Mathematical modeling for determining the replenishment policy for EMQ model with rework and multiple shipments

An improved solution to the replenishment policy for the EMQ model with rework and multiple shipments

“…This paper determines both the optimal replenishment lot size and the optimal number of shipments jointly. The solution of this paper is better than the solutions of Chiu et al [1,2].…”

“…Since then, many practical extensions to the EOQ and EPQ inventory models have been developed by academicians and researchers. Recently, Chiu et al [2] develop an inventory model based on EMQ considering rework and multiple shipments. They optimize only the replenishment lot size via differential calculus.…”

“…They optimize only the replenishment lot size via differential calculus. Chiu et al [1] revisit the Chiu et al [2]'s inventory model and also only optimize the replenishment lot size via algebraic method. Recently, the algebraic method is used amply by many researchers (i.e.…”

“…We read the papers [1,2] with a considerable interest and we found that both papers do not consider the determining of the number of shipments, they only obtain the replenishment lot size. It is important to point out that there is a more benefit for both parties (vendor-buyer) if the replenishment lot size and the number of shipments are obtained jointly.…”

“…The following notation is used throughout this paper and these are from [1,2]. Parameters C production cost ($/unit) C R rework cost ($/unit) C S disposal cost per scrap product ($/unit) C T delivery cost per product shipped to customers ($/unit) K setup cost per cycle ($/cycle; $/lot;$/run) …”