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.