Joint determination of lot-size and shipment policy for a vendor-buyer system with rework and an improving delivery plan

Abstract

This paper studies a vendor-buyer integrated system with rework and an improving delivery policy for lowering both vendor and buyer’s stock holding costs. 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 study extends the work of Chiu et al. (2011) 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 significant reduction in stock holding cost. Key words: Production lot size, vendor-buyer system, multi-deliveries, rework.