## 4 Application to Staffing Optimization of a Multi-Skill Call Center  
### A One-Period Multi-Skill Call Center  
Call centers experience a growing proportion of the world economy. A call center is a centralized office used for delivering a large volume of enquiries by telephone, e-mail, chat and text [26; 27]. Call centers offer very labor-intensive tasks, employing over millions of people around the world. Call centers play an important role in managing communications in several fields such as the banks, care hotlines, insurance companies, telemarketing, information centers, help-desks and emergency centers. Call centers usually handle various types of calls discriminated by the necessary skills to deliver a service. However, it is impossible or cost effective to train all agents to handle every type of call. Each agent group has a specified number of skills. In a multi-skill call center, agents can handle different call-types multiple types of calls. The types of calls are classified based on the type of service requested, such as the spoken language and the perceived value of customers. Agents in a multi-skill call center may not be able to handle all the different types of calls that are served by the call center. A feasible alternative is to employ agents that can handle a subset of the call-types that are offered to the call center.  
There are three challenges faced by call center managers according to forecasts of call volumes: (i) Decide the number of agents for each type at different time periods of a day, (ii) arrange working schedules of available agents, and (iii) determine the call routing rules. Decisions are made in the face of some degree of uncertainty. For example, calls arrive randomly according to a stochastic process, waiting call possibly renegades after a random time, call durations are stochastic, and few agents may fail to work. The target of decision is usually to supply the required quality of service under least staffing cost. The common metrics for measuring quality of service is the service level. A service level is the fraction of calls answered within a certain time limit, in the long run, exceeds a given threshold. The recent literature on call center operations management has focused on the following concerns: quality of service, demand forecasting, call routing, capacity planning, staffing optimization and agents scheduling.  
Multi-skill call centers are complex systems which need to optimize the trade-off between the cost for the personnel and the service level provided to the calls. The goal of multi-skill call centers is to determine an optimal number of agents for minimizing the operating costs while satisfying the service level constraints. The staffing optimization problem belongs to a computationally expensive simulation optimization problem [28]. The discontinuity of the solution space is due to variables that must take an integer value. The large solution space causes the staffing optimization problem very hard to yield an optimal solution using the existing optimization approaches in a reasonable time. In addition, the inequality constraint extremely decreases the efficiency in the search processes. Accordingly, we focus specifically on two issues: (i) Transform the staffing optimization in a one-period multi-skill call center to a SICOP, and (ii) adopt the proposed EHOO approach to find an optimal number of agents such that the staffing cost is minimal and provide services at pre-specified levels.