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Simultaneous Price-Production Decisions

Author

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  • Dov Pekelman

    (University of Chicago, Chicago, Illinois)

Abstract

This paper deals with the problem of determining the price and production schedule of a firm over a known horizon simultaneously when the demand parameters are time-dependent. It characterizes the optimal solution and shows the similarity of our problem to the well known problem of Modigliani and Hohn [ Econometrica 23, 46–66 (1955)]. It also demonstrates the possible existence of a planning horizon. These results are obtained by using control theory, in particular, by using the necessary and sufficient conditions for a state constraint in the form of a nonnegative constraint on the inventory level.

Suggested Citation

  • Dov Pekelman, 1974. "Simultaneous Price-Production Decisions," Operations Research, INFORMS, vol. 22(4), pages 788-794, August.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:4:p:788-794
    DOI: 10.1287/opre.22.4.788
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    Cited by:

    1. 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.
    2. W K Chiang & Y Feng, 2010. "Retailer or e-tailer? Strategic pricing and economic-lot-size decisions in a competitive supply chain with drop-shipping," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(11), pages 1645-1653, November.
    3. Kim, DaeSoo & Lee, Won J., 1998. "Optimal joint pricing and lot sizing with fixed and variable capacity," European Journal of Operational Research, Elsevier, vol. 109(1), pages 212-227, August.
    4. Erickson, Gary M., 2011. "A differential game model of the marketing-operations interface," European Journal of Operational Research, Elsevier, vol. 211(2), pages 394-402, June.
    5. Lamas, Alejandro & Chevalier, Philippe, 2018. "Joint dynamic pricing and lot-sizing under competition," European Journal of Operational Research, Elsevier, vol. 266(3), pages 864-876.
    6. Hyun-soo Ahn & Mehmet Gümüş & Philip Kaminsky, 2007. "Pricing and Manufacturing Decisions When Demand Is a Function of Prices in Multiple Periods," Operations Research, INFORMS, vol. 55(6), pages 1039-1057, December.
    7. Gila E. Fruchter & Hussein Naseraldin, 2021. "Coordinating Carbon Emissions via Production Quantities: A Differential Game Approach," Games, MDPI, vol. 12(1), pages 1-16, February.
    8. Chazal, Marie & Jouini, Elyès & Tahraoui, Rabah, 2008. "Production planning and inventories optimization: A backward approach in the convex storage cost case," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 997-1023, September.
    9. Atkins, Derek & Liang, Liping, 2010. "A note on competitive supply chains with generalised supply costs," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1316-1320, December.
    10. Li, Xueping & Wang, Jiao & Sawhney, Rapinder, 2012. "Reinforcement learning for joint pricing, lead-time and scheduling decisions in make-to-order systems," European Journal of Operational Research, Elsevier, vol. 221(1), pages 99-109.
    11. Erickson, Gary M., 2012. "Transfer pricing in a dynamic marketing-operations interface," European Journal of Operational Research, Elsevier, vol. 216(2), pages 326-333.
    12. Ravi Kumar, K. & Hadjinicola, George C., 1996. "Resource allocation to defensive marketing and manufacturing strategies," European Journal of Operational Research, Elsevier, vol. 94(3), pages 453-466, November.
    13. K Kogan & U Spiegel, 2006. "Optimal policies for inventory usage, production and pricing of fashion goods over a selling season," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(3), pages 304-315, March.
    14. Desai, Vijay S., 1996. "Interactions between members of a marketing-production channel under seasonal demand," European Journal of Operational Research, Elsevier, vol. 90(1), pages 115-141, April.
    15. Transchel, Sandra & Minner, Stefan, 2009. "Dynamic pricing and replenishment in the warehouse scheduling problem--A common cycle approach," International Journal of Production Economics, Elsevier, vol. 118(1), pages 331-338, March.
    16. Lihao Lu & Jianxiong Zhang & Wansheng Tang, 2016. "Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1480-1494, April.
    17. Debopriya Dey & Samarjit Kar & Dilip Kumar Bhattacharya, 2024. "Periodic review policy in the production management of a single-item inventory with deterioration," Operational Research, Springer, vol. 24(2), pages 1-25, June.
    18. Shiming Deng & Candace A. Yano, 2006. "Joint Production and Pricing Decisions with Setup Costs and Capacity Constraints," Management Science, INFORMS, vol. 52(5), pages 741-756, May.
    19. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    20. van den Berg, A.H.J. & Herings, P.J.J. & Peters, H.J.M., 2014. "The economic order decision with continuous dynamic pricing and batch supply," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    21. Sreekumar Bhaskaran & Karthik Ramachandran & John Semple, 2010. "A Dynamic Inventory Model with the Right of Refusal," Management Science, INFORMS, vol. 56(12), pages 2265-2281, December.
    22. Stephen A. Smith & Dale D. Achabal, 1998. "Clearance Pricing and Inventory Policies for Retail Chains," Management Science, INFORMS, vol. 44(3), pages 285-300, March.
    23. 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.
    24. Abhijit Upasani & Reha Uzsoy, 2008. "Incorporating manufacturing lead times in joint production-marketing models: A review and some future directions," Annals of Operations Research, Springer, vol. 161(1), pages 171-188, July.

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