“服务智能化”排队系统的顾客行为及定价研究

doi:10.16381/j.cnki.issn1003-207x.2022.2463

摘要/Abstract

摘要：

本文以具有工作休假与休假中断的延迟维修排队系统为基础，融合智能化服务机制对系统中的顾客行为和定价策略进行分析。首先，根据“报酬-损失”理论构建效用函数，研究不同信息水平下的顾客均衡策略及社会最优策略。其次，采用遗传优化算法，利用计算机仿真技术求出社会最优策略并与均衡策略进行比较，得出顾客的自私行为会导致系统由于人员过度拥堵而出现瘫痪，进而造成顾客的流失，不利于整个社会的良性发展。因此，通过设置定价策略对顾客与社会之间收益进行调节，寻求整体社会福利的最大化。最后，通过分析系统参数对性能指标的影响，为服务业管理者进行决策提供了有效的参考。

关键词: 排队博弈, 均衡策略, 定价策略, 社会福利, 优化

Abstract:

With the application and development of mobile internet technology， promoting intelligent services is an inevitable path. Intelligent services have brought convenience to our daily life， but intelligent devices cannot be accepted by all social groups， and people still have doubts about their security， so the guidance of professional staff is indispensable in the use process. In addition， the function of intelligent devices is not yet perfect， and the frequency of failures is high. Once a failure occurs， it cannot be repaired in a short time， causing a large number of customers to be stranded at the service point， resulting in an unpleasant experience for customers.The customers’ equilibrium and pricing strategy in delayed repair queue with working vacation and vacation interruption combined with intelligent service mechanisms are considered. Firstly， the utility functions are established based on a linear reward-cost structure and customers’ equilibrium and socially optimal strategies are derived under different information levels. Secondly， the socially optimal strategy is calculated by using the genetic algorithm and computer simulation. By comparing with the equilibrium strategy， it concluded that selfish behavior of customers can paralyses the system， which leads to the loss of customers and is unfavorable to the overall healthy development of society. Therefore， it seeks to social welfare optimization by setting the optimal service price to regulate the benefit relationship between customers and society. Finally， taking the failure rate as an example， the impact of system parameters on performance indicators is analyzed and some suggestions are proposed for service industry managers to make decisions：（1） improve the staff’s ability to handle failures；（2） strengthen the training of employees in enterprises；（3） a reasonable pricing strategy can effectively alleviate congestion situations.

Key words: queueing game, equilibrium strategy, pricing strategy, social welfare, optimization

中图分类号:

O226

王蕊,徐秀丽. “服务智能化”排队系统的顾客行为及定价研究[J]. 中国管理科学, 2025, 33(8): 260-270.

Rui Wang,Xiuli Xu. Customer Behavior and Pricing Analysis Based on “Service Intelligence Queueing System”[J]. Chinese Journal of Management Science, 2025, 33(8): 260-270.

图/表 13

图1

图2

图3

图4

图5

图6

图7

图8

图9

表1

完全可见下参数ε取不同值时最优社会收益与均衡社会收益"

$ε$	$0.2$	$0.3$	$0.4$	$0.5$	$0.6$
$B f o (n s (0), n s (1))$	$19.0693$	$16.6667$	$14.7736$	$13.2431$	$11.9839$
$B f o (n e (0), n e (1))$	$18.8182$	$16.3208$	$14.3368$	$12.7264$	$11.3968$

表1

表2

几乎不可见下参数ε取不同值时最优社会收益与均衡社会收益"

$ε$	$0.2$	$0.3$	$0.4$	$0.5$	$0.6$
$B a u (q s (0), q s (1))$	$19.6042$	$17.0118$	$15.0831$	$13.3176$	$12.0985$
$B a u (q e (0), q e (1))$	$19.7390$	$17.5511$	$15.8095$	$14.3895$	$13.2090$

