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Dynamic Pricing and Optimal Control for a Stochastic Inventory System with Non-Instantaneous Deteriorating Items and Partial Backlogging

Author

Listed:
  • Xuxiang Luo

    (School of Mathematics and Statistics, Central South University, Changsha 410083, China)

  • Zaiming Liu

    (School of Mathematics and Statistics, Central South University, Changsha 410083, China)

  • Jinbiao Wu

    (School of Mathematics and Statistics, Central South University, Changsha 410083, China)

Abstract

In this paper, we consider a problem of the dynamic pricing and inventory control for non-instantaneous deteriorating items with uncertain demand, in which the demand is price-sensitive and governed by a diffusion process. Shortages and remains are permitted, and the backlogging rate is variable and dependent on the waiting time for the next replenishment. In order to maximize the expected total profit, the problem of dynamic pricing and inventory control is described as a stochastic optimal control problem. Based on the dynamic programming principle, the stochastic control model is transformed into a Hamilton-Jacobi-Bellman (HJB) equation. Then, an exact expression for the optimal dynamic pricing strategy is obtained via solving the HJB equation. Moreover, the optimal initial inventory level, the optimal selling pricing, the optimal replenishment cycle and the optimal expected total profit are achieved when the replenishment cycle starts at time 0. Finally, some numerical simulations are presented to demonstrate the analytical results, and the sensitivities analysis on system parameters are carried out to provide some suggestions for managers.

Suggested Citation

  • Xuxiang Luo & Zaiming Liu & Jinbiao Wu, 2020. "Dynamic Pricing and Optimal Control for a Stochastic Inventory System with Non-Instantaneous Deteriorating Items and Partial Backlogging," Mathematics, MDPI, vol. 8(6), pages 1-22, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:906-:d:366674
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    References listed on IDEAS

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    1. Wu, Kun-Shan & Ouyang, Liang-Yuh & Yang, Chih-Te, 2006. "An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging," International Journal of Production Economics, Elsevier, vol. 101(2), pages 369-384, June.
    2. Goyal, S. K. & Giri, B. C., 2001. "Recent trends in modeling of deteriorating inventory," European Journal of Operational Research, Elsevier, vol. 134(1), pages 1-16, October.
    3. 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.
    4. Zhang, Jianxiong & Wang, Yu & Lu, Lihao & Tang, Wansheng, 2015. "Optimal dynamic pricing and replenishment cycle for non-instantaneous deterioration items with inventory-level-dependent demand," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 136-145.
    5. Bakker, Monique & Riezebos, Jan & Teunter, Ruud H., 2012. "Review of inventory systems with deterioration since 2001," European Journal of Operational Research, Elsevier, vol. 221(2), pages 275-284.
    6. 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.
    7. Papachristos, S. & Skouri, K., 2003. "An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging," International Journal of Production Economics, Elsevier, vol. 83(3), pages 247-256, March.
    8. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
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    Cited by:

    1. Ruishu Shi & Cuilian You, 2023. "Dynamic pricing and production control for perishable products under uncertain environment," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 359-386, September.

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