Study of Behavior of Optimal Replacement Model for a Block of Air Conditioners Using Markov Chains Considering the Influence of Inflation

Y. Hariprasada Reddy and C. Nadhamuni Reddy

Mathematical and stochastic models are usually tailored to fit into specific real life problems. A known fact is that it is difficult to conceive a model that reflects the reality as close as possible and simple for analysis at the same time. Consequently, different models each representing one or more parameters associated with real life situations are developed. This paper focuses on development of discrete-time stochastic model (using Markov chain) with finite state space that helps in evaluating optimal replacement decisions for a block of items (Air conditioners) with intermediate repairable states viz. minor repair, semi-major repair, and major repair between functional and complete failure states that are more realistic in practice. Further to make the model more realistic, the effect of inflation and time value of money on ‘replacement decision’ is considered. Real interest rates are computed using Fisherman’s relation that takes into account the inflation. First order Markov process, a stochastic process, is employed to compute the probabilities of transition from a given state to any other state for future time periods. Also, an attempt is made to develop block replacement model using higher (second) order Markov chains. To understand the behavior of the block replacement model, the influence of variable maintenance cost (High initial maintenance cost and lower increments during later periods, and Low initial maintenance cost and higher increments during later periods), and different trends in inflation (Rapid uptrend, Gradual uptrend, Rapid down trend, Gradual down trend, Sluggish uptrend and sluggish downtrend) are considered and the model is evaluated.

Volume 11 | 04-Special Issue

Pages: 1860-1871