| Scheduling: "The Relationship is Not Linear"
By Kay Khandpur
In these days of fierce competition and fickle customer loyalty, you certainly don't want to lose your customers because you kept them waiting on the telephones. What can you do about this? One of the most important solutions is to make sure you schedule your support reps correctly. Some of the art of scheduling is intuitive, but there are also important issues that depend on the mathematics of queuing theory. This article will explore a few basic concepts that play a role in how efficiently you schedule your staff.
In a typical call center, callers phone in to a single number and are routed to the next available support rep, drawn from a pool of similarly-skilled employees.
In such a queuing system, only three things can change: the number of calls coming in, the number of reps handling these calls, and the average time it takes to service each call. Some of the relationships between these three things and wait time are intuitively obvious: For example, the more support representatives you have, the faster you can answer the phone.
What's not so intuitive is how the average wait time varies when you change any of these three factors. The chart (above) shows what happens when staffing levels change in a fairly typical real-world call center (arrival rate of 50 calls/hour, service time of 10 minutes). As expected, the wait time decreases as the staffing level increases. But it's important to notice here that the relationship is not linear. In this situation, wait time
decreases significantly (from almost 12 minutes to about three minutes) when the staffing level goes from nine to ten people; by comparison, there is almost no change when staffing goes from 14 to 15 people.
The practical implications of this non-linear behavior are quite significant. Depending on where you are on the curve, putting a single additional support rep on the phones may have a dramatic effect on wait times, or virtually no effect at all. You may be able to use this chart to argue for additional headcount (or more likely to defend yourself against a "modest" cut in staffing). Another implication is that during peak periods, even a brief absence by one support rep will cause a dramatic deterioration in wait times...often beyond the point of possible recovery.
Another implication of this non-linear model is also not intuitive: that wait time increases as the pool of people available to take calls decreases. In other words, it's better to have as few queues as possible and to maximize the number of people who can service the calls coming into a single queue. Here's what happens to wait times when the number of queues in a typical call center is increased from one to four, with no other change in call volume or total staffing:
| Queues | 1 | 2 | 3 | 4 |
| Reps/Queue | 24 | 12 | 8 | 6 |
| Calls/Queue | 120 | 60 | 40 | 30 |
| Wait Time (secs) | 45 | 135 | 240 | 353 |
In this example, the call center gets 120 calls per hour and is staffed by 24 support reps, with an average service time of 10 minutes per call. With one queue, average wait time is 45 seconds. If we split the calls into two queues of 12 reps apiece, however, the wait time per call goes up to 135 seconds. And if we create four queues, wait time jumps to almost six minutes.
The important conclusion here is that call center performance doesn't just depend on how many reps answer the phones. The real improvement comes from how those reps are scheduled. With the right operational model, a call center can almost instantly improve its numbers with no additional staff, automation equipment, or training. And that's not a bad payback!
Navtej S. (Kay) Khandpur is the president of Practical Support & Service Techniques (Santa Clara, Calif.; 408/985-7604), a management consulting firm that specializes in tech support operations.
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