In the module of Customer Choice and Product Variety, we already introduced one

tool that helps us tame the evil forces of variability.

We introduced the concept of pooling. The purpose of this session is to help you

think about pooling benefits in the context of waiting time problems.

We will use our waiting time formula to estimate savings in terms of waiting times

that you can achieve, by introducing pooling to your service.

We will talk about some practical examples, and explore the main benefits

and costs that are associated with pooling in waiting time problems.

Consider the following two process layouts.

In the first example, option number one, I have two waiting lines for two doctors or

for two servers. People that come to this server have to be

served by this server. And people who come to the other server

have to be served by the other server. Contrast this with the example of a pooled

service. In the pooled service, no matter from

where you come in, you're going to get served by whoever is available next.

Which one will have the shorter waiting times.

Most of us I think have an intuition that this process here will have a better

waiting time. I would argue the intuition behind it,

goes something like follows. In the example up here, you might end up

in a situation where we have a lot of people waiting in the upper case, and you

have a doctor idle here in the lower case. As a result of that, that cannot be

efficient, and that's what this pooling addresses in this system down here.

Now, let's understand how this relates to our waiting time formula.

First and foremost, let's see how it influences utilization.

Recall that utilization is P divided by a times m.

You know, example here, we have, again, customers come in every four minutes, and

the inter-arrival time is five minutes, with m equals one, we simply get four

divided five equals to 80%. Now, how does it look down here if I pool

two such systems? I have no impact on the processing time,

however, I have now a shorter inter-arrival time.

I here had twelve customers arrive per hour.

If I pool, I have to have 24 customers per hour showing up.

So, pooling at least two similar systems, I move from twelve to 24 customers per

hour. Meaning an enter arrival time from five

minutes to 2.5. And notice often times students get

confused on this point. A shorter enter arrival time means more

demand. Finally, I have an m2, equals two, m2,

equaks two, p4, equals four, a2.5. Equaks 2.5, if I plot this into the

formula, p divided by a times m. I'm going to get a utilization of four

divided by two times 2.5 and voila, it's the same 80% as I had before.

So, pulling in it by itself, actually does not change the utilization but it will

impact the waiting time. Let's try this out on our Excel

spreadsheet. I'm using the same Excel spreadsheet that

I used in the last session, where you have P, as the processing time, inter-arrival

time, number of servers, CVas CVps, the utilization as defined by P divided by a

times m, and finally, the actual waiting time.

Alright, now let's take a look. Processing time stays unchanged.

Inter-arrival times, if I basically pool two similar servers with the same demand

wait together, I cut the inter-arrival time in half.

However, the server capacity doubles because I'm moving from m equals one to m

equals two. And everything else is a matter of

calculation. Notice as we saw on my calculations on the

previous slides, the utilization does not change, yet the time in the queue does.

The average time in the queue goes down from sixteen minutes to 7.2 minutes.

This is the power of pooling applied in queing.

Let me point out though that when you pool, you don't necessarily have to assume

that the inter-arrival times are going to be exactly identical, and so that the new

inter-arrival times are simply cut in half, or generally, the way that you're

going to figure out new enter arrival times is by just adding up the demand

rates and then dividing 60 minutes by the new demand rate in customers per hour and

that gives you the new enter arrival time. Early on this session, I discussed how the

utilization drives up the waiting time. We notice that as the utilization

approaches 100%,, the waiting time really goes through the roof.

I've taken the waiting time formula and I plug it in Excel and then I've entered

various level of utilization. So, this is the more exact graph that I

should have showed you early on the previous slide.

Now, what you notice here is that, as you're increasing the utilization,

Indeed, the waiting time goes up very steeply.

However, you notice that while for an m equals one already an 80% utilization is

quite a steep increase for every additional unit of utilization added.

At an m equals ten you can safely keep on adding.

Additional units of utilization. So, this is really the effect of pooling

at work. Pooled systems are much more able to be

loaded to very high volume without really experiencing a steep increase in the

waiting time. One nice way of illustrating this is

thinking about the tradeoff here when designing the service.

We have to balance the forces of responsiveness and efficiency.

Now, responsiveness means the service is responsive, as the time in the queue is

short. High time in the queue,

We would say the service is not responsive.

Efficiency we can proxy by utilization. High utilization is typically a more

efficient process than a low utilization. As we have seen previously by changing the

staffing plan by any more workers, I can move from to the lower right to the upper

left. So, a change in staffing extra m, number

of workers, will increase the responsiveness, but it comes at the

expense of the efficiency. Now, notice that when we pool the system

however, we keep the utilization constant and we're moving to a new frontier.

Now, oftentimes I get asked, what is a good utilization to have for service?

My usual academic answer is well, it depends.

If you run a fire truck, I'm not sure that you're comfortable running it at a 50%

utilization. The response time is simply too long,

given the urgency of the fire. On the other hand, if you're running the

local cable company and you're the only game in town, well, you can afford to run

a 99% utilization, have customers wait for three months for their cable TV but

there's really no threat of substitution. So, you notice again where you position

yourself on this line, there's no right or wrong.

That's a choice of strategy. Choose between being the fire truck.

It is up here, while the local cable company that us is down here.

Clever system design however, shifts the frontier and benefits you either way.

If pooling is really that great, why don't we pool everything?

Consider a company that is operating call centers in Germany, France, and Spain.

How about pooling? Well, the problem is that the Spanish

customer service representatives might have a hard time dealing with these German

customers. So, in other words, pooling really assumes

a form of flexibility that every resource is able to serve every customer.

That is a very strong assumption. Second, pooling also complicates the

workflow. The most prominent applications of pooling

have been with help desks and call centers.

Here we're dealing with digital workflows. Since transportation is cheap in the

digital world, pooling around the globe is very simple.

However, you obviously do not want to pool the primary care capacity of a healthcare

operation that has facilities in Philadelphia and Pittsburgh, it's a little

too far to drive five hours to see your primary care physician.

This gets to another disadvantage of pooling.

Pooling really interrupt a continuity of interaction between the flow unit, the

customer, and the resource. Do you really wanna be seen by different

doctor every time or talk to different agent in your bank every time that you

come? Pooling is assumed that you're going see

whoever is available next, not whoever you're used to serving.

This can hurt the customer experience but it can also lead to additional setup

times. Because the person who was serving and who

has never served you in the past, might just not be as efficient as your usual

provider. Classic examples of pooling have been in

the area of healthcare, where we have seen a strong trend towards group practices and

larger healthcare systems instead of this solo doctor offices that we saw 50 or 100

years ago. One of the hottest areas of work right now

is in the energy field. The problem of pooling is that the supply

and demand of energy, it varies wildly across the country.

So, if we're able to pool through a smart grid, our electricity, we're going to be

able to get much higher utilization levels and still provide the same quality of

service. Notice the idea of partial pooling that we

talked about in the context of flexibility and production plans.

We talked about how in the automotive industry, some companies including Nissan,

have been able to really, instead of having every plant be able to produce

every vehicle, be able to have every vehicle be produced in two plant, so that

we can get almost all the benefits of pooling without paying all the cost.

When I introduced the concept of pooling in the last module, I mentioned that

pooling is probably one of the greatest insights from the field of operations

management. The reason for that is pooling helps us

shift the frontier of the process. When we dealt with waiting time problems

through adjustments in the staffing plan, it was good, but it was simply walking up

and down the efficient frontier. We increased utilization to gain

efficiency but we decreased responsiveness and vice versa.

Pooling in contrast, lets us shift to frontier.

Pulling however, is not without cost. We have to make investment or sacrifices

to have this increased flexibility in the process.

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运营管理概论（中文版）

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