A multi-objective mean–variance mathematical programming approach to combined phase-out and clearance pricing strategy for seasonal products: case study of a Jeans retailer

  • Mahmoud Dehghan NayeriEmail author
  • Amir-Nader Haghbin
  • Abdolkarim Mohammadi-Balani
  • Karim Bayat
Research Article


This paper presents a novel multi-objective mean–variance mathematical programming approach to the dynamic pricing problem for seasonal products. The basic pricing scheme is a combination of phase-out pricing that gradually lowers the price over time and clearance pricing in which the end-of-season inventory is sold altogether at a lower price to a wholesaler in order to make room for the next season’s products. The model is then applied to a real-world case of a Jeans retailer in three different risk attitudes. Results show that the retailer should follow an almost fixed non-dynamic pricing strategy in the risk-taking attitudes, and a more flexible dynamic pricing strategy in risk-averse attitudes.


Dynamic pricing Seasonal products Multi-objective programming Phase-out pricing Clearance pricing 



  1. Adenso-Díaz, B., S. Lozano, and A. Palacio. 2017. Effects of dynamic pricing of perishable products on revenue and waste. Applied Mathematical Modelling 45: 148–164. Scholar
  2. Bogomolova, S., S. Dunn, G. Trinh, J. Taylor, and R.J. Volpe. 2015. Price promotion landscape in the US and UK: Depicting retail practice to inform future research agenda. Journal of Retailing and Consumer Services 25: 1–11. Scholar
  3. Brémaud, P. 1981. Point Processes and Queues: Martingale dynamics., Springer Series in Statistics New York: Springer.CrossRefGoogle Scholar
  4. Cachon, G.P., K.M. Daniels, and R. Lobel. 2017. The role of surge pricing on a service platform with self-scheduling capacity. M&SOM 19: 368–384. Scholar
  5. Cao, P., N. Zhao, and J. Wu. 2019. Dynamic pricing with Bayesian demand learning and reference price effect. European Journal of Operational Research 279: 540–556. Scholar
  6. Chen, B., and J. Chen. 2017. When to introduce an online channel, and offer money back guarantees and personalized pricing? European Journal of Operational Research 257: 614–624. Scholar
  7. Chen, X., J. Chen, Y. Chen, J. Yang, and D. Li. 2019. Heuristic-Q: A privacy data pricing method based on heuristic reinforcement learning. In Artificial Intelligence and Security, ed. X. Sun, Z. Pan, and E. Bertino, 553–565. Berlin: Springer International Publishing.CrossRefGoogle Scholar
  8. Courty, P., and L. Davey. 2019. The impact of variable pricing, dynamic pricing, and sponsored secondary markets in major league baseball. Journal of Sports Economics. Scholar
  9. Elmaghraby, W., and P. Keskinocak. 2003. Dynamic pricing in the presence of inventory considerations: Research overview, current practices, and future directions. Management Science 49: 1287–1309. Scholar
  10. Gallego, G., and G. van Ryzin. 1994. Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management Science 40: 999–1020. Scholar
  11. Gandal, N., J. Hamrick, T. Moore, and T. Oberman. 2018. Price manipulation in the Bitcoin ecosystem. Journal of Monetary Economics 95: 86–96. Scholar
  12. Gibson, J., and B. Kim. 2018. Economies of scale, bulk discounts, and liquidity constraints: Comparing unit value and transaction level evidence in a poor country. Review of Economics of the Household 16: 21–39. Scholar
  13. Guda, H., and U. Subramanian. 2019. Your uber is arriving: Managing on-demand workers through surge pricing, forecast communication, and worker incentives. Management Science 65: 1995–2014. Scholar
  14. He, Q.-C., and Y.-J. Chen. 2018. Dynamic pricing of electronic products with consumer reviews. Omega 80: 123–134. Scholar
  15. Hou, K.-L. 2006. An inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting. European Journal of Operational Research 168: 463–474. Scholar
  16. Hsieh, T.-P., and C.-Y. Dye. 2017. Optimal dynamic pricing for deteriorating items with reference price effects when inventories stimulate demand. European Journal of Operational Research 262: 136–150. Scholar
