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Optimal contract design in the joint economic lot size problem with multi-dimensional asymmetric information

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  • Pishchulov, Grigory
  • Richter, Knut

Abstract

Previous work has studied the classical joint economic lot size model as an adverse selection problem with asymmetric cost information. Solving this problem is challenging due to the presence of countervailing incentives and two-dimensional information asymmetry, under which the classical single-crossing condition does not need to hold. In the present work we advance the existing knowledge about the problem on hand by conducting its optimality analysis, which leads to a better informed and an easier problem solution: First, we refine the existing closed-form solution, which simplifies problem solving and its analysis. Second, we prove that Karush–Kuhn–Tucker conditions are necessary for optimality, and demonstrate that the problem may, in general, possess non-optimal stationary points due to non-convexity. Third, we prove that certain types of stationary points are always dominated, which eases the analytical solution of the problem. Fourth, we derive a simple optimality condition stating that a weak Pareto efficiency of the buyer’s possible cost structures implies optimality of any stationary point. It simplifies the analytical solution approach and ensures a successful solution of the problem by means of conventional numerical techniques, e.g. with a general-purpose solver. We further establish properties of optimal solutions and indicate how these are related with the classical results on adverse selection.

Suggested Citation

  • Pishchulov, Grigory & Richter, Knut, 2016. "Optimal contract design in the joint economic lot size problem with multi-dimensional asymmetric information," European Journal of Operational Research, Elsevier, vol. 253(3), pages 711-733.
  • Handle: RePEc:eee:ejores:v:253:y:2016:i:3:p:711-733
    DOI: 10.1016/j.ejor.2016.02.053
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    1. Affisco, John F. & Javad Paknejad, M. & Nasri, Farrokh, 2002. "Quality improvement and setup reduction in the joint economic lot size model," European Journal of Operational Research, Elsevier, vol. 142(3), pages 497-508, November.
    2. Sucky, Eric, 2006. "A bargaining model with asymmetric information for a single supplier-single buyer problem," European Journal of Operational Research, Elsevier, vol. 171(2), pages 516-535, June.
    3. Liu, Xingchu & Cetinkaya, Sila, 2007. "A note on "quality improvement and setup reduction in the joint economic lot size model"," European Journal of Operational Research, Elsevier, vol. 182(1), pages 194-204, October.
    4. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    5. Figalli, Alessio & Kim, Young-Heon & McCann, Robert J., 2011. "When is multidimensional screening a convex program?," Journal of Economic Theory, Elsevier, vol. 146(2), pages 454-478, March.
    6. Kerschbamer, Rudolf & Maderner, Nina, 1998. "Are Two a Good Representative for Many?," Journal of Economic Theory, Elsevier, vol. 83(1), pages 90-104, November.
    7. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    8. Cecchini, Mark & Ecker, Joseph & Kupferschmid, Michael & Leitch, Robert, 2013. "Solving nonlinear principal-agent problems using bilevel programming," European Journal of Operational Research, Elsevier, vol. 230(2), pages 364-373.
    9. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    10. Glock, C. H. & Kim, T., 2012. "A joint economic lot sizemodel with returnable transport items," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 59079, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    11. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    12. Charles J. Corbett & Xavier de Groote, 2000. "A Supplier's Optimal Quantity Discount Policy Under Asymmetric Information," Management Science, INFORMS, vol. 46(3), pages 444-450, March.
    13. Pibernik, Richard & Zhang, Yingying & Kerschbaum, Florian & Schröpfer, Axel, 2011. "Secure collaborative supply chain planning and inverse optimization - The JELS model," European Journal of Operational Research, Elsevier, vol. 208(1), pages 75-85, January.
    14. Araujo, Aloisio & Moreira, Humberto, 2010. "Adverse selection problems without the Spence-Mirrlees condition," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1113-1141, May.
    15. van Ackere, Ann, 1993. "The principal/agent paradigm: Its relevance to various functional fields," European Journal of Operational Research, Elsevier, vol. 70(1), pages 83-103, October.
    16. Jullien, Bruno, 2000. "Participation Constraints in Adverse Selection Models," Journal of Economic Theory, Elsevier, vol. 93(1), pages 1-47, July.
    17. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    18. Schottmüller, Christoph, 2015. "Adverse selection without single crossing: Monotone solutions," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 127-164.
    19. Glock, C. H., 2012. "The joint economic lot size problem: a review," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 57811, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    20. Wang, Jian-Cai & Lau, Hon-Shiang & Lau, Amy Hing Ling, 2009. "When should a manufacturer share truthful manufacturing cost information with a dominant retailer?," European Journal of Operational Research, Elsevier, vol. 197(1), pages 266-286, August.
    21. Ben-Daya, M. & Darwish, M. & Ertogral, K., 2008. "The joint economic lot sizing problem: Review and extensions," European Journal of Operational Research, Elsevier, vol. 185(2), pages 726-742, March.
    22. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
    23. Gérard P. Cachon & Fuqiang Zhang, 2006. "Procuring Fast Delivery: Sole Sourcing with Information Asymmetry," Management Science, INFORMS, vol. 52(6), pages 881-896, June.
    24. Glock, Christoph H., 2012. "The joint economic lot size problem: A review," International Journal of Production Economics, Elsevier, vol. 135(2), pages 671-686.
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    3. Kerkkamp, R.B.O. & van den Heuvel, W. & Wagelmans, A.P.M., 2019. "Two-echelon lot-sizing with asymmetric information and continuous type space," Omega, Elsevier, vol. 87(C), pages 158-176.

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