This study employs mathematical modeling to explore the effects of overtime option, rework, and discontinuous end-item issuing policy on the economic manufacturing quantity (EMQ) model. Conventional EMQ model assumed that all products fabricated are of good quality and are issued under continuous policy. In real world, however, nonconforming items are randomly produced, due to diverse unexpected factors in fabrication process. When finished items are to be distributed to outside locations, discontinuous multi-shipment policy is often used rather than continuous rule. In addition, with the intention of increasing short-term capacity or shortening replenishment cycle length to smooth the production planning, adopting overtime option can be an effective strategy. To cope with the aforementioned features in real production systems, this study incorporates overtime option, rework, and multi-shipment policy into the EMQ model and explores their joint effects on optimal lot size and number of shipments, and on other relevant system parameters. Mathematical modeling and Hessian matrix equations enable us to derive the optimal policies to the problem. Through the use of numerical example, the applicability of research result is exhibited and a variety of significant effects of these features on the proposed system are revealed.

This study uses an alternative fabrication scheme to study the effect of rework of nonconforming items and delayed differentiation on a multiproduct supply-chain system. Traditional economic production quantity model focuses on a single-product inventory system where all products made are assumed to be perfect quality and finished products are issued continuously. To increase machine utilization, lower quality costs in production, and reflect the real-world vendor-buyer integrated systems Chiu et al. (2016a) [Chiu, Y-S.P., Kuo, J-S., Chiu, S. W., Hsieh, Y-T. (2016a). Effect of delayed differentiation on a multiproduct vendor–buyer integrated inventory system with rework. Advances in Production Engineering & Management, 11(4), 333-344.] employed a single-machine two-stage production scheme to study the effects of rework and delayed differentiation on a multi-product supply-chain system. With the intention of further reducing fabrication cycle time, this study considers an alternative two-machine two-stage fabrication scheme to re-explore the problem in Chiu et al. (2016a). Machine one solely produces all common parts for multiple end products. Then, machine two fabricates the customized multiproduct using a common cycle time strategy. Through the use of mathematical modeling and analyses, the optimal production cycle length and distribution policy are derived. Numerical examples are provided to demonstrate practical usage of the research results, and show its significant benefit in reducing fabrication cycle time compared to that obtained from prior studies that used different schemes.