Multi-Item EPQ Model with Scrap, Rework and Multi-Delivery using Common Cycle Policy

This paper is concerned with determining the optimal common production cycle policy for a multi-item economicproduction quantity (EPQ) model with scrap, rework and multiple deliveries. The classic EPQ model considers theoptimal replenishment quantity of single product under a perfect production assumption and a continuous inventoryissuing policy. However, in real life production planning, manufacturing firms often plan to have multiple productsmade in turn on a single machine in order to maximize the machine utilization. Also, dealing with random defectiveitems during the production run seems to be an inevitable task, and the multi-delivery policy is commonly adopted fordistributing finished items to customers. In this study, we assume a portion of nonconforming items is scrap and theother portion of them can be reworked and repaired in the same production cycle with additional cost. The objective isto determine an optimal common production cycle time that minimizes the long-run average cost per unit time for sucha specific multi-item EPQ model with scrap, rework and multi-delivery policy. Mathematical modeling and analysis isused and a closed-form optimal common cycle time for multi-item production planning is obtained. A numericalexample is provided to demonstrate the practical usage of research result.

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