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The joint stochastic lot sizing and pricing problem

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  • Gurkan, M. Edib
  • Tunc, Huseyin
  • Tarim, S. Armagan

Abstract

We consider a joint stochastic lot sizing pricing problem where period demands are price dependent and stochastic. Herein, we propose an alternative joint inventory control pricing policy for the profit-optimal (s,S,p) policy. The proposed policy – referred to as (R,S,p) is an order-up-to policy where replenishment schedule and price levels for each period are set before the planning horizon starts. As such, this policy can be considered as rather static as compared to the dynamic (s,S,p) policy. We also provide a quadratic mixed integer programming formulation in order to obtain the optimal (R,S,p) policy parameters. Furthermore, (R,S,p) policy is compared against the profit-optimal (s,S,p) policy on an extensive numerical study where several different benchmark policies are additionally used. The results show that the proposed policy exhibits a competitive profit performance with respect to the profit-optimal policy especially for low or moderate levels of demand uncertainty. The results also reveal that the relative benefit of using dynamic pricing policy, as compared to that of using dynamic inventory control, diminishes as demand uncertainty escalates.

Suggested Citation

  • Gurkan, M. Edib & Tunc, Huseyin & Tarim, S. Armagan, 2022. "The joint stochastic lot sizing and pricing problem," Omega, Elsevier, vol. 108(C).
    • Handle: RePEc:eee:jomega:v:108:y:2022:i:c:s0305048321001869
    DOI: 10.1016/j.omega.2021.102577
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    1. Li, Guiping & He, Xiuli & Zhou, Jing & Wu, Hao, 2019. "Pricing, replenishment and preservation technology investment decisions for non-instantaneous deteriorating items," Omega, Elsevier, vol. 84(C), pages 114-126.
    2. Qi Feng & J. George Shanthikumar, 2018. "Supply and Demand Functions in Inventory Models," Operations Research, INFORMS, vol. 66(1), pages 77-91, 1-2.
    3. Özen, Ulaş & Doğru, Mustafa K. & Armagan Tarim, S., 2012. "Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem," Omega, Elsevier, vol. 40(3), pages 348-357.
    4. Heisig, Gerald, 2001. "Comparison of (s,S) and (s,nQ) inventory control rules with respect to planning stability," International Journal of Production Economics, Elsevier, vol. 73(1), pages 59-82, August.
    5. James H. Bookbinder & Jin-Yan Tan, 1988. "Strategies for the Probabilistic Lot-Sizing Problem with Service-Level Constraints," Management Science, INFORMS, vol. 34(9), pages 1096-1108, September.
    6. L. Joseph Thomas, 1974. "Technical Note—Price and Production Decisions with Random Demand," Operations Research, INFORMS, vol. 22(3), pages 513-518, June.
    7. Ioannis Stamatopoulos & Achal Bassamboo & Antonio Moreno, 2021. "The Effects of Menu Costs on Retail Performance: Evidence from Adoption of the Electronic Shelf Label Technology," Management Science, INFORMS, vol. 67(1), pages 242-256, January.
    8. Hao, Zhaowei & Qi, Wei & Gong, Tianxiao & Chen, Lihua & Shen, Zuo-Jun Max, 2019. "Innovation uncertainty, new product press timing and strategic consumers," Omega, Elsevier, vol. 89(C), pages 122-135.
    9. Wang, Qiang & Zhao, Nenggui & Wu, Jie & Zhu, Qingyuan, 2021. "Optimal pricing and inventory policies with reference price effect and loss-Averse customers," Omega, Elsevier, vol. 99(C).
    10. Kilic, Onur A. & Tarim, S. Armagan, 2011. "An investigation of setup instability in non-stationary stochastic inventory systems," International Journal of Production Economics, Elsevier, vol. 133(1), pages 286-292, September.
    11. Yi Yang & Youhua (Frank) Chen & Yun Zhou, 2014. "Coordinating Inventory Control and Pricing Strategies Under Batch Ordering," Operations Research, INFORMS, vol. 62(1), pages 25-37, February.
    12. 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.
    13. Retsef Levi & Martin Pál & Robin O. Roundy & David B. Shmoys, 2007. "Approximation Algorithms for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 284-302, May.
