Solving a vendor-buyer integrated problem with rework and a specific multi-delivery policy by a two-phase algebraic approach

This paper is concerned with solving a vendor-buyer integrated inventory problem with rework and a specific multi-delivery policy by a two-phase algebraic approach. Conventional method to the problem is to use differential calculus and Hessian matrix equations to prove convexity of system cost function first before determining the optimal production-shipment policy for such a vendor-buyer integrated system (Chiu et al., 2013b). This study presents an alternative two-phase algebraic approach to derive the same optimal policy. The proposed straightforward algebraic derivations can assist practitioners who may not have sufficient knowledge of calculus in understanding with ease such a real life vendor-buyer integrated system.