Achieving sharp deliveries in supply chains through variance pool allocation

Abstract

In this paper, our objective is to come up with a sound methodology to design supply chains with outstanding delivery performance. As the first step towards this objective, we consider supply chains with a linear workflow, which we call pipelined supply chains. We define a new index of delivery performance called delivery sharpness which measures the precision as well as the accuracy with which products are delivered to the customers. The specific problem we solve is: given the delivery sharpness to be achieved, how can we allocate variability across individual stages of the supply chain in a cost-effective way. We call this the variance pool allocation (VPA) problem. In formulating and solving the VPA problem, we explore interesting relationships among process capability indices C_p, C_Pk, and C_Pm, and generalize the notion of Motorola six sigma performance. The VPA problem leads to a four step design methodology and the resulting optimization problem is solved using the method of Lagrange multipliers. We present an interesting example of a supply chain in the plastics industry and illustrate the different steps of our methodology.