Replenishment Lot Size and Number of Shipments for EPQ Model Derived Without Derivatives

Abstract

This paper investigates optimal replenishment lot size and optimal number of shipments for economic production quantity (EPQ) model with rework process using an algebraic approach. The classic EPQ model assumes a perfect quality production for all items produced and a continuous issuing policy for satisfying customer"s demand. However, in a real life vendor-buyer integrated-production-inventory system, a multidelivery policy is commonly used in lieu of a continuous issuing policy and generation of defective items during a production run seems to be inevitable. A recent published work examined such an identical problem using mathematical modeling and differential calculus to derive the optimal replenishment lot size and optimal number of deliveries that minimizes overall production-inventory-shipment costs. This paper proposes a straightforward algebraic approach to replace the use of calculus on the cost function for determining optimal production-shipment policies. It also presents a simpler form for calculating the long-run average cost for such an imperfect EPQ problem.

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.…”

“…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.…”

“…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].…”