The Food Truck: A Multi-product Newsvendor with Trans-shipment Cost

The Newsvendor Problem is a key model in supply chain management that focuses on determining the optimal order quantity to minimize costs under uncertain demand. This thesis introduces the Food Truck Problem, an extension of the Newsvendor model that incorporates nonlinear transshipment costs for inventory transportation. In this context, a Food Truck must determine the optimal stock levels for multiple products while minimizing costs related to stock shortages, excess inventory, and transportation. Unlike traditional Newsvendor models, our approach explicitly considers a quadratic transshipment cost, which necessitates the use of Lagrangian duality and Karush-Kuhn-Tucker (KKT) conditions for analysis. Moreover, we apply Stochastic Gradient Descent (SGD), a technique from machine learning, to optimize the model and derive its closed-form optimal solution. By developing and solving the Food Truck Problem, this research advances supply chain optimization, providing valuable insights for mobile and decentralized inventory systems.