In traditional inventory models such as the economic order quantity (EOQ) and the economic production quantity (EPQ) the sole objective is to minimize the total inventory-related costs, typically holding cost and ordering cost. These models do not consider the presence of defective products in the lot or rework of them. Recently, Jamal, Sarker, and Mondal (Jamal, A. A. M., Sarker, B. R., & Mondal, S., (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77–89) proposed a model, which dealt with the optimum batch quantity in a single-stage system in which rework is done by addressing two different operational policies to minimize the total system cost, but their models do not consider planned backorders. In this direction, this paper develops an EPQ type inventory model with planned backorders for determining the economic production quantity for a single product, which is manufactured in a single-stage manufacturing system that generates imperfect quality products, and all these defective products are reworked in the same cycle. We also establish the range of real values of the proportion of defective products for which there is an optimal solution, and the close form for the total cost of inventory system. The use of the inventory model is illustrated with numerical examples. The classical EOQ, EPQ inventory models with or without planned backorders and Jamal, Sarker and Mondal’s model (Jamal, A. A. M., Sarker, B. R., & Mondal, S., (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77–89) are shown to be special cases of the EPQ inventory model presented in this paper.
Economic lot size models have been studied extensively since Harris (1913) presented the famous EOQ formulae in 1913. Then in 1918, the economic production quantity (EPQ) inventory model was proposed by Taft (1918). In traditional inventory models such as the economic order quantity (EOQ) and the economic production quantity (EPQ) the sole objective is to minimize the total inventory-related costs, typically holding cost and ordering cost. Those models do not consider the presence of defective products in the lot and rework of them. The EOQ and EPQ inventory models have been used in many practical applications because these inventory models are simple and easy to implement in organizations. In addition, these models have one important feature which is their robustness with respect to small changes in the parameters. But the EOQ and EPQ inventory models have several assumptions that are very restrictive; one of them is that the manufacturing process necessarily generates good quality products. In fact, there are many situations in practice where the manufacturing process produces defective products due to reasons such as imperfect raw materials, skill level of the workers, machine capability, maintenance policies, or when the manufacturing process goes out of control, among others. However, many researchers and practitioners have developed inventory models for modeling different real world situations, two of which are the cases of economic order quantity (EOQ) and economic production quantity (EPQ) with planned backorders.
In this paper, we developed an EPQ inventory model with planned backorders for determining the economic production quantity and the size of backorders for a single product, which is made in a single-stage manufacturing process that generates imperfect quality products and all defective products must be reworked at the same cycle. We also established the range of real values of proportion of defectives products for which there is an optimal solution, and the closed form for the total cost of the inventory system. The use of the inventory model was illustrated with numerical examples.
