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The optimal quantity discount that a supplier should offer

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Journal of the Operational Research Society

Abstract

Quantity discounts are a useful mechanism for coordination. Here we investigate such discounts from the supplier's perspective, both from a non-cooperative game-theoretical approach and a joint decision model. Taking into account the price elasticity of demand, this analysis aids a sole supplier in establishing an all-unit quantity discount policy in light of the buyer's best reaction. The Stackelberg equilibrium and Pareto optimal solution set are derived for the non-cooperative and joint-decision cases, respectively. Our research indicates that channel efficiency can be improved significantly if the quantity discount decision is made jointly rather than non-cooperatively. Moreover, we extend our model in three directions: (1) the product is transported by a private fleet; (2) the buyer may choose to offer her customers a different percentage discount than that she obtained from the supplier; and (3) the case of heterogeneous buyers. Numerical case studies are employed throughout the paper to illustrate the practical applications of the models presented and the sensitivity to model parameters.

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References

  • Banerjee A (1986). Note on “A quantity discount pricing model to increase vendor profits”. Mngt Sci 32 (11): 1513–1517.

    Article  Google Scholar 

  • Chakravarty AK and Martin GE (1988). An optimal joint buyer-seller discount pricing model. Comput Opl Res 15: 271–281.

    Article  Google Scholar 

  • Chakravarty AK and Martin GE (1991). Operational economies of a process positioning determinant. Comput Opl Res 18: 515–530.

    Article  Google Scholar 

  • Chiang W-C, Fitzsimmons J, Huang Z and Li SX (1994). A game-theoretic approach to quantity discount problems. Decis Sci 25 (1): 153–168.

    Article  Google Scholar 

  • Choi SC, Lei L and Wang Q (2005). Quantity discounts for supply chain coordination. In: Chakravarty AK and Eliashberg J (eds). Managing Business Interfaces: Marketing and Engineering Issues in the Supply Chain and Internet Domains. Springer: New York, pp 133–171.

    Chapter  Google Scholar 

  • Cohon JL (1978). Multiobjective Programming and Planning. Academic Press: New York.

    Google Scholar 

  • Dada M and Srikanth KN (1987). Pricing policies for quantity discounts. Mngt Sci 33 (10): 1247–1252.

    Article  Google Scholar 

  • Dolan RJ (1978). A normative model of industrial buyer response to quantity discounts. In: Jain SC (ed). Research Frontiers in Marketing: Dialogues and Directions. American Marketing Association: Chicago, pp 121–125.

    Google Scholar 

  • Gibbons R (1992). Game Theory for Applied Economists. Princeton University Press: Princeton, NJ.

    Google Scholar 

  • Joglekar PN (1988). Note—Comments on “A quantity discount pricing model to increase vendor profits”. Mngt Sci 34 (11): 1391–1398.

    Article  Google Scholar 

  • Kohli R and Park H (1989). A cooperative game theory model of quantity discounts. Mngt Sci 35 (6): 693–707.

    Article  Google Scholar 

  • Lal R and Staelin R (1984). An approach for developing an optimal discount pricing policy. Mngt Sci 30 (12): 1524(1516)–1540.

    Article  Google Scholar 

  • Lau AHL, Lau H-S and Wang J-C (2007). Pricing and volume discounting for a dominant retailer with uncertain manufacturing cost information. Eur J Opl Res 183 (2): 848–870.

    Article  Google Scholar 

  • Lee HL and Rosenblatt MJ (1986). A generalized quantity discount pricing model to increase supplier's profits. Mngt Sci 32 (9): 1177–1185.

    Article  Google Scholar 

  • Li X and Wang Q (2007). Coordination mechanisms of supply chain systems. Eur J Opl Res 179 (1): 1–16.

    Article  Google Scholar 

  • Monahan JP (1984). A quantity discount pricing model to increase vendor profits. Mngt Sci 30 (6): 720–726.

    Article  Google Scholar 

  • Parlar M and Wang Q (1994). Discounting decisions in a supplier-buyer relationship with a linear buyer's demand. IIE Trans 26 (2): 34–41.

    Article  Google Scholar 

  • Qin Y, Tang H and Guo C (2007). Channel coordination and volume discounts with price-sensitive demand. Int J Prod Econ 105 (1): 43–53.

    Article  Google Scholar 

  • Rubin PA and Benton WC (2003). A generalized framework for quantity discount pricing schedules. Decis Sci 34 (1): 173–187.

    Article  Google Scholar 

  • Stackelberg H von (1934). Market Form und Gleichgewicht. Springer: Berlin.

    Google Scholar 

  • Viswanathan S and Wang Q (2003). Discount pricing decisions in distribution channels with price-sensitive demand. Eur J Opl Res 149 (3): 571–587.

    Article  Google Scholar 

  • Wang Q (1997). Determination of suppliers' optimal quantity discount schedules with heterogeneous buyers. Technical Report. Nanyang Business School, Nanyang Technological University, Singapore.

    Google Scholar 

  • Wang Q (2002). Determination of suppliers’ optimal quantity discount schedules with heterogeneous buyers. Nav Res Logist 49 (1): 46–59.

    Article  Google Scholar 

  • Wang Q and Wang R (2005). Quantity discount pricing policies for heterogeneous retailers with price sensitive demand. Nav Res Logist 52 (7): 645–658.

    Article  Google Scholar 

  • Yang S-L and Zhou Y-W (2006). Unified discount pricing models of a two-echelon channel with a monopolistic manufacturer and heterogeneous retailers. Int Trans Opl Res 13 (2): 143–168.

    Article  Google Scholar 

  • Zhou Y-W (2007). A comparison of different quantity discount pricing policies in a two-echelon channel with stochastic and asymmetric demand information. Eur J Opl Res 181 (2): 686–703.

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Waterloo, Waterloo, Canada

    G Y Ke & J H Bookbinder

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  1. G Y Ke
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  2. J H Bookbinder
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Correspondence to J H Bookbinder.

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Ke, G., Bookbinder, J. The optimal quantity discount that a supplier should offer. J Oper Res Soc 63, 354–367 (2012). https://doi.org/10.1057/jors.2011.35

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  • DOI: https://doi.org/10.1057/jors.2011.35

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