A note on joint determination of the rotation cycle time and number of shipments for a multiitem EPQ model with a random defective rate

This study proposes a two-phase, algebraic approach to resolve the rotation cycle time and number of shipments for a multi-item, economic production quantity (EPQ) model with a random defective rate. A conventional method for solving a multi-item EPQ model is to use differential calculus and Hessian matrix equations on system cost function to prove convexity first and then derive an optimal production-shipment policy [1], whereas the proposed approach obtains the optimal operating policy in a simplified, two-phase algebraic way, using neither differential calculus nor Hessian matrix equations. The simplification enables managing practitioners to effectively determine real-life, vendor-buyer integrated multi-item EPQ systems