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Technical Note—Price and Production Decisions with Random Demand

Author

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  • L. Joseph Thomas

    (Cornell University, Ithaca, New York)

Abstract

This note studies the problem of setting price and production levels simultaneously in a series of N periods, where price is a parameter in the probability distribution of demand. It develops a simple policy characterized by two stock levels and an optimal price line in the price-inventory plane, gives an algorithm to compute such a policy and check conditions for its optimality, and presents a counterexample to the simple policy, using a small set of allowable prices, along with a discussion of both the counterexample and some characteristics of the model.

Suggested Citation

  • L. Joseph Thomas, 1974. "Technical Note—Price and Production Decisions with Random Demand," Operations Research, INFORMS, vol. 22(3), pages 513-518, June.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:3:p:513-518
    DOI: 10.1287/opre.22.3.513
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    Cited by:

    1. Hong Chen & Zhan Zhang, 2014. "Technical Note—Joint Inventory and Pricing Control with General Additive Demand," Operations Research, INFORMS, vol. 62(6), pages 1335-1343, December.
    2. Sirong Luo & Jianrong Wang, 2017. "A technical note on the dynamic nonstationary inventory-pricing control model with lost sale," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5816-5825, October.
    3. Peng Hu & Ye Lu & Miao Song, 2019. "Joint Pricing and Inventory Control with Fixed and Convex/Concave Variable Production Costs," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 847-877, April.
    4. Kaijie Zhu & Ulrich W. Thonemann, 2009. "Coordination of pricing and inventory control across products," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 175-190, March.
    5. Qing Li & Shaohui Zheng, 2006. "Joint Inventory Replenishment and Pricing Control for Systems with Uncertain Yield and Demand," Operations Research, INFORMS, vol. 54(4), pages 696-705, August.
    6. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    7. Sandro Brusco & Ornella Tarola & Sandro Trento, 2016. "Timing Of Lumpy Investment, Pricing And Technical Progress," Bulletin of Economic Research, Wiley Blackwell, vol. 68(1), pages 16-33, January.
    8. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    9. Youhua (Frank) Chen & Saibal Ray & Yuyue Song, 2006. "Optimal pricing and inventory control policy in periodic‐review systems with fixed ordering cost and lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(2), pages 117-136, March.
    10. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case," Operations Research, INFORMS, vol. 52(6), pages 887-896, December.
    11. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    12. Akartunalı, Kerem & Dauzère-Pérès, Stéphane, 2022. "Dynamic lot sizing with stochastic demand timing," European Journal of Operational Research, Elsevier, vol. 302(1), pages 221-229.
    13. Awi Federgruen & Zhe Liu & Lijian Lu, 2020. "Synthesis and Generalization of Structural Results in Inventory Management: A Generalized Convexity Property," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 547-575, May.
    14. Wen Chen & Adam J. Fleischhacker & Michael N. Katehakis, 2015. "Dynamic pricing in a dual‐market environment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 531-549, October.
    15. Lawrence R. Weatherford, 1997. "Using Prices More Realistically as Decision Variables in Perishable-Asset Revenue Management Problems," Journal of Combinatorial Optimization, Springer, vol. 1(3), pages 277-304, October.
    16. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    17. Garrett van Ryzin & Gustavo Vulcano, 2004. "Optimal Auctioning and Ordering in an Infinite Horizon Inventory-Pricing System," Operations Research, INFORMS, vol. 52(3), pages 346-367, June.
    18. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 698-723, August.
    19. Xiong‐zhi Wang & Guo‐qing Wang, 2019. "Integrating dynamic pricing and inventory control for fresh‐agri product under consumer choice," Australian Economic Papers, Wiley Blackwell, vol. 58(1), pages 96-111, March.
    20. Zheng Shi & Zheng Wen, 2014. "Optimal Sales Discount Decision Model with Fixed Ordered Quantities," Journal of Systems Science and Information, De Gruyter, vol. 2(4), pages 345-357, August.
    21. Joseph Geunes & H. Edwin Romeijn & Kevin Taaffe, 2006. "Requirements Planning with Pricing and Order Selection Flexibility," Operations Research, INFORMS, vol. 54(2), pages 394-401, April.
    22. Boxiao Chen & David Simchi-Levi & Yining Wang & Yuan Zhou, 2022. "Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information," Management Science, INFORMS, vol. 68(8), pages 5684-5703, August.
    23. Gurkan, M. Edib & Tunc, Huseyin & Tarim, S. Armagan, 2022. "The joint stochastic lot sizing and pricing problem," Omega, Elsevier, vol. 108(C).
    24. Hemant K. Bhargava & Daewon Sun & Susan H. Xu, 2006. "Stockout Compensation: Joint Inventory and Price Optimization in Electronic Retailing," INFORMS Journal on Computing, INFORMS, vol. 18(2), pages 255-266, May.

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