Manufacturing and Shipment Policy Making for an Integrated System with Rework and a Cost Lessening Product Delivery Plan

This paper derives the optimal production-shipment policy for a vendor-buyer integrated system with rework process and a cost lessening product delivery plan. The objective is to derive the optimal production lot size and number of deliveries that minimizes total costs for the proposed vendor-buyer integrated system. This paper extends the work of Chiu et al. [Joint determination of the production lot size and number of shipments for EPQ model with rework. Mathematical and Computational Applications 16(2), 317-328] by incorporating an improving n+1 shipment policy into their model, with the purpose of reducing both vendor and buyer’s stock holding costs. Under such an enhancing policy, one extra upfront delivery of finished items is distributed to buyer for satisfying product demand during supplier’s production and rework times. Then fixed quantity n installments of finished items are delivered to customer at the end of rework. Mathematical modeling along with Hessian matrix equations is employed to derive and prove convexity of the long-run cost function. Closed-form solution in terms of lot size and number of deliveries is obtained. A numerical example is provided to show its practical usage and demonstrate the significant reduction in stock holding cost. Key-Words: Production lot size, Vendor-buyer system, Multi-deliveries, Rework, Optimization, Production, Inventory