ ﻦ ﻣﻮﺟﻮﺩ ﻳ ﺣﺎﻟﺖ ﺖ ﻳ ﺳ ﮑﻨﻮﺍﺧﺖ ﻴ ﺍﺳﺖ ﺷﺪﻩ ﺣﻞ ﻫﻀﻢ، ﺴﺘﻢ. ﻫﻤﭽﻨ ﻴ ﺯ ﻫﺮ ﻋﻤﻠﮑﺮﺩ ﻦ، ﻳ ﺮﺳ ﻴ ﺳ ﺍﺯ ﺴﺘﻢ ﻴ ﺩﺭ ﻫﻀﻢ ﺴﺘﻢ ﺍﻟﮕﻮﺭ ﺍﺯ ﺍﺳﺘﻔﺎﺩﻩ ﺑﺎ ﮐﺎﻏﺬ ﮐﺎﺭﺧﺎﻧﻪ ﻳ ﮊﻧﺘ ﺘﻢ ﻴ ﺑﻬ ﮏ ﻴ ﺍﺳﺖ ﺷﺪﻩ ﻨﻪ. ﺑﻨﺎﺑﺮﺍ ﻳ ﻦ، ﻳ ﻫﺎ ﺎﻓﺘﻪ ﻱ ﺑﺮﺍ ﺣﺎﺿﺮ ﻣﻘﺎﻟﻪ ﻱ ﻣﺪ ﻳ ﺮ ﻳ ﺖ ﺑﺮﺍ ﮐﺎﺭﺧﺎﻧﻪ ﻱ ﺗﺼﻤ ﺍﺟﺮﺍ ﻴ ﻤﻬﺎ ﻱ ﻧﮕﻬﺪﺍﺭ ﻣﻮﺭﺩ ﺩﺭ ﻱ ﺩﺭﻧﺘ ﻭ ﻣﻨﺎﺳﺐ ﻴ ﺍﻓﺰﺍ ﺠﻪ ﻳ ﺳ ﻋﻤﻠﮑﺮﺩ ﺶ ﻴ ﺑﺴ ﺴﺘﻢ ﻴ ﻣﻔ ﺎﺭ ﻴ ﺧﻮﺍﻫﺪ ﺪ ﺑﻮﺩ. 1. INTRODUCTION The paper industry comprises of large complex engineering systems arranged in series, parallel or a combination of both the configurations. Some of these systems are chipping, cooking, washing, bleaching, screening, stock preparation and paper pctewari1@rediffmail.com dinesfme@iitr.ernet.in