Transnational corporations, which operate in competitive global marketplaces, have to build the best possible intra-supply chain model for meeting, on time, clients' need for multiple products with the requisite quality. Since fabrication capacity is always limited, the introduction of the external provider option can assist in leveling utilization, smoothing manufacturing schedules, eliminating overtime usage, and shortening the length of the fabrication cycle. Seeking to support intra-supply chain planning, this research aims to provide a concurrent decision on rotation cycle length and delivery frequency for a multi-item vendor-buyer incorporated type of intra-supply chain system with an external provider and rework. First, a model is built to represent this hybrid inventory replenishing problem. Then, renewal reward theory, mathematical derivation, and Hessian matrix equations are utilized to arrive at the expected total cost of the model, as well as the best policies for both cycle time and distribution. Last, the applicability and sensitivity analyses of our results are exhibited by a numerical demonstration. The insights obtained from this study about critical system-related information, such as the individual and joint impacts of the variation in outsourcing and reworking-related features on the system's optimal operating policy and various performance parameters, will offer crucial help to the managerial functions of planning and decision making in firms using this realistic multi-item hybrid intra-supply chain system.

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Facing global market's rigid competition, today's manufacturers need not only to satisfy the timely demands of multiproduct, but also to ensure quality of their goods. For the purpose of reducing fabrication cycle time so as to meet timely demands, outsourcing is always a helpful option in production planning. To address the aforementioned real issues, the present study derives the optimal common manufacturing cycle length for a multi-product inventory system, wherein a part of lot-size of each end product is supplied by an outside contractor, and in each cycle a rework process repairs random defects produced by the in-house process. The schedule of receipt time for outsourced items is practically assumed to be in the end of rework. A specific decision model is built to cautiously portray such a hybrid inventory problem. Through modeling, analysis, and derivation the expected annual system cost is obtained, and using optimization technique the optimal cycle length that minimizes system cost is gained. The proposed decision model not only can help find optimal solution to the problem, but also enables manufacturers to obtain diverse essential information, such as the critical outsourcing rate, individual manufacturing related cost for each end product, and influence or joint effects of variations in different system factor(s) on the problem. Without our in-depth exploration, the aforementioned information will still be unavailable to support managerial decision makings. KEY WORDS:common manufacturing cycle length; multi-product inventory system; outsource; rework.