Joint Determination of the Production Lot Size and Number of Shipments for EPQ Model with Rework

Abstract

This paper is concerned with joint determination of the optimal lot size and optimal number of shipments for an economic production quantity (EPQ) model with the reworking of random defective items produced. The classic EPQ model assumes a continuous issuing policy for satisfying product demand and perfect quality production for all items produced. However, in a real life vendor-buyer integrated-productioninventory system, a multi-delivery policy is used practically in lieu of the continuous issuing policy, and it is inevitable to generate defective items during a production run. In this study, all nonconforming items produced are considered to be repairable and are reworked in each cycle after the end of a production run. The fixed-quantity multiple installments of the finished batch can only be delivered to customers if the whole lot is quality assured at the end of the rework. Mathematical modeling is used and the longrun average integrated cost per unit time is derived. Convexity of the cost function is proved by the use of the Hessian matrix equations. A closed-form optimal productionshipment policy to the problem is obtained. A special case to the model is discussed. Finally, a numerical example is provided to demonstrate the model's practical usage.

Easy and Improved Algorithms to Joint Determination of the Replenishment Lot Size and Number of Shipments for an EPQ Model with Rework

“…Recently, Mathematical and Computational Applications Journal have published some extensions of EOQ and EPQ inventory models i.e. [1][2][5][6][7][8][9][10][11][12]. Also other journals do the same, i.e.…”

“…However, the number of shipments must be considered as discrete variable. In this direction, this paper revisits and solves the inventory problem of [1][2] considering the decision variables according to their nature. Two easy and improved algorithms are proposed which simplify and complement the research works of [1][2].…”

“…We read [1][2] with a considerable interest. We found that in both papers the authors considered the number of shipments (n) as continuous variable and then they round off it in order to obtain the discrete value.…”

“…The research works of Chiu et al [1] and Chen and Chiu [2] deal with the same type of inventory problem which is the joint determination of the replenishment lot size and the number of shipments for a vendor-buyer integrated production-inventory system based on an EPQ model with rework. We read [1][2] with a considerable interest.…”

“…This action could carry us to a non-optimal solution. In this direction, our paper revisits and solves the inventory model of [1][2] considering the decision variables according their nature. Two cases are considered: Case 1) the replenishment lot size (Q) continuous and the number of shipments (n) discrete, and Case 2) the replenishment lot size (Q) discrete and the number of shipments (n) discrete.…”