A multi-product FPR model with rework and an improved delivery policy

A multi-item finite production rate (FPR) model with rework and an improved delivery policy is examined in this paper. Unlike the classic FPR model whose purpose is to derive the most economic lot size for a single-product production system with perfect quality and a continuous issuing policy, this paper considers a production of multiple products on a single machine, rework of all nonconforming items produced, and a cost-reduction, multi-delivery policy. We extend the work of Chiu et al. [1] by incorporating an improved n+1 shipment policy into their model. According to such a policy, one extra delivery of finished items is made during vendor’s production uptime to satisfy product demands during the period of vendor’s uptime and rework time. When the rest of the production lot is quality assured and the rework has been finished as well, n fixed-quantity installments of finished items are delivered to customers. The objectives are to determine an optimal, common-production cycle time that minimizes the long-run average system cost per time unit, study the effects of rework and the improved delivery policy on the optimal production. Mathematical modelling and analysis is used to derive a closed-form, optimal, common-cycle time. Finally, practical usages of the obtained results are demonstrated by a numerical example