Book excerpt: (cont.) In the second part of the thesis, we focus on the design and analysis of simple, possibly non-coordinating contracts in a single-supplier, multi-retailer supply chain where retailers make both pricing and inventory decisions. Specifically, we introduce a buy-back menu contract to improve supply chain efficiency, and compare two systems, one in which the retailers compete against each other, and another in which the retailers coordinate their decisions to maximize total expected retailer profit. In a linear additive demand setting, we show that for either retailer configuration, the proposed buy-back menu guarantees the supplier, and hence the supply chain, at least 50% of the optimal global supply chain profit. In particular, in a coordinated retailers system, the contract guarantees the supply chain at least 75% of the optimal global supply chain profit. We also analyze the impact of retail price caps on supply chain performance in this setting.