Joint Shift Scheduling Method for Call Center with Mechanism of Delay Information

doi:10.16182/j.issn1004731x.joss.21-0273

Abstract

Abstract:

A joint shift scheduling method is studied for call center with delay information. According to the queue model of call center with delay information, the influence rule of the customer's patience and abandonment behavior is addressed, and a mechanism of delay information is proposed to estimate the waiting time of customers. Considering the influence of non-stationary arrival and other factors, the scheduling model of the call centers is established by the discrete Event-Scheduling approach. Based on the proposed evaluation method of delay information, the joint shift scheduling method by simulation optimization is designed to solve the scheduling problem with improved genetic algorithm. Based on the actual operation data of a call center, a comparative analysis with the traditional two-stage method is conducted to verify the superiority and significant application value of the proposed method for solving the scheduling problem.

Key words: delay information, simulation optimization, two-stages method, joint scheduling method, improved genetic algorithm

CLC Number:

N945

Miao Yu, Manru Li, Yu Zhao. Joint Shift Scheduling Method for Call Center with Mechanism of Delay Information[J]. Journal of System Simulation, 2022, 34(7): 1651-1661.

Figures/Tables 13

Fig. 1

Table 1

Fig. 2

Fig. 3

Fig. 4

Table 2

Related experimental parameters

重拨概率	接受服务概率约束值/%	服务率	初始耐心时间参数	新耐心时间参数	直接放弃率	重拨延迟	种群规模	交叉概率	变异概率	保留精英个体数目
$τ$	$l$	$μ$	$γ$	$γ'$	$α 0$	$δ$	$n$	$p c$	$p m$	$s$
0.2	85	0.5	0.8	0.26	0.05	0.5	100	0.65	0.25	30

Table 2

Fig. 5

Fig. 6

Fig. 7

Table 3

Comparative analysis between two-stages method and joint scheduling method

$λ ¯$	方法	4个班次			6个班次			10个班次
$λ ¯$	方法	$Δ p s / %$	$Δ t p$	$Δ x$ $/ %$	$Δ p s / %$	$Δ t p$	$Δ x$ $/ %$	$Δ p s / %$	$Δ t p$	$Δ x$ $/ %$
1	两阶段	0	0	-8.33	0	0	-6.25	0	0	0
1	联合	0	0	-8.33	0	0	-6.25	0	0	0
3	两阶段	0	0	-7.14	0	0	-5.41	0	0	0
3	联合	0	0	-7.14	0	0	-5.41	0	0	0
5	两阶段	1.39	1	0	1.42	1	-3.5	1.84	1	0
5	联合	0	0	0	0	0	-3.5	0	0	0
7	两阶段	2.01	2	-1.72	3.36	3	0	3.16	2	5.45
7	联合	0	0	-1.72	0	0	0	0	0	5.45
9	两阶段	3.67	3	-1.369	4.32	3	1.06	4.77	3	4.29
9	联合	0	0	-1.369	0	0	1.06	0	0	4.29
11	两阶段	1.05	2	0	4.52	3	2.65	4.85	3	5.95
11	联合	0	0	0	0	0	2.65	0	0	5.95
13	两阶段	1.43	2	0	5.83	3	3.03	6.15	3	9.09
13	联合	0	0	0	0	0	3.03	0	0	9.09
15	两阶段	1.38	2	0	7.03	3	1.32	6.96	3	7.96
15	联合	0	0	0	0	0	1.32	0	0	7.96