  17. Hu, S., X. Hu, and Q. Ye. 2017. Optimal rebate strategies under dynamic pricing. Operations Research 65: 1546–1561. Scholar
  18. Lee, H., and J.-S. Lee. 2017. An exploratory study of factors that exhibition organizers look for when selecting convention and exhibition centers. Journal of Travel & Tourism Marketing 34: 1001–1017. Scholar
  19. Li, X., G. Sun, and Y. Li. 2016. A multi-period ordering and clearance pricing model considering the competition between new and out-of-season products. Annals of Operations Research 242: 207–221. Scholar
  20. Lin, K.Y., F. Li. 2004. Optimal dynamic pricing for a line of substitutable products. Presented at the INFORMS Annual. Meeting, p. 10.Google Scholar
  21. Littlewood, K. 1972. Forecasting and control of passenger bookings. Agifors 12th annul symposium proceedings, in: AGIFORS Proceedings XII: Proceedings of the Twelfth AGIFORS Symposium. Presented at the 12th AGIFORS Symposium, American Airlinees Incorporated, Nathanya, Israel, pp. 95–117.Google Scholar
  22. Maglaras, C., and J. Meissner. 2006. Dynamic pricing strategies for multiproduct revenue management problems. M&SOM 8: 136–148. Scholar
  23. Mitra, S. 2018. Newsvendor problem with clearance pricing. European Journal of Operational Research 268: 193–202. Scholar
  24. Narwal, P., and J.K. Nayak. 2019. Investigating relative impact of reference prices on customers’ price evaluation in absence of posted prices: A case of Pay-What-You-Want (PWYW) pricing. Journal of Revenue and Pricing Management. Scholar
  25. Niemi, J., and L. Hirvonen. 2018. Money talks: Customer-initiated price negotiation in business-to-business sales interaction. Discourse & Communication 13: 95–118. Scholar
  26. Pan, A., and T.-M. Choi. 2016. An agent-based negotiation model on price and delivery date in a fashion supply chain. Annals of Operations Research 242: 529–557. Scholar
  27. Papanastasiou, Y., and N. Savva. 2016. Dynamic pricing in the presence of social learning and strategic consumers. Management Science 63: 919–939. Scholar
  28. Phillips, R.L., M.S. Gordon, O. Ozluk, S. Alberti, R.A. Flint, J.K. Andersson, K.P. Rangarajan, T. Grossman, R.M. Cooke, J.S. Cohen. 2006. Dynamic pricing system.Google Scholar
  29. Schütz, P., A. Tomasgard, and S. Ahmed. 2009. Supply chain design under uncertainty using sample average approximation and dual decomposition. European Journal of Operational Research 199: 409–419. Scholar
  30. Shirazi, E., and S. Jadid. 2015. Optimal residential appliance scheduling under dynamic pricing scheme via HEMDAS. Energy and Buildings 93: 40–49. Scholar
  31. Souiden, N., W. Chaouali, and M. Baccouche. 2019. Consumers’ attitude and adoption of location-based coupons: The case of the retail fast food sector. Journal of Retailing and Consumer Services 47: 116–132. Scholar
  32. Sturm, D., and K. Fischer. 2019. A cabin capacity allocation model for revenue management in the cruise industry. Journal of Revenue and Pricing Management. Scholar
  33. Suh, M., and G. Aydin. 2011. Dynamic pricing of substitutable products with limited inventories under logit demand. IIE Transactions 43: 323–331. Scholar
  34. Talluri, K.T., and G.J. Van Ryzin. 2004. Single-resource capacity control. In The Theory and Practice of Revenue Management, ed. K.T. Talluri and G.J. Van Ryzin, 27–80. Boston: Springer. Scholar
  35. Tan Pei Jie. 2016. A descriptive analysis of consumer’s price promotion literacy skills. International Journal of Retail & Distribution Management 44: 1223–1244. Scholar
  36. Zaarour, N., E. Melachrinoudis, and M.M. Solomon. 2016. Maximizing revenue of end of life items in retail stores. European Journal of Operational Research 255: 133–141. Scholar

Copyright information

© Springer Nature Limited 2019

Authors and Affiliations

  • Mahmoud Dehghan Nayeri
    • 1
    Email author
  • Amir-Nader Haghbin
    • 1
  • Abdolkarim Mohammadi-Balani
    • 1
  • Karim Bayat
    • 2
  1. 1.Department of Industrial Management, Faculty of Management and EconomicsTarbiat Modares UniversityTehranIran
  2. 2.Tarbiat Modares UniversityTehranIran

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