The Staffing Problem For Multi-skill Call Centers Based On Queueing Model

In the era of big data,the call center is closely related to everyone's daily life.The governments,social service agencies and enterprises are communicating with their customers through call centers.With the development of science and technology,the call center industry has developed rapidly,especially in multi-skill,which is the most important characteristic of the modern call center.Any call center wants to keep the customer satisfaction on an acceptable level with minimum costs,in the operating costs,the labor cost accounts for a large proportion,however,calculated the optimal agent number can greatly reduce labor costs.Therefore,the staffing problem becomes one of the issues that call centers concerned most.The research of staffing problem is to figure out how many agents with different skills are needed to meet a certain service level given the traffic volume.This paper is to study the staffing problem in N-design and M-design multi-skill call centers.The main work of this dissertation is summarized as follows:Firstly,the queuing models of the multi-skill call center in N-design and M-design are studied.A new state space division method is proposed,according to the different state of each agent groups,dividing the infinite number of system states into several finite state sets,and the state sets transfer diagram is given.The state-transition rates are obtained,and the equations for the steady-state probabilities of the system are established.Then,the steady-state probability of the state sets are calculated.On the basis of the above results,the computational formulas for the service level are obtained and a numerical example is also analyzed.Secondly,the staffing problem of multi-skill call centers in N-design and M-design is studied.Using the calculation formula of the service level,the staffing calculation model for optimal number of the agents in each groups is established,the model is a nonlinear integer program.With the characteristics of the model itself,the implicit enumeration method is adopted and Matlab software programming is applied to find the solution.At last,the effects of model's parameters on the results are also investigated through numerical examples,and the instance analysis is also given.Thirdly,the staffing problem of the multi-skill call centers in N-design and M-design with impatient customers is studied.It is necessary to consider the customer's impatience features in the model.Queuing model is also applied to figure out the performance of the system and the computational formulas of the service level.The staffing calculation model is established,and the model has been generalized to the case of many types of calls and multiple agent groups,and a heuristic algorithm-the ant colony algorithm is used to solve the staffing model.The algorithm process is analyzed,and Matlab software is used to programming.The effects of the impatient factors are also investigated through numerical examples,and the instance analysis is also given.Finally,the model of the multi-skill call centers in N-design and M-design model with delay information are studied,in which customers will be informed to wait a certain time upon their arrival.There are two types of calls in the model.For the model with infinite patience customers,the computational formulas to estimate virtual delays of the two types of calls is given.For the model with finite patience customers,a method based on Markov chains was applied to estimate how long customers need to wait,and the effects of the delay information on the staffing problem are also investigated through numerical examples.In conclusion,this paper studied the staffing problem of the current widely used multi-skill call centers.The main innovative achievements are as follows: For the multi-skill call center in N-design and M-design,the analytic calculation formulas of the service level are obtained,and the staffing calculation model for optimal number of the agents in each agent group is established,and the solution and analysis are given.Further more,the staffing problem of the multi-skill call centers in N-design and M-design with impatient customers is established and solved.In addition,the model of the multi-skill call centers in N-design and M-design with delay information is proposed,and the computational formulas to estimate virtual delays are obtained.The research in this paper enriched the theoretical achievements of the multi-skill call center,and it can provide some reference to the staffing problem of the actual call centers.