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A Simple Heuristic for Joint Inventory and Pricing Models with Lead Time and Backorders

Author

Listed:
  • Fernando Bernstein

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Yang Li

    (California State University, Sacramento, California 95819)

  • Kevin Shang

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

We study a joint inventory and pricing problem in a single-stage system with a positive lead time. We consider both additive and multiplicative demand forms. This problem is, in general, intractable due to its computational complexity. We develop a simple heuristic that resolves this issue. The heuristic involves a myopic pricing policy that generates each period’s price as a function of the initial inventory level and a base-stock policy for inventory replenishment. In each period, the firm monitors its so-called price-deflated inventory position and places an order to reach a target base-stock level. The price-deflated inventory position weights the on-hand and pipeline inventory according to a factor that reflects the sensitivity of price to the net inventory level. To assess the effectiveness of our heuristic, we construct an upper bound to the exact system. The upper bound is based on an information-relaxation approach and involves a penalty function derived from the proposed heuristic. A numerical study suggests that the heuristic is near-optimal. The heuristic approach can be applied to a wide variety of inventory systems, such as systems with fixed ordering costs or fixed batch sizes. The heuristic enables us to explore the use of price as a lever to balance supply and demand. Our findings indicate that a responsive strategy (that effectively reduces the replenishment lead time) leads to a more stable pricing policy and that the value of dynamic pricing increases with lead time. This paper was accepted by Martin Lariviere, operations management .

Suggested Citation

  • Fernando Bernstein & Yang Li & Kevin Shang, 2016. "A Simple Heuristic for Joint Inventory and Pricing Models with Lead Time and Backorders," Management Science, INFORMS, vol. 62(8), pages 2358-2373, August.
  • Handle: RePEc:inm:ormnsc:v:62:y:2016:i:8:p:2358-2373
    DOI: 10.1287/mnsc.2015.2227
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    References listed on IDEAS

    as
    1. Nicholas C. Petruzzi & Maqbool Dada, 1999. "Pricing and the Newsvendor Problem: A Review with Extensions," Operations Research, INFORMS, vol. 47(2), pages 183-194, April.
    2. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    3. Edwin S. Mills, 1959. "Uncertainty and Price Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 73(1), pages 116-130.
    4. John M. Bossert & Sean P. Willems, 2007. "A Periodic-Review Modeling Approach for Guaranteed Service Supply Chains," Interfaces, INFORMS, vol. 37(5), pages 420-436, October.
    5. Salal Humair & John D. Ruark & Brian Tomlin & Sean P. Willems, 2013. "Incorporating Stochastic Lead Times Into the Guaranteed Service Model of Safety Stock Optimization," Interfaces, INFORMS, vol. 43(5), pages 421-434, October.
    6. Fangruo Chen & Yu-Sheng Zheng, 1998. "Near-Optimal Echelon-Stock (R, nQ) Policies in Multistage Serial Systems," Operations Research, INFORMS, vol. 46(4), pages 592-602, August.
    7. Donald L. Iglehart, 1963. "Optimality of (s, S) Policies in the Infinite Horizon Dynamic Inventory Problem," Management Science, INFORMS, vol. 9(2), pages 259-267, January.
    8. Mahesh Nagarajan & S. Rajagopalan, 2009. "Technical Note---A Multiperiod Model of Inventory Competition," Operations Research, INFORMS, vol. 57(3), pages 785-790, June.
    9. Yuyue Song & Saibal Ray & Tamer Boyaci, 2009. "Technical Note---Optimal Dynamic Joint Inventory-Pricing Control for Multiplicative Demand with Fixed Order Costs and Lost Sales," Operations Research, INFORMS, vol. 57(1), pages 245-250, February.
    10. Woonghee Tim Huh & Ganesh Janakiraman & John A. Muckstadt & Paat Rusmevichientong, 2009. "Asymptotic Optimality of Order-Up-To Policies in Lost Sales Inventory Systems," Management Science, INFORMS, vol. 55(3), pages 404-420, March.
    11. Tingliang Huang & Jan A. Van Mieghem, 2014. "Clickstream Data and Inventory Management: Model and Empirical Analysis," Production and Operations Management, Production and Operations Management Society, vol. 23(3), pages 333-347, March.
    12. Woonghee Tim Huh & Ganesh Janakiraman, 2012. "Technical Note---On Optimal Policies for Inventory Systems with Batch Ordering," Operations Research, INFORMS, vol. 60(4), pages 797-802, August.
    13. Kevin H. Shang & Sean X. Zhou, 2010. "Optimal and Heuristic Echelon ( r, nQ, T ) Policies in Serial Inventory Systems with Fixed Costs," Operations Research, INFORMS, vol. 58(2), pages 414-427, April.
    14. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    15. David B. Brown & James E. Smith & Peng Sun, 2010. "Information Relaxations and Duality in Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 58(4-part-1), pages 785-801, August.
    16. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
    17. Fangruo Chen, 2000. "Optimal Policies for Multi-Echelon Inventory Problems with Batch Ordering," Operations Research, INFORMS, vol. 48(3), pages 376-389, June.
    18. 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.
    19. Brian Wieland & Pat Mastrantonio & Sean P. Willems & Karl G. Kempf, 2012. "Optimizing Inventory Levels Within Intel's Channel Supply Demand Operations," Interfaces, INFORMS, vol. 42(6), pages 517-527, December.
    20. Youyi Feng & Youhua (Frank) Chen, 2011. "TECHNICAL NOTE---A Computational Approach for Optimal Joint Inventory-Pricing Control in an Infinite-Horizon Periodic-Review System," Operations Research, INFORMS, vol. 59(5), pages 1297-1303, October.
    21. 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.
    22. Woonghee Tim Huh & Ganesh Janakiraman, 2008. "( s, S ) Optimality in Joint Inventory-Pricing Control: An Alternate Approach," Operations Research, INFORMS, vol. 56(3), pages 783-790, June.
    23. Yin, Rui & Rajaram, Kumar, 2007. "Joint pricing and inventory control with a Markovian demand model," European Journal of Operational Research, Elsevier, vol. 182(1), pages 113-126, October.
    24. Qi Feng, 2010. "Integrating Dynamic Pricing and Replenishment Decisions Under Supply Capacity Uncertainty," Management Science, INFORMS, vol. 56(12), pages 2154-2172, December.
    25. Ingrid Farasyn & Salal Humair & Joel I. Kahn & John J. Neale & Oscar Rosen & John Ruark & William Tarlton & Wim Van de Velde & Glenn Wegryn & Sean P. Willems, 2011. "Inventory Optimization at Procter & Gamble: Achieving Real Benefits Through User Adoption of Inventory Tools," Interfaces, INFORMS, vol. 41(1), pages 66-78, February.
    26. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
    27. Zhan Pang & Frank Y. Chen & Youyi Feng, 2012. "Technical Note---A Note on the Structure of Joint Inventory-Pricing Control with Leadtimes," Operations Research, INFORMS, vol. 60(3), pages 581-587, June.
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