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.
Highlights
In the production and inventory management field, “when should a replenishment lot be initiated?” and “how many to be produced in a lot?” are two fundamental questions that must be answered by production-inventory practitioners for the products they routinely manufacture [1,2] in order to minimize the long-run average costs per unit time
For the reason that little attention was paid to investigate the joint effect of a multi-shipment policy and a rework process on the optimal replenishment lot size and optimal number of shipments of economic production quantity (EPQ) model, this paper intends to bridge the gap
Unlike the classic EPQ model assuming a continuous issuing policy for satisfying demand λ, this paper considers a multi-delivery policy
Summary
In the production and inventory management field, “when should a replenishment lot be initiated?” and “how many to be produced in a lot?” are two fundamental questions that must be answered by production-inventory practitioners for the products they routinely manufacture [1,2] in order to minimize the long-run average costs per unit time. Sarker and Parija [6] considered a manufacturing system which procures raw materials from suppliers and processes them to convert to finished products They proposed a model that was used to determine an optimal ordering policy for procurement of raw materials, and the manufacturing batch size to minimize the total cost for meeting equal shipments of the finished products, at fixed intervals, to the buyers. A general cost model was formulated considering both raw materials and finished products Using this model, a simple procedure was developed to determine optimal ordering policy for procurement of raw materials as well as manufacturing batch size, to minimize the total cost of meeting customer demands in time. For the reason that little attention was paid to investigate the joint effect of a multi-shipment policy and a rework process on the optimal replenishment lot size and optimal number of shipments of EPQ model, this paper intends to bridge the gap
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