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Lot-sizing and pricing decisions under attraction demand models and multi-channel environment: New efficient formulations

Author

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  • Terzi, Mourad
  • Ouazene, Yassine
  • Yalaoui, Alice
  • Yalaoui, Farouk

Abstract

The presented paper considers the pricing and lot-sizing decisions for a manufacturer who produces and sells a single product in different selling channels i.e physical stock, website, mobile, etc. The objective is to find the production plan and prices of each channel to maximize the total profit defined from difference between the revenues and the productions, holding and setups costs. The consumers’ demand in each channel is represented by attraction demand models which include the multinomial logit (MNL), multiplicative competitive interaction (MCI) and linear demand models. The addressed problem is formulated as a non-convex mixed-integer nonlinear program (MINLP). Based on properties of attraction functions, an efficient reformulation which transforms the initial non-convex problem into a convex one is presented. Therefore, an optimization approach based on the outer approximation algorithm is presented to solve the problem. Numerical tests based on large benchmark of real inspired instances show the efficiency of the proposed approach to solve the addressed problem compared to the initial non-convex model.

Suggested Citation

  • Terzi, Mourad & Ouazene, Yassine & Yalaoui, Alice & Yalaoui, Farouk, 2023. "Lot-sizing and pricing decisions under attraction demand models and multi-channel environment: New efficient formulations," Operations Research Perspectives, Elsevier, vol. 10(C).
    • Handle: RePEc:eee:oprepe:v:10:y:2023:i:c:s2214716023000040
    DOI: 10.1016/j.orp.2023.100269
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    1. Ford W. Harris, 1990. "How Many Parts to Make at Once," Operations Research, INFORMS, vol. 38(6), pages 947-950, December.
    2. Barry C. Smith & John F. Leimkuhler & Ross M. Darrow, 1992. "Yield Management at American Airlines," Interfaces, INFORMS, vol. 22(1), pages 8-31, February.
    3. Omprakash K. Gupta & A. Ravindran, 1985. "Branch and Bound Experiments in Convex Nonlinear Integer Programming," Management Science, INFORMS, vol. 31(12), pages 1533-1546, December.
    4. Kut C. So, 2000. "Price and Time Competition for Service Delivery," Manufacturing & Service Operations Management, INFORMS, vol. 2(4), pages 392-409, April.
    5. Maihami, Reza & Nakhai Kamalabadi, Isa, 2012. "Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand," International Journal of Production Economics, Elsevier, vol. 136(1), pages 116-122.
    6. Naeem Bajwa & Charles R. Sox, 2015. "Coordination of pricing, advertising, and production decisions for multiple products," International Journal of Services and Operations Management, Inderscience Enterprises Ltd, vol. 22(4), pages 495-521.
    7. Zhang, Ju-Liang & Chen, Jian & Lee, Chung-Yee, 2008. "Joint optimization on pricing, promotion and inventory control with stochastic demand," International Journal of Production Economics, Elsevier, vol. 116(2), pages 190-198, December.
    8. S. Panda & S. Saha & M. Basu, 2013. "Optimal pricing and lot-sizing for perishable inventory with price and time dependent ramp-type demand," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(1), pages 127-138.
    9. Gabriel R. Bitran & Susana V. Mondschein, 1995. "An Application of Yield Management to the Hotel Industry Considering Multiple Day Stays," Operations Research, INFORMS, vol. 43(3), pages 427-443, June.
    10. San-José, Luis A. & Sicilia, Joaquín & Alcaide-López-de-Pablo, David, 2018. "An inventory system with demand dependent on both time and price assuming backlogged shortages," European Journal of Operational Research, Elsevier, vol. 270(3), pages 889-897.
    11. Gabriel R. Bitran & Horacio H. Yanasse, 1982. "Computational Complexity of the Capacitated Lot Size Problem," Management Science, INFORMS, vol. 28(10), pages 1174-1186, October.
    12. Khouja, Moutaz, 2006. "A joint optimal pricing, rebate value, and lot sizing model," European Journal of Operational Research, Elsevier, vol. 174(2), pages 706-723, October.
    13. Lingxiu Dong & Panos Kouvelis & Zhongjun Tian, 2009. "Dynamic Pricing and Inventory Control of Substitute Products," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 317-339, December.
    14. Haugen, Kjetil K. & Olstad, Asmund & Pettersen, Bard I., 2007. "The profit maximizing capacitated lot-size (PCLSP) problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 165-176, January.
    15. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387.
    16. Maher A. N. Agi & Hardik N. Soni, 2020. "Joint pricing and inventory decisions for perishable products with age-, stock-, and price-dependent demand rate," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(1), pages 85-99, January.
    17. Tang, Christopher S., 2010. "A review of marketing-operations interface models: From co-existence to coordination and collaboration," International Journal of Production Economics, Elsevier, vol. 125(1), pages 22-40, May.
    18. Goker Aydin & Evan L. Porteus, 2008. "Joint Inventory and Pricing Decisions for an Assortment," Operations Research, INFORMS, vol. 56(5), pages 1247-1255, October.
    19. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
    20. Joseph Thomas, 1970. "Price-Production Decisions with Deterministic Demand," Management Science, INFORMS, vol. 16(11), pages 747-750, July.
    21. R. Ghasemy Yaghin & M Goh, 2021. "Procurement, production, and price planning under visibility and risk: a generalised Benders decomposition method," International Journal of Production Research, Taylor & Francis Journals, vol. 59(18), pages 5626-5646, September.
    22. Li, Ruihai & Liu, YuPing & Teng, Jinn-Tsair & Tsao, Yu-Chung, 2019. "Optimal pricing, lot-sizing and backordering decisions when a seller demands an advance-cash-credit payment scheme," European Journal of Operational Research, Elsevier, vol. 278(1), pages 283-295.
    23. Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, October.
    24. M. Florian & J. K. Lenstra & A. H. G. Rinnooy Kan, 1980. "Deterministic Production Planning: Algorithms and Complexity," Management Science, INFORMS, vol. 26(7), pages 669-679, July.
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