Supply chain optimization is a key component for any business providing supply chain services. In today's competitive environment, it is essential to maintain operations at their peak efficiency. We study various discrete optimization problems related to supply chain optimization. First, we study the so called warehouse problem arising in production planning and inventory management. We provide some of the first known polynomial time algorithms in certain settings conjectured to be NP-Hard. The warehouse problem has also received increased attention in recent years due to its relevance in studying energy markets. Next, we look at the network design aspect of supply chain optimization and study various classical and recent discrete optimization problems arising here. The goal of network design is to construct cheap networks that satisfy certain connectivity requirements. These problems are often NP-Hard and we devise approximation algorithms for them. The problems studied include F-augmentation, capacitated network design, and the flexible graph connectivity.