Coordination of a Supply Chain with Risk-Averse Agents

Abstract:  The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk-averse agents.  We take up this issue and begin with defining a coordinating contract as one that results in a Pareto-optimal solution acceptable to each agent.  Our definition generalizes the standard one in the risk-neutral case.  We then develop coordinating contracts in three specific cases:  (i) the supplier is risk neutral and the retailer maximizes his expected profit subject a a downside risk constraint, (ii) the supplier and the retailer each maximizes his own mean-variance trade-off, and (iii) the supplier and the retailer each maximize his own expected utility.  Moreover, in case (iii) we show that our contract yields the Nash Bargaining solution.  In each case, we show how we can find the set of Pareto-optimal solutions, and then design a contract to achieve the solutions.  We also exhibit a case in which we obtain Pareto-optimal sharing rules explicitly, and outline a procedure to obtain Pareto-optimal solutions.