Manzana insurance process flow diagram

Variability and Variability Management

Instructor: Mani Lakshmanan

Variability in Various Contexts

Inputs

Outputs

Transformation

Resources: Capital, Labor

Customers that look for service

Arrival time

Request (Service type)

Customers’ demand for a product

Quantity

Product character

Providing service

Service time

Quality (satisfy customers’ request)

Producing products

Production time (Equipment/Labor availability)

Quality (meet standard)

Not constant over time

Talk something about input variability: wet vs. dry berries, horizontal / vertical heterogeneity of customers

2

Outline

Two types of variability

Predictable and Stochastic

Variability’s impact on the system

Waiting

Throughput Loss

Variability Management

Two Types of Variability

Predictable

A regular or predictable pattern over time

Seasonal demand trend for electricity, pumpkins…

Random (Stochastic)

No discernible pattern

Unknown until it realizes

Two Types of Variability

Compare the following two statements:

(A restaurant manager) We expect more customers coming for Friday / Saturday dinner compared with other days.

(A restaurant manager) On average, we serve 200 customers each day at dinner time. However, we have no idea on the exact number of customers that will arrive today.

Examples of Predictable Variability

Industry Predictable Variability
Restaurant
Cranberry Production
Police Department
Tourism Attractions
Smartphone production
Daily, Seasonally, etc…

Seasonally

Weather, holiday

Seasonally

Increasing

Two Types of Variability

Guess: which one is worse for a process, Predictable or Stochastic?

Process can be carefully planned and designed for predictable variability

For stochastic variability, little can be done except for acknowledging it…

Point out that the inventory build up diagram is related to predictable variability

7

Learning Goals

Two types of variability

Predictable and Stochastic

Variability’s impact on the system

Waiting

Throughput Loss

The benefit and cost of buffering

An ATM with Stochastic Customer Arrivals

Based on earlier “static process analysis”, what will happen if:

Demand rate = ? /min

Capacity rate = 15/min

What will happen with variability?

ATM

Line

Talk about simulation here

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Variability Leads to Waiting

The average person spends 5 years waiting in line!!

Call center

Grocery stores

Theme parks

Emergency room

Office Hour

Etc…

A main source of service dissatisfaction

© 1995 Corel Corp.

Thank you for holding. Hello...are you there?

Why Do Queues Form?

A fantastic ATM:

Customer arrives exactly every 5 min.

“Sorry, 4 minutes are over, the ATM is closing for your session, thanks!”

No waiting, but so unrealistic…

customer 1

customer 2

customer 3

customer 4

customer 5

customer 6

customer 7

customer 8

customer 9

customer 10

customer 11

customer 12

7:00

7:10

7:20

7:30

7:40

7:50

8:00

Time

Why Do Queues Form?

7:00

7:10

7:20

7:30

7:40

7:50

Inventory

(customers in system)

5

4

3

2

1

0

8:00

customer 1

customer 2

customer 3

customer 4

customer 5

customer 6

customer 7

customer 8

customer 9

customer 10

customer 11

customer 12

7:00

7:10

7:20

7:30

7:40

7:50

8:00

Wait time

Service time

Time

Most customers wait considerable amount of time; service quality hence not consistent

Long queues to hold (Little’s Law)

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Lessons from the ATM

Service happens only when capacity and demand are available at the same time

Capacity can never “run ahead” of demand

Demand, however, can never “run ahead” of capacity: Queue

Queues form from variability

Customer arrival variability

Service time variability

Pollaczek-Khinchin (PK) Formula

PK Formula for 1 server:

r is long-term utilization (not theoretical)

Ca is coefficient of variability for arrivals

( = standard deviation of interarrival time / average interarrival time)

Cs is coefficient of variability for service

( = standard deviation of service time / average service time )

utilization effect

variability effect

inventory in queue

I think this is a great place to introduce PK formula to you. PK formula, if you only look at its formulation, is quite complicated. But when you understand its implication, it is very intuitive. PK formula, actually, is composed by three parts, just as Little’s Law. The first part is on the left hand side of the equation. Capital I sub q, which means inventory in queue. What does this queue mean? I will not talk about its details today, which will become clear to you after Wednesday’s class. What you need to remember is that the first component in PK formula is the inventory, the WIP before your system or workstation, or the goods you need to prepare before hand.

The other parts are on the right hand side of the equation. First of them is this part, which characterizes the utilization effect. This Greek letter rho here stands for the long-term utilization. Rho here is what we call utilization rate, measuring what fraction of time is occupied, is busy. So, in some sense, it is the efficiency we talked before. But still this rho is about the relative capacity compared to the demand. When demand rate is given, the higher the capacity rate, the lower the rho, the utilization. In fact, one fundamental requirement for PK formula to be valid is that in our system, the long term average demand rate is smaller than the long term average capacity rate. In such a system, although there are some moments that inventory will grow up, eventually, all the arrived demand will be processed completely. That is, the inventory will never grow out of control. We call such a system as the stable system. On the opposite, when the average demand is bigger than the average capacity rate, as time goes on, the inventory in your system is more and more, and can reach infinity. We call such a system unstable system. PK formula can only be applied to a stable system.

