Coordination of Supply Chains with Risk-Averse Agents

  • Xianghua Gan
  • Suresh P. Sethi
  • Houmin Yan
Part of the International Handbooks on Information Systems book series (INFOSYS)


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 (1) the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint, (2) the supplier and the retailer each maximizes his own mean-variance trade-off, and (3) the supplier and the retailer each maximizes his own expected utility. Moreover, in case (3) 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.


Capacity Coordination Nash bargaining Pareto-optimality Risk averse Supply chain management 


  1. Agrawal V, Seshadri S (2000a) Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem. Manuf Serv Oper Manage 4:410–423CrossRefGoogle Scholar
  2. Agrawal V, Seshadri S (2000b) Risk intermediation in supply chains. IIE Trans 32:819–831Google Scholar
  3. Arrow KJ (1951) Social choice and individual values. Wiley, New YorkGoogle Scholar
  4. Bouakiz M, Sobel MJ (1992) Inventory control with an expected utility criterion. Oper Res 40:603–608CrossRefGoogle Scholar
  5. Buzacott J, Yan H, Zhang H (2002) Optimality criteria and risk analysis in inventory models with demand forecast updating. Working paper, The Chinese University of Hong Kong, ShatinGoogle Scholar
  6. Cachon GP (2003) Supply coordination with contracts. In: Kok T, Graves S (eds) Handbooks in operations research and management science. North-Holland, AmsterdamGoogle Scholar
  7. Cachon GP, Lariviere M (2005) Supply chain coordination with revenue-sharing contracts: strengths and limitations. Manage Sci 51:30–44CrossRefGoogle Scholar
  8. Chen F, Federgruen A (2000) Mean-variance analysis of basic inventory models. Working paper, Columbia University, New YorkGoogle Scholar
  9. Chen X, Sim M, Simchi-Levi D, Sun P (2007) Risk aversion in inventory management. Oper Res 55:828–842CrossRefGoogle Scholar
  10. Chopra S, Meindl P (2001) Supply chain management. Prentice-Hall, New Jersey, NJGoogle Scholar
  11. Eeckhoudt L, Gollier C, Schlesinger H (1995) The risk averse (and prudent) newsboy. Manage Sci 41:786–794CrossRefGoogle Scholar
  12. Eliashberg J, Winkler RL (1981) Risk sharing and group decision making. Manage Sci 27:1221–1535CrossRefGoogle Scholar
  13. Gan X, Sethi SP, Yan H (2005) Coordination of a supply chain with a risk-averse retailer and a risk-neutral supplier. Prod Oper Manage 14:80–89CrossRefGoogle Scholar
  14. Gaur V, Seshadri S (2005) Hedging inventory risk through market instruments. Manuf Serv Oper Manage 7(2):103–120CrossRefGoogle Scholar
  15. Harsanyi JC (1955) Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J Polit Econ 63:309–321CrossRefGoogle Scholar
  16. Jorion P (2006) Value at risk. McGraw-Hill, New York, NYGoogle Scholar
  17. Lau HS (1980) The newsboy problem under alternative optimization objectives. J Oper Res Soc 31:393–403Google Scholar
  18. Lau HS, Lau AHL (1999) Manufacturer’s pricing strategy and return policy for a single-period commodity. Eur J Oper Res 116:291–304CrossRefGoogle Scholar
  19. Lavalle IH (1978) Fundamentals of decision analysis. Holt, Rinehart, and Winston, New YorkGoogle Scholar
  20. Levi H, Markowitz H (1979) Approximating expected utility by a function of mean and variance. Am Econ Rev 69:308–317Google Scholar
  21. Markowitz H (1959) Portfolio selection: efficient diversification of investment. Cowles foundation monograph 16, Yale University Press, New Haven, CTGoogle Scholar
  22. Nagarajan M, Bassok Y (2008) A bargaining framework in supply chains: the assembly problem. Manage Sci 54:1482–1496CrossRefGoogle Scholar
  23. Nash JF (1950) The bargaining problem. Econometrica 18:155–162CrossRefGoogle Scholar
  24. Pasternack BA (1985) Optimal pricing and returns policies for perishable commodities. Mark Sci 4:166–176CrossRefGoogle Scholar
  25. Pratt WJ (1964) Risk aversion in the small and in the large. Econometrica 32:122–136CrossRefGoogle Scholar
  26. Raiffa H (1970) Decision analysis. Addison-Wesley, Reading, MAGoogle Scholar
  27. Schweitzer ME, Cachon GP (2000) Decision bias in the newsvendor problem with a known demand distribution: experimental evidence. Manage Sci 46:404–420CrossRefGoogle Scholar
  28. Szegö G (ed) (2004) New risk measures for the 21st century. Wiley, West SussexGoogle Scholar
  29. Tayur S, Ganeshan R, Magazine M (eds) (1999) Quantitative models for supply chain management. Kluwer, Boston, MAGoogle Scholar
  30. Tsay A (2002) Risk sensitivity in distribution channel partnerships: implications for manufacturer return policies. J Retailing 78:147–160CrossRefGoogle Scholar
  31. Van Mieghem JA (2003) Capacity management, investment, and hedging: review and recent developments. Manuf Serv Oper Manage 5:269–302CrossRefGoogle Scholar
  32. Van Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton, NJGoogle Scholar
  33. Wilson R (1968) The theory of syndicates. Econometrica 18:155–162Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Logistics and Maritime StudiesThe Hong Kong Polytechnic UniversityKowloonHong Kong
  2. 2.School of Management, SM30The University of Texas at DallasRichardsonUSA
  3. 3.Department of Systems Engineering and Engineering ManagementThe Chinese University of Hong KongShatinHong Kong

Personalised recommendations