本文考虑了有限资源约束下串联排队系统的速率控制以及动态定价问题. 管理者不仅需要制定合适的动态价格来增加收益, 还需要在资源有限的约束下, 为串联的两个服务台分配合适的资源, 达到减少成本, 提高总体社会福利的目的. 文中首先采用灵敏度分析技术求得依赖于状态的最优到达率和两个服务台各自的最优服务率. 通过边际收益函数, 建立了价格和到达率之间的关系表达式. 然后在已得到的最优速率基础上, 利用递归算法给出平均逗留时间, 进而得到依赖于状态的最优价格. 最后将上述理论应用到汽车检测场的动态定价问题之中.
Abstract
This paper considers the rate control and dynamic pricing in a tandem queue with limited resources. To improve the long-run average social welfare, managers not only need to set appropriate dynamic prices to increase revenue, but also need to allocate appropriate resources to two servers with limited resources with the goal of reducing costs. This paper uses sensitivity-based optimization to obtain the optimal state-dependent arrival rates and service rates firstly. Through the marginal revenue function, the relationship between price and arrival rate is established. Then, based on the optimal rates, the sojourn time is derived by using a recursive algorithm and the corresponding dynamic prices are also given. Finally, the above theory is applied to the dynamic pricing in an automobile inspection company.
关键词
串联排队 /
灵敏度优化 /
速率控制 /
动态定价
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Key words
tandem queue /
sensitivity-based optimization /
rate control /
dynamic pricing
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中图分类号：
O226
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参考文献
[1] 张笑菊, 曾庆成, 王泽浩. 集装箱码头集卡配置优化的闭合排队网络模型[J]. 系统工程理论与实践, 2019, 39(2): 409-417.Zhang X J, Zeng Q C, Wang Z H. Modeling the closed queueing network of truck allocation optimization in container terminals[J]. Systems Engineering—Theory & Practice, 2019, 39(2): 409-417.
[3] Ata B, Shneorson S. Dynamic control of an M/M/1 service system with adjustable arrival and service rates[J]. Management Science, 2006, 52(11): 1778-1791.
[4] Chen H, Frank M Z. State dependent pricing with a queue[J]. IIE Transactions, 2001, 33(10): 847-860.
[5] Borgs C, Chayes J T, Doroudi S, et al. The optimal admission threshold in observable queues with state dependent pricing[J]. Probability in the Engineering and Informational Sciences, 2014, 28(1): 101-119.
[7] Cil E B, Karaesmen F, Oermeci E L. Dynamic pricing and scheduling in a multi-class single-server queueing system[J]. Queueing Systems: Theory Applications, 2011, 67(4): 305-331.
[8] Gallego G, Li M, Liu Y. Dynamic nonlinear pricing of inventories over finite sales horizons[J]. Operations Research, 2020, 68(3): 655-670.
[9] Balseiro S R, Brown D B, Chen C. Dynamic pricing of relocating resources in large networks[J]. Management Science, 2021, 67(7): 4075-4094.
[11] Ching W K, Li T, Choi S M, et al. A tandem queueing system with applications to pricing strategy[J]. Journal of Industrial Management Optimization, 2008, 5(1): 103-114.
[13] Wang X, Andradottir S, Ayhan H. Optimal pricing for tandem queues with finite buffers[J]. Queueing Systems: Theory and Applications, 2019, 92(3): 323-396.
[14] Wang X, Andradóttir S, Ayhan H, et al. Revenue maximization in two station tandem queueing systems[J]. Naval Research Logistics, 2020, 67: 77-107.
[15] Masuda Y, Whang S. Dynamic pricing for network service: Equilibrium and stability[J]. Management Science, 1999, 45(6): 857-869.
[17] Xia L, Chen S. Dynamic pricing control for open queueing networks[J]. IEEE Transactions on Automatic Control, 2018, 63(10): 3290-3300.
[18] Banerjee S, Riquelme C, Johari R. Pricing in ride-share platforms: A queueing-theoretic approach[J]. Social Science Electronic Publishing, 2015: 601-639. doi: 10.2139/ssrn.2568258.
[19] 彭向, 胡天宇, 孙俊芳, 等. 基于社会福利最大 化的网约车平台定价模型研究[J]. 系统工程理论与实践, 2021, 41(7): 1806-1818.Peng X, Hu T Y, Sun J F, et al. Pricing of ridesourcing platform with maximizing social welfare[J]. Systems Engineering—Theory & Practice, 2021, 41(7): 1806-1818.
[21] Yom-Tov G B, Chan C W. Balancing admission control, speedup, and waiting in service systems[J]. Queueing Systems, 2021, 97(1-2): 163-219.
[22] George J M, Harrison J M. Dynamic control of a queue with adjustable service rate[J]. Operations Research, 2001, 49(5): 720-731.
[23] Xia L. Service rate control of closed Jackson networks from game theoretic perspective[J]. European Journal of Operational Research, 2014, 237(2): 546-554.
[24] Xia L, Miller D, Zhou Z, et al. Service rate control of tandem queues with power constraints[J]. IEEE Transactions on Automatic Control, 2017, 62(10): 5111-5123.
[25] Cao X R. Stochastic learning and optimization—A sensitivity-based approach[J]. Annual Reviews in Control, 2007, 33(1): 11-24.
[26] 黄文婷. 机动车检测站排队系统建模及设备优化配置研究[D]. 广州: 华南农业大学, 2012.Huang W T. Automotive inspect station queue system modeling and resourse configuration optimization[D]. Guangzhou: South China Agricultural University, 2012.
[27] 郭庆钢. 沈阳市汽车检测中心成本分析与控制的研究[D]. 长春: 吉林大学, 2013.Guo Q G. The analysis and control of operating costs about automotive test center, Shenyang[D]. Changchun: Jilin University, 2013.
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脚注
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基金
国家自然科学基金(61973084,62070206)
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