Table 3

Fig. 8

Fig. 9

Fig. 10

References 16

1	Kim J, Randhawa R S, Ward A R. Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems[J]. Manufacturing & Service Operation Management (S1523-4614), 2018, 20(2): 285-301.
2	Yu M, Tang J F, Kong F W,et al. Fluid Models for Call Centers with Delay Announcement and Retrials[J]. Knowledge-Based Systems (S0950-7051), 2018, 149(1): 99-109.
3	宫俊, 贾倩倩, 张家生, 等. 呼叫中心人力资源配置鲁棒规划模型[J]. 东北大学学报, 2018, 39(1): 21-25.
	Gong Jun, Jia Qianqian, Zhang Jiasheng, et al. Robust Program Model of Human Resource Management for Staffing Call Centers[J]. Journal of Northeastern University, 2018, 39(1): 21-25.
4	于淼, 李丹丹, 宫俊. 到达不确定呼叫中心人员配置的鲁棒优化模型[J]. 运筹与管理, 2018, 27(6):107-114.
	Yu Miao, Li Dandan, Gong Jun. Robust Optimization Model for Staffing Call Centers with Uncertain Arrival Rates[J]. Operations Research and Management Science. 2018, 27(6):107-114.
5	Atlason J, Epelman M A, Henderson S G. Optimizing Call Center Staffing Using Simulation and Analytic Center Cutting Plane Methods[J]. Management Science (S0025-1909), 2005, 54(2): 295-309.
6	李曼茹. 考虑顾客行为的呼叫中心排班问题的仿真与优化研究[D]. 沈阳: 东北大学, 2015.
	Li Manru. Simulation and Optimization of Shift Scheduling in Call Centers Based on Customer Behavior [D]. Shenyang: Northeastern University, 2015.
7	Bergantios G, Gómez-Rúa M, Llorca N, et al. Allocating Costs in Set Covering problems[J]. European Journal of Operational Research (S0377-2217), 2020, 284(3): 1074-1087.
8	胡修武, 王瑞程, 王秀利. 考虑班种约束的呼叫中心排班优化模型与算法[J]. 工业工程与管理, 2020, 25(2): 51-66.
	Hu Xiuwu, Wang Ruicheng, Wang Xiuli. Model and Algorithm for the Shift Scheduling and Rostering Problem of Call Centers with Shift-Type Constraints[J]. Industrial Engineering and Management, 2020, 25(2): 51-66.
9	Thompson G. Improved Implicit Optimal Modeling of the Labor Shift Scheduling Problem[J]. Management Science (S0025-1909), 1995, 41(4): 595-607.
10	Lvarez E., Ferrer J.C., Muoz J. C., et al. Efficient Shift Scheduling with Multiple Breaks for Full-time Employees: A Retail Industry Case[J]. Computers & Industrial Engineering (S0360-8352), 2020, 150: 106884.
11	Ingolfsson A, Haque M A, Umnikov A. Accounting for Time-varying Queueing Effects in Workforce Scheduling[J]. European Journal of Operational Research (S0377-2217), 2002, 139(3): 585-597.
12	Bhulai S, Koole G, Pot A. Simple Methods for Shift Scheduling in Multiskill Call Centers[J]. Management Science (S0025-1909), 2008, 10(3): 411-420.
13	李军祥, 藏万斌. 基于耐心阈值下联络中心放弃率的仿真研究[J]. 系统仿真学报, 2021, 33(1): 169-179.
	Li Junxiang, Zang Wanbin. Simulation Research on Abandonment Rate of Contact Center Based on Patience Threshold[J]. Journal of System Simulation, 2021, 33(1): 169-179.
14	Ibrahim R. Managing Queueing Systems Where Capacity is Random and Customers are Impatient[J]. Production and Operations Management (S1059-1478), 2018, 27(2):234-250.
15	于淼. 考虑延迟提醒的呼叫中心排队系统建模及人员配置方法研究[D]. 沈阳: 东北大学, 2016.
	Yu Miao. Modelling of Queueing Systems and Staffing for Call Centers with Delay Announcements[D]. Shenyang: Northeastern University, 2016.
16	王吉权, 程志文, 张攀利, 等. 求解有约束优化问题的实数遗传算法改进研究[J]. 控制与决策, 2019, 34(5):937-945.
	Wang Jiquan, Cheng Zhiwen, Zhang Panli, et al. Research on Improvement of Real-coded Genetic Algorithm for Solving Constrained Optimization Problems[J]. Control and Decision, 2019, 34(5): 937-945.

班次	工作时间	班次	工作时间
1	09:00—12:00，13:00—16:00	6	14:00—17:00，18:00—21:00
2	10:00—13:00，14:00—17:00	7	09:00—13:00，14:00—18:00
3	11:00—14:00，15:00—18:00	8	10:00—14:00，15:00—19:00
4	12:00—15:00，16:00—19:00	9	11:00—15:00，16:00—20:00
5	13:00—16:00，17:00—20:00	10	12:00—16:00，17:00—21:00

[1]	Jia Xu, Fengqing Han, Qixin Liu, Xiaoxia Xue. Bioinformation Heuristic Genetic Algorithm for Solving TSP [J]. Journal of System Simulation, 2022, 34(8): 1811-1819.
[2]	Fei Ye, Ziqing Li, Yuanjun Laili. Simulation Optimization on Joint Production and Preventive Maintenance Scheduling for Distributed Job-shop [J]. Journal of System Simulation, 2022, 34(4): 688-699.
[3]	Cong Jiping, Cui Lijie, Ding Gang, Ren Bo. Simulation on Aviation Maintenance Support System Based on Goal-driven [J]. Journal of System Simulation, 2021, 33(9): 2157-2165.
[4]	Luo Yongliang, Zhang Zhihui, Zhang Jun, Qin Yuanhui. Simulation Optimization Design Method of Model Driven Aviation Command and Support System [J]. Journal of System Simulation, 2018, 30(8): 2817-2825.
[5]	Zhang Yu, Cheng Huimin, Xu Jin, Tian Wei, Sun Junfeng. Simulation Optimization on Multi-Ports Slot Plan Problem Considering Dispatching Sequence of Containers in Yard [J]. Journal of System Simulation, 2018, 30(3): 831-839.
[6]	Wang Xianlun, Yu Yang, Cui Yuxia. Research on Robot Processing Path Optimization for Multi-contour [J]. Journal of System Simulation, 2017, 29(2): 355-359.
[7]	Wang Dayong, Wang Hui. Study on Comprehensive Performance of Roadheader Shovel Based on Simulation Optimization Method [J]. Journal of System Simulation, 2016, 28(2): 434-441.