A production-inventory model with imperfect production process and partial backlogging under learning considerations in fuzzy random environments

In this paper, we investigates the learning effect of the unit production time on optimal lot size for the imperfect production process with partial backlogging of shortage quantity in fuzzy random environments. It is assumed that the setup cost, the average holding cost, the backorder cost, the raw material cost and the labour cost are characterized as fuzzy variables and the elapsed time until the machine shifts from "in-control" state to "out-of-control" state is characterized as a fuzzy random variable. As a function of these parameters, the average total cost is also a random fuzzy variable. Based on the credibility measure of fuzzy event, the fuzzy random total cost function is transformed into an equivalent crisp function. We propose an algorithm to determine the optimal solution. Furthermore, the model is illustrated with the help of numerical example. Finally, sensitivity analysis of the optimal solution with respect to major parameters is carried out.