process analysis ii

12/27/2011

1

1

COMM 399 Logistics and Operations Management

Topic 4

Process Analysis (Continued)

1

2

Process Analysis: Review

• Process mapping basics – Key steps in process analysis – Get feedback and validate maps

• Process analysis basics (3 keywords)

2

Flow time (or Throughput Time): Length of time a unit spends in the system

Capacity rate: Max rate at which units can flow through a process

Bottleneck: Resource with the slowest capacity rate in a process Determines the capacity rate of a process

12/27/2011

2

3

Learning Objectives

• Discuss the Kristen’s Cookie Case

• More on Process Analysis

– Utilization and detailed Utilization Profiles

– Inventory Build-Up Diagram

– Little’s Law

3

4

Kristen’s Cookie Linear Flow Chart

4

Spoon Load Bake Mix Cool Pack Pay Unload

Hold

12/27/2011

3

5

Resources Activities

You

Roommate Oven

Oven

Roommate

Kristen’s Cookie Swim-Lane (Deployment) Flow Chart

5

Spoon

Load

Bake

Mix

Cool

Pack Pay

6

Kristen’s Cookie Discussions

• How long will it take to fill a rush order? • How many orders can you fill in a night (4 hours)? • How much of your own and your roommate’s

time will it take to fill each order? • Any discount for two-dozen orders? Will it take

you any longer to fill a two-dozen order than a one-dozen order?

• How many food processors? Baking trays? • Any change to the production plans? Bottleneck?

Another oven?

6

12/27/2011

4

7

More on Process Analysis

• Utilization and detailed Utilization Profiles

• Inventory Build-Up Diagram

• Little’s Law

7

8

Capacity Rate vs. Throughput Rate

• Both the capacity rate and the throughput rate measure the output rate of a process

8

Capacity rate: Maximum possible output rate

Throughput rate or Flow rate: Actual output rate

• The throughput rate depends on both:

Capacity rate

Input rate (also called the arrival rate) Rate at which flow units arrive at the process e.g. Arrival of customers (demand rate), or Raw material arrival into a factory (planned or scheduled arrivals)

12/27/2011

5

9

Basic Process Characteristics

9

Inventory [units] Throughput rate

[units/hr]

... ...

Flow Time [hrs]

... ... ...

Input rate [units/hr]

Capacity rate [units/hr]

Flow time = average time for a unit to move through the system

Cycle time = average time between completion of units

Throughput rate is the lower of two rates (input rate and capacity rate)

Throughput Rate:

What if Demand rate < Capacity rate?

Throughput Rate:

What if Demand rate > Capacity rate?

10

Process Flows

• Identify “flow units”

• Flow rates (input rate and output rate)

• Flow times (time spent in the process)

• Stocks (inventory build-up)

10

12/27/2011

6

11

… and Process Characteristics

11

Flow Process Process Characteristics

Identify “Flow Units” What is my “product”?

Flow rates (Input rates and output rates)

What is the demand on my system? What is my capacity?

Flow times (time spent in process)

How long does it take me to produce one “unit”?

Stocks (inventory build-up)

How much inventory (of flow units) do I need to hold? E.g., queue of patients at a hospital, cars at a dealership, or a-warehouse-full of materials.

12

Basic Process Measures In Production and Service

12

Production Process Service Process

Flow Unit Materials Customers

Input Rate Raw material releasing rate Customer arrival rate

Output Rate Finished goods output rate Customers departure rate (service completion rate)

Flow Time Time required to turn materials into a product

Time that a customer is being served

Inventory Amount of work-in-process Number of customers being served

Capacity Maximum output rate Maximum service completion rate

12/27/2011

7

13

Utilization

• Utilization gives us information about “excess capacity”

• The utilization of each resource in a process can be presented with a utilization profile

13

%100rateoutput maximum

rateoutput Actual

RateCapacity

Rate Throughput n Utilizatio

• What is the optimal utilization of a resource?

