We examine and compare simulation-based algorithms for solving the agent scheduling problem in a multiskill call center. This problem consists in minimizing the total costs of agents under constraints on the expected service level per call type, per period, and aggregated. We propose a solution approach that combines simulation with integer or linear programming, with cut generation. In our numerical experiments with realistic problem instances, this approach performs better than all other 1 methods proposed previously for this problem. We also show that the two-step approach, which is the standard method for solving this problem, sometimes yield solutions that are highly suboptimal and inferior to those obtained by our proposed method.
Abstract. We address a multi-skill staffing problem in a call center where the agent skill sets are exogenous and the call routing policy has well-specified features of overflow between different agent types. Constraints are imposed on the service level for each call class, defined here as the steady-state fraction of calls served within a given time threshold, where calls that abandon after having waited for service less than the threshold are excluded. We develop an approximation of these service levels, allowing an arbitrary overflow mechanism and allowing customer abandonment.We then develop a two-stage heuristic that finds good solutions to mathematical programs with such constraints. The first stage uses search methods supported by the approximation. Because service-level approximation errors may be substantial, we adjust the solution in a second stage in which performance is estimated by simulation. We solve realistic problems of varying size and routing policy. Our approach is shown to be competitive with (and often better than) previously available methods.
International audienceWe study call routing policies for call centers with multiple call types and multiple agent groups. We introduce new weight-based routing policies where each pair (call type, agent group) is given a matching priority defined as an affine combination of the longest waiting time for that call type and the longest idle time or the number of idle agents in that agent group. The coefficients in this combination are parameters to be optimized. This type of policy is more flexible than traditional ones found in practice, and it performs better in many situations. We consider objective functions that account for the service levels, the abandonment ratios, and the fairness of occupancy across agent groups. We select the parameters of all considered policies via simulation-based optimization heuristics. This requires only the availability of a simulation model of the call center, which can be much more detailed and realistic than the models used elsewhere in the literature to study the optimality of certain types of routing rules. We offer a first numerical study of realistic routing rules that takes into account the complexity of real-life call centers
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