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Most multinational/transnational manufacturers that own internal supply chains and operate in turbulent world markets apply strategies related to product quality, low-cost, and timely delivery. This study aims to assist such firms with making accurate decisions to enable their competitive strategies and cope with the realities of limited capacity and unreliable equipment. We examine a vendor-buyer coordinated system featuring batch fabrication, outsourcing, quality reassurance, discontinuous deliveries, and an unreliable machine. The system outsources a portion of a lot to reduce manufacturing uptime, and the in-house fabrication system experiences undesirable defective items and Poisson distributed breakdowns. In each cycle, corrective action and rework/disposal of defective stocks are undertaken as these incidents occur, and upon receipt of outsourced products and when the entire batch is quality ensured, it makes multiple deliveries of the end products. Using modeling, formulation, derivation, and an optimization methodology, we obtain the problem’s cost function and justify its convexity. We then apply differential calculus and propose a recursive algorithm to derive the problem’s optimal replenishment runtime. A numerical illustration is offered to show the applicability of the result that reveals various important system characteristics/ capabilities, such as the distinct and combined influences of breakdowns, outsourcing, rework, scrap, and delivery-frequency factors on various system parameters, performance, and optimal runtime. The methods proposed here can facilitate managerial operations planning and strategic decision making in an intra-supply chain setting in practice.

Optimal hybrid inventory replenishment runtime for a vendor- buyer coordinated system with breakdowns and rework/disposal of nonconforming items