Master's thesis

Optimisation stochastique pour l'affectation du personnel polyvalent dans un centre d'appels téléphoniques

(Translation: Stochastic optimization of the staffing in multi-skill call centers)


Call centers occupy an undeniable place in our society, whether for customer services, purchases or sales. Following the technology advances, modern call center operations became more complex : multi-skill agents, inbounds and outbounds calls and skill-based routing policies. With the growing activity in the service sector, research advancement opportunities present great interest for the industry.

In this thesis, we present heuristic stochastic optimisation algorithms to minimize the staffing cost for a single period, a simplified version of the scheduling problem in workforce management. In contrast with the current literature, we suppose the call center manager operates with limited power such that the routing policy is fixed and he must assure a service level threshold for each call type and for the whole center.

The optimization via linear programming and simulation is based on subgradient based cuts, calculated by simulation. Starting with an infeasible solution, cuts are added until feasibility is reached. The linear problems are solved by an external library solver such as Cplex.

The randomized search is a neighborhood search within the feasible domain. Because of the high number of solutions that need to be evaluated, we developed a loss-delay analytic approximation based on continuous time Markov chain formulas.

The performance of our algorithms is competitive when compared through different examples. We present the sensitivities of different parameters for each algorithm and also the results of alternative variations.

Keywords: heuristic methods, linear optimization, randomized neighborhood search.

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