表2

图10

图11

参考文献 16

[1]	Naor P. The regulation of queue size by levying tolls［J］. Econometrica， 1969， 37（1）： 15-24.
[2]	Edelson N M， Hilderbrand D K. Congestion tolls for Poisson queuing processes［J］. Econometrica， 1975， 43（1）： 81-92.
[3]	Economou A， Kanta S. Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs［J］. Operations Research Letters， 2008， 36（6）： 696-699.
[4]	Wang J， Zhang F. Equilibrium analysis of the observable queues with balking and delayed repairs［J］. Applied Mathematics and Computation， 2011， 218（6）： 2716-2729.
[5]	张峰，王金亭. 完全信息下可修M/M/1排队系统的均衡分析［J］.北京交通大学学报，2012，36（3）： 129-132.
	Zhang F， Wang J T. Equilibrium analysis of a fully observable M/M/1 queueing system with breakdowns and repairs［J］. Journal of Beijing Jiaotong University， 2012， 36（3）： 129-132.
[6]	Li L， Wang J， Zhang F. Equilibrium customer strategies in Markovian queues with partial breakdowns［J］. Computers & Industrial Engineering，2013，66（4）： 751-757.
[7]	Xu B， Xu X. Equilibrium strategic behavior of customers in the M/M/1 queue with partial failures and repairs［J］. Operational Research， 2018， 18（2）： 273-292.
[8]	张淞钛，徐秀丽. 具有两类故障特性的M/M/1排队系统均衡分析［J］. 运筹学学报， 2019， 23（4）： 131-142.
	Zhang S T， Xu X L. Equilibrium analysis in the M/M/1 queue with two types of breakdowns［J］.Operations Research Transactions，2019，23（4）：131-142.
[9]	Tian R， Hu L， Wu X. Equilibrium and optimal strategies in M/M/1 queues with working vacations and vacation interruptions［J］. Mathematical Problems in Engineering， 2016， 2016（1）： 9746962.
[10]	Lee D H. Equilibrium balking strategies in Markovian queues with a single working vacation and vacation interruption［J］. Quality Technology & Quantitative Management， 2019， 16（3）： 355-376.
[11]	Wang J， Zhang X， Huang P. Strategic behavior and social optimization in a constant retrial queue with the N-policy［J］.European Journal of Operational Research， 2017， 256（3）： 841-849.
[12]	刘健，赵洪款，刘思峰. 基于顾客不公平规避的服务定价研究［J］. 中国管理科学， 2018， 26（2）： 46-53.
	Liu J， Zhao H K， Liu S F. A study of service pricing with unfairness averse customers［J］. Chinese Journal of Management Science， 2018， 26（2）： 46-53.
[13]	Tian R. Social optimization and pricing strategies in unobservable queues with delayed multiple vacations［J］. Mathematical Problems in Engineering， 2019， 2019（1）： 4684957.
[14]	李继红，赵仕静. 不同价格水平下排队策略研究［J］. 系统科学与数学， 2020， 40（3）： 510-520.
	Li J H， Zhao S J. Analysis of strategies in queueing system based on different prices［J］. Journal of Systems Science and Mathematical Sciences， 2020， 40（3）： 510-520.
[15]	李世勇，张芷源，孙微. 部分服务员休假M/M/c可视排队系统中的顾客行为与定价策略研究［J］. 系统科学与数学， 2022， 42（5）： 1282-1299.
	Li S Y， Zhang Z Y， Sun W. Customer behavior and pricing strategy in the observable M/M/c queue with vacations of partial servers［J］. Journal of Systems Science and Mathematical Sciences， 2022， 42（5）： 1282-1299.
[16]	孙微，王豪，李世勇. 部分服务员休假的M/M/c排队系统中的顾客行为及定价策略研究［J］. 系统工程理论与实践， 2022， 42（3）： 767-777.
	Sun W， Wang H， Li S Y. Customer behavior and pricing strategy in the M/M/c queue with vacations of partial servers［J］. Systems Engineering-Theory & Practice， 2022， 42（3）： 767-777.