Inventory Management Review: Service Capacity

December 14, 2005

Service Capacity

Considering the service sector of the United States' economy accounts for nearly 80% of the gross domestic product, I thought I would share my operations knowledge on the subject. After all, ample capacity is pretty closely related to ample inventory. That said, I'll start by explaining the benefits that inventory provides that the service sector can't take advantage of.

Storing work
Inventory is essentially stored capacity. If your plant can produce 100 units/hour then it's possible, depending on holding costs, that it should regardless of whether or not there is a customer waiting for the product at the end of the assembly line at the exact moment it comes off, so long as the firm thinks the products will eventually sell. This is great because you can schedule workers to assemble products at the most efficient rate possible. Services however are drastically different.

In services, the work often needs to be performed at the exact moment that the customer demands it. For example, if manufacture frozen food, you can store it as inventory until you have buyers. If however, you run a restaurant, you cannot have your waitstaff show up when they want and store their services for when the customer shows up. For every second that there is no demand for a service, time has been wasted. For every second that there is no demand for a physical good, well who cares, they can buy what you already made at a later date.

So how should services be scheduled?
The scheduling of services can be very tricky. You obviously don't want to have too much excess capacity because if you do, then you're paying for workers that you simply aren't using.

On the other hand, if your capacity is very high, and if customers show up randomly, which is very common in most services, then you're almost definitely making customers wait for a very long amount of time. This is because if capacity is very high, say around 90%, then there is almost definitely going to be periods of time when customers will have to wait.

Because customers show up randomly, there will be periods of time when capacity utilization is low. In order to bring up the average capacity utilization to 90%, then it will have to be very high during certain times of the day. The following example will help explain this situation:

Suppose you run a valet service for a hotel. You have determined that there are 2 types of car pickups: standard pickup which takes 5 minutes, and car pickups with luggage loading, which takes 10 minutes. Standard pickups account for 80% of the pickups and luggage loading pickups account for the remaining 20%.

In order to calculate the average time per guest, you need to take a weighted average of the pickup times. That is multiply the probability of the pickup type by the time of the pickup type and add them together:

(80%*5 minutes)+(20%*10 minutes)=6 minutes

On average, it takes a valet 6 minutes to get a car. This means that the valet can get 10 cars per hour.

Now, we wanted a 90% capacity utilization. So, if there are 18 guests per hour then we would need 2 valets to achieve the 90% capacity utilization that we discussed earlier (combined the valets can get 20 cars in an hour, so 18 cars in that hour divided by the 20 they are capable of is 90%).

Let's see what happens if we only have two valets:

First, everything could run smoothly and no one ever has to wait. There's a fundamental reason that this will not work. The only way this can work is if the guests arrive exactly when we want them to. For example, if the first two guests of the shift come in at exactly 3 pm and if one of them is a luggage guest and the other a regular guest, then everything is ok. Then, if the third guest comes in at exactly 3:05 then he won't have to wait because the first pickup, which was a 5 minute regular guest, just ended, so the valet is ready for another pickup. Continuing at this perfect rate, no one will have to wait and there is a 90% capacity utilization.

But what if the 4th guest comes in at 3:06? There won't be a valet available until 3:10 when the first luggage guest is finished being served. I hope the guest that came in at 3:10 won't mind that no one will start to get his car until 3:10 and that he won't be driving away until 3:15...probably should have parked his own car.

The point is, the service level provided to the guests is highly dependant upon the exact arrival of the guests. Additionally, it is dependant upon the exact time of each pickup. While the average pickup times may not deviate too much (and they don't as I've seen from my experience in the industry) sometimes you will get that 25 minute car pickup where the car won't start and then the guest has 30 bags he wants he needs help stuffing into his car. What do you do when that happens and all of the sudden 25 minutes worth of work gets dumped on one valet right when 3 other guests come down at once?

With such a high capacity utilization, there isn't much you can do. This high of a capacity utilization in such a time-sensitive business is just asking for trouble. If it truly is imperative that a customer will rarely have to wait, then capacity utilization cannot be 90%.

Time sensitivity
The more time sensitive a service, the lower the capacity utilization is. Even at 50% capacity utilization, there is still a fairly decent probability that a guest will have to wait. Consider if there were four valets instead of 2, making capacity utilization 45%. Is it so improbable that 5 guests could request their car to be picked up at the same time? Actually, it's fairly probable that this could occur. Imagine if 5 people were having lunch and they all drove seperately, or if a conference in the hotel gets out. The conference is an example of when 80% of your demand for an afternoon can come in within a 30 minute time period. That is, you may have 10 guests in an hour, but 8 of them may come in the first half hour.

So if something is truly time-sensitive, then capacity utilization needs to be set lower. A good example of this is 9-1-1. When you call 911, you need someone to pick up right away and you can generally get someone to pick up (depending on the state you live in, I understand Los Angeles has a little problem with this). Compare 9-1-1 with a customer service line for your cable company. Is there a reason why you always have to wait with a customer service line, but rarely have to wait with 9-1-1? Does 9-1-1 know some secret that customer service lines all of the country don't know about? No. 9-1-1's big secret is that their capacity utilization is under 20%. Lots of dead time. But this is what you've got to do if you want to be ready when the customers are. Services aren't physical, so you can't store them, and when you store extra capacity, you need to maintain constant excess capacity.

One final note before I wrap up and get back to my in-flight movie, customers don't give a damn about your average ability to service a customer. Generally, they concerned more with themselves than with averages. For example:

You run a barbershop and there are 3 different types of haircuts:
Buzzcuts: 7 minutes; accounts for 50% of business
Scissor Cut: 20 minutes; accounts for 30% of business
Shampoo, dye-job, and haircut: 80 minutes; accounts for 20% of business.

If you have three barbers when the shop opens. Your first 4 customers of the afternoon walk in when the shop re-opens after lunch. Three customers are seated right away, and one has to wait. How long is the 4th customer going to have to wait to be served?

First thing you're probably tempted to do is figure out the weighted average of the types of haircuts. If you do this, you will find that the average haircut takes 25.5 minutes. {=(0.5*7)+(0.3*20)+(0.2*80)}

So you it looks like the customer will have to wait this long. Well, on average, you would expect a customer to wait this long. But like I said, customers don't give a damn about the average. What he wants to know is how long he is going to wait. Considering NONE of the haircut types offered at this barbershop are 25.5 minutes, then I am having a hard time figuring out how the 4th customer would have to wait that long.

Instead, the customer will wait as long as he needs to (unless he leaves) until 1 and only 1 of the customers in front of him is finished being served.

He will either wait 7 minutes, or 20 minutes, or 80 minutes because these are the different types of haircut times that have the possible of actually happening. So whoever in front of him is having the shortest haircut will finish and then he will be up. For example if one person is getting a buzzcut, it doesn't matter what the others are getting because when the buzzcut finishes in 7 minutes, he's up.

The probably that he will wait 7 minutes is very high (87.5%). Because in order for him to wait longer than that, all three of the customers in front of him will have to get a non-buzzcut which is 50% of their business.

The probability that he will have to wait 20 minutes is the next highest (11.7%), and the probability of him waiting 80 minutes is by far the lowest (.8%). Of course, this is with only 4 customers. As the line gets longer, the odds that there will be 3 dye-jobs in front of customer begin to grow.

I hope that these examples have provided some insight regarding the complexities of scheduling services. If you would like additional help or further specificity regarding how I calculated certain probabilities, please leave a comment with your email address, or email the author.

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December 14, 2005 | Permalink