Sensitivity Analysis

By Ric Kosiba, Real Numbers

A Picture Paints a Thousand Words

The old adage is so true, even when it comes to math.

Last month, I was fortunate to present a session during the SWPP/CrmXchange virtual workforce management conference about how to use sensitivity analysis. I thought I would write about it here as well.

I learned about sensitivity analysis when I was in modeling school, learning to be a super model(er) (that’s a 30 year old joke). It is a simple and powerful concept: If you have an accurate capacity planning model of your operation, you can use it to do small experiments and draw out how your operation responds to changes in your performance drivers.

Here is an example. Say you want to know what will happen to your service levels if you hire more agents. You could try to build a statistical model that predicts the impact of additional headcount, but that data is messy enough that I’d doubt a statistical model would work well.

Instead, we should lean on our capacity planning model.

Pick a specific week or month. Ask your spreadsheet or system, how many bodies in chairs would you need to have on staff in order to get an 80/20 service level. Plot the result on a grap — 80 on the Y-axis, and the number of staff needed on the X-Axis. Then do it again, use the same volume and handle time and ask how many FTEs are required to get a 90/20. Then solve for a 95/20. Put each point on a graph.

Let’s go the other way. Ask your strategic planning spreadsheet how much staff would be required to achieve a 70/20? Then a 60/20. Continue using your cap planning tool at lower and lower service levels, on down to a 20/20. Put it all on a graph.

If you plotted it all, it would look something like Figure 1, below.

Figure 1. Sensitivity Analysis of Staffing Vs. Service Level.

Think of how enlightening this one graph can be for a decision-maker. If you wanted to know how many people you need at various service goals, this graph would tell you at a glance. If you knew that agent attrition was creeping up, you could use this graph to show you the possible impact. If HR suddenly dropped a huge training requirement on the operation, this graph could tell you how low service would drop while the team was in training. Is shrinkage starting to increase? This graph would show you the repercussions of more shrinkage.

Each Contact Center Really is Different

I’ve seen many of these graphs, describing hundreds of different contact centers. They all have the same general shape, but each graph will have different inflection points and different slopes on its curve. They all differ significantly, based on handle times, economies of scale, customer patience, arrival distributions, center efficiency, etc… One rule of thumb, that many of us know, is that small centers tend to have a much steeper service drop off than larger centers, when short-staffed. Their low economies-of-scale means that missing even a few agents has a huge service impact for a smaller center.

Let’s Look at a Few More Fun Graphs

A high-quality capacity planning process would also model your customer patience. If so, then you could also use it to draw a graph like Figure 2.

Figure 2. A Sensitivity Analysis of Staffing Vs. Abandonment Rate

Similar to Figure 1, the relationship between staffing and abandons will vary tremendously depending on your customer’s patience. For example, customers calling technical support tend to be very patient and will wait a long time before abandoning. Their curve will look very different than a run-of-the-mill customer service operation with impatient customers. This curve can help decision-makers understand how their staffing policies sit with your customer’s expectations for service. If they choose to staff the operation at a level that has high abandons, it likely will not be perceived as appropriate by their customers. Abandons are a great proxy for customer satisfaction.

Here is another fun sensitivity graph. In this graph, we vary staffing, keeping track of both service level and abandons, to see the relationship between the two outputs. Figure 3 tells us how many abandons we can expect at each service level achieved.

Figure 3. Service Level Vs. Abandon Rate

When choosing a service level goal, there are a few items to be aware of. Certainly, the cost of service is important (see Figure 4 below). But maybe, the next most important relationship is with callers abandoning. When you think about it, an abandoned call by definition is a dissatisfied experience. By balancing cost to service with abandons, you are choosing the number of upset customers.

Let’s look at cost to service in Figure 4.

Figure 4. Service Level Vs. Weekly Variable Labor Cost

This may be the single most useful graph for choosing a service standard. Of course, there are many considerations when choosing what your service level goals should be, your brand, the expected pace of work at various standards, your customer’s expectations, the competition’s reputation, etc. But cost is right up there. By plotting cost (a function of staffing) and service level, you can lay bare — again, at a glance — the relationship between your budget and the service you can afford.

I don’t know how you could really develop a goal without this simple tool.

Let’s close with Figure 5. In this graph, we plot agents staffed against calls handled per agent.

Figure 5. Sensitivity Analysis of Staffed Agents Vs. Calls Handled per Agent

Figure 5 is another take on agent efficiency. As the number of agents increase, the number of contacts answered per agent will necessarily decrease, as agent occupancy also decreases. There is simply more idle time per agent, and fewer calls to spread around. In effect, by choosing a staffing level, you are also choosing how busy all of your agents will be. Interesting?

Capacity Planning Models Can Do Much More Than Build a Plan

With one caveat, your capacity planning process can be used for a host of great analyses, like sensitivity curves. By creating sensitivity graphs for your decision-makers, you can present these and simply ask your team to choose the goals or staffing levels they prefer. You are drawing graphs that make clear the expected repercussions of their decisions. Cool, huh?

The caveat is, of course, that your capacity planning process is accurate. I believe I have written about validating your models in a past article, and will likely do it again in a future On Target. It is so important.

Ric Kosiba is a charter member of SWPP. He can be reached at ric@realnumbers.com or (410) 562-1217. Please know that he is *very* interested in learning about your business problems and challenges (and what you think of these articles). Want to improve that capacity plan? You can find his calendar and can schedule time with him at realnumbers.com. Follow him on LinkedIn! (www.linkedin.com/in/ric-kosiba/)