    14. Boxiao Chen & Xiuli Chao & Cong Shi, 2021. "Nonparametric Learning Algorithms for Joint Pricing and Inventory Control with Lost Sales and Censored Demand," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 726-756, May.
    15. Xin Chen & Peng Hu & Stephen Shum & Yuhan Zhang, 2016. "Dynamic Stochastic Inventory Management with Reference Price Effects," Operations Research, INFORMS, vol. 64(6), pages 1529-1536, December.
    16. 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.
    17. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    18. Cong Shi & Huanan Zhang & Xiuli Chao & Retsef Levi, 2014. "Approximation algorithms for capacitated stochastic inventory systems with setup costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(4), pages 304-319, June.
    19. 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.
    20. 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.
    21. Fatih Mutlu & Sila Çetinkaya & James Bookbinder, 2010. "An analytical model for computing the optimal time-and-quantity-based policy for consolidated shipments," IISE Transactions, Taylor & Francis Journals, vol. 42(5), pages 367-377.
    22. 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.
    23. Tarim, S. Armagan & Kingsman, Brian G., 2004. "The stochastic dynamic production/inventory lot-sizing problem with service-level constraints," International Journal of Production Economics, Elsevier, vol. 88(1), pages 105-119, March.
    24. Xin Chen & Zhan Pang & Limeng Pan, 2014. "Coordinating Inventory Control and Pricing Strategies for Perishable Products," Operations Research, INFORMS, vol. 62(2), pages 284-300, April.
    25. Polatoglu, Hakan & Sahin, Izzet, 2000. "Optimal procurement policies under price-dependent demand," International Journal of Production Economics, Elsevier, vol. 65(2), pages 141-171, April.
    26. Tunc, Huseyin & Kilic, Onur A. & Tarim, S. Armagan & Eksioglu, Burak, 2013. "A simple approach for assessing the cost of system nervousness," International Journal of Production Economics, Elsevier, vol. 141(2), pages 619-625.
    27. 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.
    28. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2007. "Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 821-839, November.
    29. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
    30. Yiwei Chen & Vivek F. Farias & Nikolaos Trichakis, 2019. "On the Efficacy of Static Prices for Revenue Management in the Face of Strategic Customers," Management Science, INFORMS, vol. 65(12), pages 5535-5555, December.
    31. Tarim, S. Armagan & Dogru, Mustafa K. & Özen, Ulas & Rossi, Roberto, 2011. "An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints," European Journal of Operational Research, Elsevier, vol. 215(3), pages 563-571, December.
    32. Retsef Levi & Robin O. Roundy & David B. Shmoys & Van Anh Truong, 2008. "Approximation Algorithms for Capacitated Stochastic Inventory Control Models," Operations Research, INFORMS, vol. 56(5), pages 1184-1199, October.
    33. 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.
    34. Tarim, S. Armagan & Kingsman, Brian G., 2006. "Modelling and computing (Rn, Sn) policies for inventory systems with non-stationary stochastic demand," European Journal of Operational Research, Elsevier, vol. 174(1), pages 581-599, October.
    35. 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.
    36. Qi Feng, 2010. "Integrating Dynamic Pricing and Replenishment Decisions Under Supply Capacity Uncertainty," Management Science, INFORMS, vol. 56(12), pages 2154-2172, December.
    37. Xin Chen & Peng Hu & Zhenyu Hu, 2017. "Efficient Algorithms for the Dynamic Pricing Problem with Reference Price Effect," Management Science, INFORMS, vol. 63(12), pages 4389-4406, December.
    38. Edward A. Silver, 1981. "Operations Research in Inventory Management: A Review and Critique," Operations Research, INFORMS, vol. 29(4), pages 628-645, August.
    39. Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2015. "Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing," Omega, Elsevier, vol. 50(C), pages 126-140.
    40. Chen, Jing & Dong, Ming & Rong, Ying & Yang, Liang, 2018. "Dynamic pricing for deteriorating products with menu cost," Omega, Elsevier, vol. 75(C), pages 13-26.
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