Economic order quantity model for growing items with imperfect quality

While the basic economic order quantity model has found some practical applications, it makes a number of assumptions which do not reflect most real life inventory systems. This paper proposes an inventory system where the items ordered are capable of growing during the course of the inventory replenishment cycle, for example livestock. Furthermore, it is assumed that a certain fraction of the items is of poorer quality than desired. It is also assumed that live newborn items are ordered and fed until they grow to a customer-preferred weight, after which they are slaughtered. Before all the slaughtered items are put on sale, they are screened so as to separate the good quality items from those of poorer quality. In order to determine the optimal inventory policy, a model, which aims to maximize the expected total profit, is developed and numerical examples are provided to illustrate the model and the solution procedure. The logistic growth function is compared to the linear and split linear growth functions. The margin of error between the results of the split linear function and the logistic growth function were found to be smaller than between the logistic and linear function. In addition, it was found that the optimal order quantity was most sensitive to the target slaughter weight.