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1999) studied inter-firm coordination processes characterized by effective communication, information exchange, partnering, and performance monitoring. Lee (2000) proposes supply chain coordination as a vehicle to redesign decision rights, workflow, and resources between chain members to leverage better performance such as higher profit margins, improved customer service performance, and faster response time. A Review on Supply Chain Coordination 41 Though, there are efforts in literature regarding coordination of different functions of the supply chain, the study of coordinating functions in isolation may not help to coordinate the whole supply chain.

Some papers incorporate financial instruments into inventory management, for example, Gaur and Seshadri (2005), Martı´nez-de-Albe´niz and Simchi-Levi (2005), and Chen et al. (2008). Choi et al. (2009) study a multi-product newsvendor under lawinvariant coherent risk measures. In the following, we limit our review to papers that focus on supply chain coordination. Gan et al. (2005) examine coordinating contracts for a supply chain consisting of one risk-neutral supplier and one risk-averse retailer.

Coordination of Supply Chains with Risk-Averse Agents 21 5 Coordinating a Supply Chain Consisting of Agents with Concave Utility Functions In this case, we assume that agent i has an increasing concave utility function gi ðÁÞ of his profit, and wants to maximize his expected utility, i ¼ r; s. Then his payoff function is E½gi ðÁފ . To compute the set of Pareto-optimal actions, we first find the Pareto-optimal sharing rules given an external action s. t: Pr ðs; uðsÞÞ þ Ps ðs; uðsÞÞ ¼ PðsÞ; (35) u2Y where ar ; as >0, ar þ as ¼ 1.

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