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Call Center Optimization for Staffing


The Challenge

Minimize the total daily personnel expenses, satisfying a certain service level target for expected number of incoming calls.

The Arena Solution

The procedures to seek the optimal solution can be itemized as follows:

  1. Obtain an initial feasible solution via integer linear programming, as described in section 3.2.
  2. Obtain a better feasible solution by modifying recesses for each agent by applying the proposed method as described in section 3.3.
  3. Obtain an optimal solution in terms of the minimum number of selected agents by performing simulation together with constrained direct-search methods, as described in section 3.4. The recesses for each agent should be modified before performing simulation.
  4. Repeat Step 3 for all designated agents in turn. 


A simulation model of an inbound call center of a city-gas company was constructed and used to examine the service level target. A special-purpose system was designed and produced to modify the planned recesses of the agents to meet the frequency of customer calls.

A stepwise procedure of operations planning was proposed to minimize the total daily personnel expenses, by performing a simulation together with integer programming and the constrained direct-search methods. The initial solution was obtained by solving the integer programming problem, and the service level was evaluated by performing the simulation. It is found that the proposed procedure is applicable and effective to the real situation. 

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An inbound call center of a city-gas company was simulated to examine the proper target of the service level procedures were proposed to find the optimal number of agents, considering their skills and the scheduling of the agents to meet the frequency of customer calls. First, integer programming was adopted to obtain an initial feasible solution. Second, a special-purpose system was designed and developed to modify planned recesses for each agent. Then, optimal solutions were obtained by performing simulation together with direct-search methods. The proposed procedure was applied to a real case in order to confirm its effectiveness. 

Call-center managers wish to improve call-center performance, and need powerful decision-making tools to visualize, analyze, and enhance call-center business processes. The best tools available today to perform these functions are simulation tools (Anton, Bapat, and Hall 1999). Several studies have focused on various issues concerned with call centers. For example, large call-center models were modeled and analyzed by Tanir and Booth (1999). Performance was measured within the call center at the service level, which was defined as the percentage of customers served within some fixed time period, known as the service level target. The issue of service level was treated based on the length of the processing time in research by Klunge (1999). Both inbound and outbound calls were treated and analyzed from the standpoint of the agents skill by Mehrotra and Fama (2003) and Pichitlamken et al. (2003). Henderson and Mason (1998) proposed that simulation modeling in conjunction with integer programming be used for staff allocations. Analysis on skillbased routing has been made for online routing of incoming calls (Koole et al. 2003; Mazzuchi and Wallace 2004). Furthermore, a manager-friendly platform for simulation modeling was introduced by utilizing Excel spreadsheet (Saltzman and Mehrotra 2004).