Now the last part in PK formula is this one, which describes the variability effect. We have this C sub a for the variability in demand, and this C sub s for the variability for process. This sub a stands for arrivals, and sub s for service. Why do we use these terminology? Also what does it mean by PK formula for 1 server? All those questions will be addressed in the next class. I won’t spend time on it right now.

What you need to understand today is that what is the implication of PK formula. It is, PK formula shows that inventory is driven by both utilization and variability. If we have no variability at all, what will be our inventory? Zero. Does this make sense? Remember what is the prerequisite for using PK formula? Average demand is smaller average capacity. If there is no variability in both demand and capacity, then what are those average numbers equal to? The moment demand and the moment capacity. So average demand smaller means exactly at every moment demand is smaller. OK, will we see inventory in such scenario? No. PK formula shows that when variability increases, inventory is increasing correspondingly. How about the utilization effect on inventory? Similar amplifying effect. Why? Let us see how will the utilization effect part behaves to the value of rho. As rho increases, this part will have this increasing shape. Consequently, our inventory will increase again, right? So, this is our PK formula.

Variability + Utilization = Waiting

Synergy between variability and utilization:

Theoretical

Flow Time

Actual

Average

Cycle

Time,

W

Utilization

r

100%

Actual (average)

flowtime, T

variability

Put it in another way. It just means that variability and utilization together will contribute to the long waiting. Graphically, let us show the relationship between the throughput and delay. Remember we now only consider the stable system, so demand rate is smaller than capacity rate. Our throughput rate is equal to demand rate. Given capacity rate, as demand rate increase, we will have utilization increase. So, we label the x-axis by utilization rho. For y-axis, it is ok for us to use actual flow time, since the delay is included in it.

If there is no variability, since utilization is smaller than 100%, there is no inventory shown up, no delay. The actual flow time is exactly equal to the theoretical flow time. But when there is variability, for a given utilization, we can find the inventory shown up, delay appeared. The actual flow time is longer than the theoretical flow time. So, in a variable system, the average cannot tell the whole story. In this case, average demand is smaller than the average capacity rate, but due to variability, inventory still occurs.

On the other hand, if we check the effect of utilization, we can find that the bigger the utilization, the longer the actual flow time. And such zooming effect is non-linear. This is a graphic presentation of PK formula.

Outline

Two types of variability

Predictable and Stochastic

Variability’s impact on the system

Waiting

Throughput Loss

Variability management

A Restaurant with One Seat

Customers have so many other choices!

Go home

Go competitors’

Lucky Express:

Seat

Empty?

Full?

Variability Leads to Throughput Loss

Healthcare: “diversion status”

When lacking staffing or facilities to accept additional emergency patients.

Direct en route ambulances to other hospital

DVD renting

Demand loss when a specific movie is out of stock.

Call center in the old days:

Maximum number of calls that can be on hold

No chance for classic music if all occupied (busy signal)

20% of US hospitals are on diversion status for more than 2.4 hours per day

Variability Leads to Throughput Loss

Throughput Rate assuming no demand loss:

Assuming demand loss:

7:00

7:10

7:20

7:30

7:40

7:50

8:00

Customer 1

Customer 2

Customer 3

Customer 4

Customer 5

With

Loss

Customer 1

Customer 2

Customer 3

Customer 4

Customer 5

Without

Loss

5 customer/hour

3 customer/hour

leave

leave

Why throughput is important?

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Variability in Various Contexts

Inputs

Outputs

Transformation

Resources: Capital, Labor

Customers that look for service

Arrival time

Request (Service type)

Customers’ demand for a product

Quantity

Product characters

Providing service

Service time

Quality (satisfy customers’ request)

Producing products

Production time (Equipment/Labor availability)

Quality (meet standard)

Talk something about input variability: wet vs. dry berries, horizontal / vertical heterogeneity of customers

20

Outline

Two types of variability

Predictable and Stochastic

Variability’s impact on the system

Waiting

Throughput Loss

Variability Management

Variability Management

How to reduce customers’ waiting time and/or throughput loss?

Reduce variability

Increase capacity

?

Buffering

This OM triangle. We have capacity, variability reduction, and inventory to take one corner of a triangle. This exactly means the substitutable relationship between them three.

What is a Buffer?

Buffer in a car:

Make our driving smooth

Think about driving a car without a buffer…

Buffer (The spring)

Ground: The demand

Car: The system

Buffering: Good or Bad?

The most usually seen buffer is inventory

Queue of demand

Final products

Good:

Preventing throughput loss

Bad:

Inventory cost: both space and inventory itself

long flow time: slow responsiveness

OM Triangle

Capacity

Inventory

Variability

reduction

Capacity, inventory, and variability reduction (information) are substitute ways to satisfy customers’ demand for products/services.

Queuing Analysis

Case IV: Manzana Insurance

Quality and Six Sigma

House Building Game

Lean Operations and TPS

Newsvendor Problem

Economic Order Quantity

Case V: Blanchard Importing and Distributing

Bear Game and Bullwhip effect

Demand Forecast

Demand management

This OM triangle. We have capacity, variability reduction, and inventory to take one corner of a triangle. This exactly means the substitutable relationship between them three.

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2

12

as

q

CC

I

r

r

+

=

-