Flexible system design has received increasingly more attention in the last a few decades. Flexibility can increase systems' ability to adjust against fast-changing environment, and thereby improves efficiency and reliability, and avoids huge cost from rare but severe disruptions, or loss due to congestions caused by system uncertainties. In this dissertation, we focus on the design and management of flexible systems. In particular, we study three types of flexibility: process flexibility, network flexibility, and payment flexibility. We present quantitative formulations for these problems, and develop different methodologies to solve them. We further conduct numerical studies to generate insights as guidelines for the design of flexible systems in practice. \
Flexible supply chains have been widely used by companies to deal with uncertainties. It is well known that chaining structure is very efficient in balanced supply chains. However, it is not clear whether it will work well when supply chains are unbalanced. We study the flexibility design problem of a general supply chain with unbalanced and nonhomogeneous structure. Both demand uncertainty and disruptions are considered in our model. We derive exact solutions for several special cases of the uncapacitated problem where the number of links is fixed, propose an efficient algorithm for solving the general uncapacitated problem, and use simulations to derive some managerial insights for the capacitated problem.\
A similar idea is applied to network design. Air transportation networks suffer a lot from disruptions caused by severe weather, natural disasters, power outage, etc. We propose a flexible hub-and-spoke structure in which airports are allowed to have up to $N$ hubs, and formulate the problem as a mixed-integer program that minimizes fixed cost, flexibility cost, and expected transportation cost and penalty cost. Benders decomposition algorithm is applied to solve this problem. Numerical studies show that the performance of the network can be improved substantially with flexible hub assignment, and a flexible structure with $N=2$ can achieve most of the benefit of those with greater $N$. We also demonstrate the impact of the correlation between airport disruptions and address the importance of considering it in stochastic air transportation models.\
Trade credit, as a form of flexible payment, is a major tool used by small businesses to obtain external finance. It benefits the buyer and the supplier in multiple ways, and brings risk to them at the same time. We investigate the impact of trade credit on growing small businesses and their suppliers. By looking at a one-supplier-one-retailer supply chain, we study the expansion and inventory policies of the retailer when trade credit is extended or not. It is shown that the retailer grows faster and orders more with trade credit. It is also shown by numerical study that the effect of trade credit depends on demand correlation. When demand is positively correlated, trade credit makes the retailer more likely to go bankrupt, and thereby lowers the supplier's long-term profit and may even cause the failure of the supplier.