Multiscale and Dirichlet Methods for Supply Chain Order Simulation

Supply chains are complex systems. Researchers in the Social and Decision Analytics Laboratory (SDAL) at Virginia Tech worked with a major global supply chain company to simulate an end-to-end supply chain. The supply chain data includes raw materials, production lines, inventory, customer orders, and shipments. Including contributions of this author, Pires, Sabin, Higdon et al. (2017) developed simulations for the production, customer orders, and shipments. Customer orders are at the center of understanding behavior in a supply chain. This dissertation continues the supply chain simulation work by improving the order simulation. Orders come from a diverse set of customers with different habits. These habits can differ when it comes to which products they order, how often they order, how spaced out those orders times are, and how much of each of those products are ordered. This dissertation is unique in that it relies extensively on Dirichlet and multiscale methods to tackle supply-chain order simulation. Multiscale model methodology is furthered to include Dirichlet models which are used to simulate order times for each customer and the collective system on different scales.