Determination of production-shipment policy using a two-phase algebraic approach

The optimal production-shipment policy for end products using mathematicalmodeling and a two-phase algebraic approach is investigated. A manufacturing systemwith a random defective rate, a rework process, and multiple deliveries is studied with thepurpose of deriving the optimal replenishment lot size and shipment policy that minimisestotal production-delivery costs. The conventional method uses differential calculus on thesystem cost function to determine the economic lot size and optimal number of shipmentsfor such an integrated vendor-buyer system, whereas the proposed two-phase algebraicapproach is a straightforward method that enables practitioners who may not havesufficient knowledge of calculus to manage real-world systems more effectively.