Resource Capacity Rate (units/hour)

Input Rate (units/hour)

Utilization

1 6 4 66.67%

2 7 4 57.14%

3 8 4 50.00%

4 6 4 66.67%

5 5 4 80.00%

14

Operational Challenge Mismatch between demand and supply

• In any process, the input and output rates will vary over time

• A key operational challenge is matching supply and demand

– i.e., matching the input and output rates

• For a variety of reasons, a perfect match is not possible

– What are some of these reasons?

14

12/27/2011

8

15

An example: Security screening at YVR

15

Time

Input rate (passengers/15 min slot)

Capacity rate (passengers/15 min slot)

Excess Demand

Excess Capacity

6:15 7 15 0 8

6:30 10 15 0 5

6:45 8 15 0 7

7:00 12 15 0 3

7:15 9 15 0 6

7:30 16 15 1 0

7:45 14 15 0 1

8:00 19 15 4 0

8:15 22 15 7 0

8:30 17 15 2 0

8:45 13 15 0 2

9:00 11 15 0 4

9:15 12 15 0 3

9:30 8 15 0 7

9:45 10 15 0 5

10:00 7 15 0 8

TOTAL 195 240

Enough capacity for the

shift …

Data for a 4-hour shift in 15-min time slows: 7 arrive between 6:00 and 6:30 etc.

…but not at all times

Do we have enough

capacity?

16

Short-run vs. Long-run Averages

• Since the input and output rates may vary over time, both the short-run average and the long-run average rates provide useful information.

16

• Long-run average input rate must be less than the long-run average capacity rate

• Short-run average input rate can be greater than the short-run average capacity rate

But what would this lead to?

Why?

12/27/2011

9

17

RateCapacity

Rate Throughput n Utilizatio

Implied Utilization

• Implied utilization also allows us to capture the idea of overtime

– Organizations often budget for a fixed amount of capacity, and work overtime to meet excess demand

17

• To capture the idea that there may be excess demand in the short-run, another measure of utilization is often useful

RateCapacity

RateInput on UtilizatiImplied

18

Security Screening Example Revisited

• What is the capacity rate? Note: In this example, the capacity rate is given. In practice, it

may not be obvious. Finding the capacity rate will involve drawing a process flow map, identifying activities, times, resources, etc, and finding the bottleneck

• What is the (average) size of the line?

• How long do passengers wait (flow time)?

18

12/27/2011

10

19

Inventory Build-Up Diagram

19

Time

Input rate (passengers/15 min slot)

Capacity rate (passengers/15 min slot)

Excess Demand

Excess Capacity

INVENTORYBUILD-UP

6:15 7 15 0 8 0

6:30 10 15 0 5 0

6:45 8 15 0 7 0

7:00 12 15 0 3 0

7:15 9 15 0 6 0

7:30 16 15 1 0 1

7:45 14 15 0 1 0

8:00 19 15 4 0 4

8:15 22 15 7 0 11

8:30 17 15 2 0 13

8:45 13 15 0 2 11

9:00 11 15 0 4 7

9:15 12 15 0 3 4

9:30 8 15 0 7 0

9:45 10 15 0 5 0

10:00 7 15 0 8 0

TOTAL 195 240

20


20

0

2

4

6

8

10

12

14

6:15 6:30 6:45 7:00 7:15 7:30 7:45 8:00 8:15 8:30 8:45 9:00 9:15 9:30 9:45 10:00

Inventory Build-Up

• What is the “average inventory” in the buffer?

