Incorporating an expedited rate, rework, and a multi-shipment policy into a multi-item stock refilling system

Facing harsh competition in global marketplaces, management must construct the best possible supply chains to meet client requirements of quality, timely, and diverse products. To accelerate the fabrication rate can help shorten the length of the refilling cycle, and the reworking of repairable defectives can retain the requisite quality standard as well as reduce cost in production. Seeking to build an integrated fabrication-delivery model to help satisfy client timely multiproduct needs with quality goods and minimum cost, this study explores a multi-item stock refilling system incorporating an expedited rate, rework, and multiple shipments plan. An explicit mathematical model is developed to clearly represent various features of the problem. Analytical derivations are used to find the relevant cost function of the system. Applying the Hessian matrix equations to the cost function obtained from our model, the optimal length of the refilling cycle and frequency of delivery can be concurrently determined. This particular model and its analytical results reveal the individual and joint impact of various features on the problem, and can assist operational managers in determining a strategy regarding the expedited rate, controlling requisite product quality levels, and planning the most economic frequency of delivery.