Matching and sorting theory are widely applied to operations management. Our analysis focuses on the matching in supply chains and sorting between projects and heterogeneous firms. In chapter 1, we investigate the decentralized allocation in pharmaceutical research and development (R&D) projects. We construct a theoretical framework of R&D competition between heterogeneous firms for differentiated drugs. The decentralized allocation features a mismatch between firms and R&D projects. Efficient outcome prescribes that each firm works on a separate R&D project with the more valuable R&D project being allocated to the established firm. The impact of transparency on efficiency is contingent on the disclosure rules and may not improve the welfare. We also demonstrate the trade-off between the firm revenue and positive externality of the development of new drugs. Our research extends the R&D competition to a two-sided heterogeneous case and enriches the transparency analysis. In chapter two, we analyze a decentralized assortative matching model for bilateral supply chains. The risk-averse suppliers and retailers match mutually to form as supply chains, in which each supply chain optimally determines production plans and revenue sharing contracts. We show that in equilibrium, the less risk averse firm is not always matched with higher risk averse firm to share risk and revenue. We find that both positive assortative matching (PAM) and negative assortative matching (NAM) can occur in equilibrium. Equilibrium sorting pattern depends on the trade-off between the expected revenue and demand uncertainty. The main results extend the supply chain matching research by endogenizing both production choice and risk sharing contract
