Optimizing daily agent scheduling in a multiskill call center

TLDR: This work examines and compares simulation-based algorithms for solving the agent scheduling problem in a multiskill call center and proposes a solution approach that combines simulation with integer or linear programming, with cut generation.

About: This article is published in European Journal of Operational Research.The article was published on 2010-02-01 and is currently open access. It has received 131 citations till now. The article focuses on the topics: Job shop scheduling & Integer programming.

Figures

Table 9: L52: results obtained with a target SL of 0.81

Table 1: Description of the 285 shifts for our examples

Table 4: Medium-sized center: skill sets

Figure 3: Medium-sized center: arrival rates

Figure 4: Small center: staffing solutions with 105, 267 and 285 shift types

Table 6: M2: results obtained with CP-LP and TS varying the CPU time budget

Frequently asked questions

Q1. What are the contributions in "Optimizing daily agent scheduling in a multiskill call center" ?

The authors examine and compare simulation-based algorithms for solving the agent scheduling problem in a multiskill call center. The authors propose a solution approach that combines simulation with integer or linear programming, with cut generation. In their numerical experiments with realistic problem instances, this approach performs better than all other 

Q2. What have the authors stated for future works in "Optimizing daily agent scheduling in a multiskill call center" ?

Future research on this problem includes the search for faster ways of estimating the subgradients, refining the algorithm to further reduce the noise in the returned solution, and extending the technique to simultaneously optimize the scheduling and the routing of calls ( via dynamic rules ). 

Q3. How many batches are used to collect statistics?

Each batch is constituted by a minimum number of 30 simulation time units and statistical observations are collected on a minimum of 50 batches, using 2 warmup batches before starting to collect statistics. 

Q4. How did the proposed algorithm solve a number of problem instances?

In order to assess the performance of the proposed algorithm, as well as the impact of flexibility on solutions, a number of problem instances were solved with the proposed algorithm and the two-step (TS) method. 

Q5. How do the authors replace the functions g?

Since the authors cannot evaluate the functions g exactly, the authors replace them by a sample average over n independent days, obtained by simulation. 

Q6. What are the main reasons for the SL constraints in call centers?

For certain call centers that provide public services, SL constraints are imposed by external authorities, and violations may result in stiff penalties (CRTC 2000). 

Q7. Why do the authors need to consider SL constraints for each call type?

This is motivated by the idea that the available shift types and the SL constraints may have a significant impact on the performance of the algorithm, as well as on the cost of the solution. 

Q8. What is the cost vector of an agent of type i with shift q?

A vector x = (x1,1, . . . ,x1,Q, . . . ,xI,1, . . . ,xI,Q)t, where xi,q is the number of agents of type i working shift q, is a schedule. 

Q9. What is the skill transfer variable for a type-i agent?

For each i and j ∈S −i and each period p, the authors define the skill transfer variable zi, j,p, which represents the number of type-i agents that are temporarily downgraded to type j during period p. 

Q10. What are the SLs for a given period?

Given acceptable waiting times τp, τk, and τ , the aggregate SLs are denoted by gp(y), gk(y) and g(y) for period p, call type k, and overall, respectively.