EPQ models with bivariate random imperfect proportions and learningdependent production and demand rates

In this paper,three production inventory models are constructed for an imperfect manufacturing system by considering a warm-up production run,shortages during the hybrid maintenance period,and the rework of imperfect items.The proportions of imperfect items produced during the warm-up and regular production runs are random and they are represented using a bivariate random variable.The shortage quantity is partially backordered and the supply of backorder quantity is planned simultaneously with regular demand satisfaction.The learning models are designed to accommodate the different learning capabilities of workers in unit production time during warm-up and regular production periods.The production and demand rates of these models are made dependent on the learning exponents.As the resulting models are highly nonlinear in the decision variable,they are optimized using a genetic algorithm.The models are illustrated using numerical examples and sensitivity studies are performed to find the influence of the key parameters.