Evaluating the Expected Total Cost for Imperfect Production Processes Using a Markovian Approach

Abstract

The expected total cost function is developed by using a Markovian approach. The imperfect production and inventory control model is considered and integrated with an irreducible discrete time Markov Chain. Two Markov Chain models are developed with/without time factor. The former model with time factor has higher accuracy in the expected total cost. The optimal total cost and detailed production plan for each state are accomplished. Two applications for the developed Markov Chain models are established. The scheduling hard time windows between two production processes. Moreover, optimal maintenance actions for the preventive maintenance, inspection, and minimal repair are attained. Finally, sensitivity analysis is performed in two categories. The first category is the by varying of the production and demand rates and the second category is by varying the production and inventory control model’s parameters. Their effects are realized on the developed Markov Chain model.