Wyean Chan

Optimizing daily agent scheduling in a multiskill call center

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 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.

Dynamic Call Center Routing Policies Using Call Waiting and Agent Idle Times

We 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.

Speeding up call center simulation and optimization by Markov chain uniformization

Staffing and scheduling optimization in large multi-skill call centers is time-consuming, mainly because it requires lengthy simulations to evaluate performance measures and their sensitivity. Simplified models that provide tractable formulas are unrealistic in general. In this paper we explore an intermediate solution, based on an approximate continuous-time Markov chain model of the call center. This model is more accurate than the commonly used approximations, and yet can be simulated faster than a more realistic simulation (based on non-exponential distributions and additional details). To speed up the simulation, we uniformize the Markov chain and simulate only its discrete-time version. We show how performance measures such as the fraction of calls of each type answered within a given waiting time limit can be recovered from this simulation, how to synchronize common random numbers in this setting, and how to use this in the first phase of an optimization algorithm based on the cutting plane method. We also discuss various implementation issues and provide empirical results.

New history-based delay predictors for service systems

We are interested in predicting the wait time of customers upon their arrival in some service system such as a call center or emergency service. We propose two new predictors that are very simple to implement and can be used in multiskill settings. They are based on the wait times of previous customers of the same class. The first one estimates the delay of a new customer by extrapolating the wait history (so far) of customers currently in queue, plus the last one that started service, and taking a weighted average. The second one takes a weighted average of the delays of the past customers of the same class that have found the same queue length when they arrived. In our simulation experiments, these new predictors are very competitive with the optimal ones for a simple queue, and for multiskill centers they perform better than other predictors of comparable simplicity.

Two-stage chance-constrained staffing with agent recourse for multi-skill call centers

We consider a stochastic staffing problem with uncertain arrival rates. The objective is to minimize the total cost of agents under some chance constraints, defined over the randomness of the service level in a given time period. In the first stage, an initial staffing must be determined in advance based on imperfect forecast of the arrival rates. At a later time, when the forecast becomes more accurate, this staffing can be corrected with recourse actions, by adding or removing agents at the price of some penalty costs. We present a method that combines simulation, mixed integer programming, and cut generation to solve this problem.

Chance-constrained scheduling with recourse for multi-skill call centers with arrival-rate and absenteeism uncertainty

We consider a chance-constrained two-stage stochastic scheduling problem for multi-skill call centers with uncertainty on arrival rate and absenteeism. We first determine an initial schedule based on an imperfect forecast on arrival rate and absenteeism. Then, this schedule is corrected applying recourse actions when the forecast becomes more accurate in order to satisfy the service levels and average waiting times constraints with some predefined probabilities. We propose a method that combines simulation with integer programming and cut generation to solve the problem.