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A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation

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  • Lim, Sungmook

Abstract

We consider a robust optimization model of determining a joint optimal bundle of price and order quantity for a retailer in a two-stage supply chain under uncertainty of parameters in demand and purchase cost functions. Demand is modeled as a decreasing power function of product price, and unit purchase cost is modeled as a decreasing power function of order quantity and demand. While the general form of the power functions are given, it is assumed that parameters defining the two power functions involve a certain degree of uncertainty and their possible values can be characterized by ellipsoids. We show that the robust optimization problem can be transformed into an equivalent convex optimization which can be solved efficiently and effectively using interior-point methods. In addition, we propose a practical implementation of the model, where the stochastic characteristics of parameters are obtained from regression analysis on past sales and production data, and ellipsoidal representations of the parameter uncertainties are obtained based on a combined use of genetic algorithm and Monte Carlo simulation. An illustrative example is provided to demonstrate the model and its implementation.

Suggested Citation

  • Lim, Sungmook, 2013. "A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation," Omega, Elsevier, vol. 41(6), pages 998-1007.
  • Handle: RePEc:eee:jomega:v:41:y:2013:i:6:p:998-1007
    DOI: 10.1016/j.omega.2012.12.003
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    Cited by:

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    4. Li, Yi & Shou, Biying, 2021. "Managing supply risk: Robust procurement strategy for capacity improvement," Omega, Elsevier, vol. 102(C).
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    6. Yanıkoğlu, İhsan & Gorissen, Bram L. & den Hertog, Dick, 2019. "A survey of adjustable robust optimization," European Journal of Operational Research, Elsevier, vol. 277(3), pages 799-813.
    7. Bajwa, Naeem & Sox, Charles R. & Ishfaq, Rafay, 2016. "Coordinating pricing and production decisions for multiple products," Omega, Elsevier, vol. 64(C), pages 86-101.
    8. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    9. Caceres-Hernandez, Jose Juan & Martin-Rodriguez, Gloria & González Gómez, José Ignacio & Nuez Yánez, Juan Sebastian, 2013. "Canary banana exports. Are product withdrawal decisions rational?," Economia Agraria y Recursos Naturales, Spanish Association of Agricultural Economists, vol. 13(02), pages 1-26, December.
    10. Ghoniem, Ahmed & Maddah, Bacel, 2015. "Integrated retail decisions with multiple selling periods and customer segments: Optimization and insights," Omega, Elsevier, vol. 55(C), pages 38-52.
    11. Xiang, Xi & Liu, Changchun, 2021. "An almost robust optimization model for integrated berth allocation and quay crane assignment problem," Omega, Elsevier, vol. 104(C).
    12. Ata Allah Taleizadeh & Mahsa Noori-daryan, 2016. "Pricing, inventory and production policies in a supply chain of pharmacological products with rework process: a game theoretic approach," Operational Research, Springer, vol. 16(1), pages 89-115, April.
    13. Gorissen, Bram L. & Yanıkoğlu, İhsan & den Hertog, Dick, 2015. "A practical guide to robust optimization," Omega, Elsevier, vol. 53(C), pages 124-137.
    14. Zhou, Yuan & Xie, Jinxing, 2014. "Potentially self-defeating: Group buying in a two-tier supply chain," Omega, Elsevier, vol. 49(C), pages 42-52.

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