A call centre server allocation problem

  • by

Keith Royston (Probegroup) and Peter Taylor (The University of Melbourne)

In this session we shall discuss a real data-driven queueing problem faced by a call centre management company. The Excel spreadsheet [see below] gives data on callers who rang a call centre in each of 72 quarter of an hour periods from 6.00am until midnight on September 15, 2021.

There are four classes of enquiry Tier 0.5, Tier 1, Tier 2 and Tier 3, which roughly correspond to the complexity of the issue that the caller has. Servers with different skill sets handle the enquiries: Tier 0.5 enquiries can be handled by servers who have just started, while Tier 3 enquiries require the most knowledgeable servers.

For each Tier

(i)                 Vol gives the number of calls

(ii)                AHT gives the `average handle time’, the average service time of the calls listed in the Vol column

(iii)               ABN is the number of calls from those in the Vol column who abandoned their call before being served

(iv)               GOS gives the `grade of service’, the percentage of calls in the Vol column who were answered within 30 seconds. For the purposes of this exercise, abandoned calls are considered not to be answered within 30 seconds.

The total number of servers is given in STAFF, but the data does not tell us how many servers were allocated to each tier in each quarter of an hour period. 

The call centre generates a forecast of the arrival processes of calls in each tier using historical information and knowledge about forthcoming events that might affect call arrival rates. This forecast is plotted against the actual arrivals in the column.

The call centre has a service level agreement with its client that stipulates that its combined GOS over all tiers and all time periods, averaged over a month, should be 80%. For its own purposes, the company would like to achieve this GOS every day. That is, 80% of all calls in each day should be answered within 30 seconds. The combined GOS on September 15 was 79.87%.

The levers that the call centre managers can use to achieve this GOS goal are the overall staffing and the numbers of staff allocated to each tier, as well as the call allocation algorithm via which calls are allocated to tiers. Currently overall staffing levels are determined using the Erlang C formula and calls are allocated to the tier most appropriate to the enquiry (in an Interactive Voice Response (IVR), callers press numbers on their phone keypad (DTMF) to indicate what their enquiry is about). But if their call is not answered within 15 seconds and there are no available staff in the selected queue, the call is escalated to the next highest tier.

The broad question that the company would like to answer is: what staffing configuration would be needed to reliably achieve an 80% GOS each day and what is the best call allocation algorithm that would help them achieve this? 

The plan for the session is to have a discussion about the sort of strategies that could be used. Keith and I will answer any questions about the data. It would be great if delegates could attend the session with ideas to contribute.