Reexamining a Specific Vendor-buyer System with Rework and an Improving Delivery Plan Using an Alternative Approach

This paper uses an alternative approach to reexamine a prior study on joint determination of manufacturing lot-size and shipment policy in a vendor-buyer system with rework process and an improving delivery plan. The proposed method is a straightforward approach in terms of algebraic derivations. It is different from the conventional method that needs to apply the first-order and second-order differentiations to the system cost function for proof of convexity before derivation of the optimal production-shipment policy. The research result obtained in this paper is confirmed to be identical to what was derived by the use of the conventional method. The proposed algebraic approach may assist practitioners who may not have sufficient knowledge of differential calculus in understanding the solution procedures of such a real world integrated production-shipment problem in supply chain environments. Key-Words: Manufacturing lot-size, Multiple deliveries, Algebraic approach, Production-shipment policy, Optimization, Production planning