This dissertation studies a few models in two categories of operations management. The first part of the dissertation focuses on supply chain management related topics. We consider a supply chain model with one supplier and one retailer who acts as a newsvendor. The first model in this dissertation focuses on the supplier and the retailer's optimal policies in a multi-period newsvendor model. We derive the optimal pricing and ordering policies for demand with Increasing Generalized Failure Rate (IGFR) property and obtain comparative statics for the optimal prices. We discover that under certain conditions of the demand distribution, the supplier's optimal prices are increasing in time. Moreover, the price increments are increasing in the backorder cost and the optimal prices are increasing in the backorder cost as well. We also perform a distribution-free analysis of the multi-period newsvendor model and provide the structure of the worst-case distribution. In addition to the pricing and ordering decisions, we also analyze the risk-return trade-off in single-period newsvendor models using the mean-variance approach. We discuss the classic newsvendor model which uses the wholesale-price contract and two variations of the model, a spot market model and a revenue-sharing contract model. We derive the risk-return curve for the retailer and the corresponding distribution in closed-form for a two-point distribution and a three-point distribution in the classic model. When the demand follows a multi-point distribution or a continuous distribution, we provide a linear program to compute the risk-return curves and show the curves' upper bounds. An approximation algorithm is introduced to efficiently calculate the risk-return curve in the continuous distribution models. Introducing some variation to the basic model, we consider a supply chain setting with a spot market where unsatisfied demand can purchase from the supplier at the market price. The supplier's decisions are the wholesale price and the buffer inventory for the spot market. We derive the supplier's optimal decisions and study the supplier's risk-return trade-off under uniform and exponential distributions. Another problem that we consider is the risk-return analysis under a revenue-sharing model. We derive the supplier's optimal pricing policy and characterize the effect of φ on both the supplier and the retailer's decisions and risks. Numerical experiments are conducted to demonstrate the results. The second part of this thesis concerns resource allocation in an online setting, specifically, the online matching problems. Online matching problems are used as the backstage algorithm by search engines to match advertisements with each search. We focus on the online matching problem with concave return functions and a random permutation model. In this dissertation, we introduce two online learning algorithms to solve the associated matching problem. The main idea is to utilize the observed data in the allocation process and project it into the future. We begin with the one-time learning algorithm that only uses the data to compute an allocation rule once. This algorithm achieves near-optimal performance when input data satisfy certain conditions. To further improve the performance, we introduce a dynamic learning algorithm which updates the allocation rule at a geometric pace, at time εn, 2εn, 4εn and so on. This algorithm achieves near-optimal performance with fewer restrictions on the input data conditions. We compare the performance of the one-time learning algorithm, the dynamic learning algorithm, and the greedy algorithm in numerical experiments.