12/27/2011

11

21

Calculating “Average Inventory”

21

Time

Input rate (passengers/15

min slot)

Capacity rate (passengers

/ 15 min slot) Excess

Demand

Excess Capacity

INVENTORY BUILD-UP

6:15 7 15 0 8 0

6:30 10 15 0 5 0

6:45 8 15 0 7 0

7:00 12 15 0 3 0

7:15 9 15 0 6 0

7:30 16 15 1 0 1

7:45 14 15 0 1 0

8:00 19 15 4 0 4

8:15 22 15 7 0 11

8:30 17 15 2 0 13

8:45 13 15 0 2 11

9:00 11 15 0 4 7

9:15 12 15 0 3 4

9:30 8 15 0 7 0

9:45 10 15 0 5 0

10:00 7 15 0 8 0

195 240 3.1875

Empty Buffer (No Queue)

Buffer NOT empty

Average Inventory = 3.1875

22

Consider another example: 30 min time intervals

…

22

Time


min slot)



Demand

Excess Capacity

INVENTORY BUILD-UP

6:30 17 30 0 13 0

7:00 20 30 0 10 0

7:30 25 30 0 5 0

8:00 33 30 3 0 3

8:30 39 30 9 0 12

9:00 24 30 0 6 6

9:30 20 30 0 10 0

10:00 17 30 0 13 0

195 240 2.625

0

2

4

6

8

10

12

14

7:00 8:00 9:00 10:00 8:30 9:00 9:30 10:00

Inventory Build-Up

Average Inventory

12/27/2011

12

23

… and another: 60 min time slots…

23

Time


min slot)



Demand

Excess Capacity

INVENTORY BUILD-UP

7:00 37 60 0 23 0

8:00 58 60 0 2 0

9:00 63 60 3 0 3

10:00 37 60 0 23 0

195 240 0.75

Average Inventory

0

0.5

1

1.5

2

2.5

3

3.5

7:00 8:00 9:00 10:00

Inventory Build-Up

24

… and another: 2 hour slots

24

Time


min slot)



Demand

Excess Capacity

INVENTORY BUILD-UP

8:00 95 120 0 25 0

10:00 100 120 0 0 0

195 240 0

0 Average Inventory

0

0.2

0.4

0.6

0.8

1

7:00 8:00

Inventory Build-Up

Caution:

Aggregation reduces/hides variability in

the data: demand (input) and inventory

12/27/2011

13

25

Estimating Process Measures • Process measures changes over time

– Depending on the mismatch between input rate and the capacity rate the inevitably occurs over time

• We are interested in averages of these quantities

• “Average” values of process can be misleading

• It is often convenient to assume continuous input and output processes

25

26

Definitions

• Instantaneous Flow Rates

26

Ri(t) The input rate to the process at time t

Ro(t) The output rate of the process at time t

∆R(t) = Ri(t) – Ro(t) Instantaneous inventory accumulation at time t

• Inventory Level

• Flow Time

I(t) The number of units within the process boundaries at time t

T(t) The time that a unit which enters (leaves) the process at time t spends (has spent) within the process

This can be defined in many ways

12/27/2011

14

27

Inventory and Flow Dynamics

• Let (t1,t2) denote an interval of time starting at t1 and ending at t2

• Suppose ∆R(t) is constant over (t1,t2) and equals ∆R. Then,

27

t1 t2

I(t1)

I(t2)

I(t)

t

∆R *(t2-t1)

)()()( 1212 ttRtItI

2

Inventory EndingInventory StartingInventory Average

Ending Inventory

Starting Inventory

Change in Inventory

28


Capacity rate = 100/hr

28

10AM

50

200

Input Rate/hr

12PM 2PM 6PM

10AM

100

200

Inventory (or Backlog)

12PM 2PM 6PM

Assumes inventory level changes in “discrete amounts”

Assumes inventory level changes in “continuous amounts”

12/27/2011

15

29

Another Inventory Build-Up Example

29 0

200

400

I(t) Inventory in week t

1 2 3

Week Input Rate Throughput Rate Inventory

0 400

1 900 800 500

2 900 1200 200

3 900 1000 100

Week

30

Under the continuous assumption:

The average inventory? “Area under the curve”

Average Inventory

Average inventory depends on whether inventory is assumed to change in discrete steps, or continuously

30 0

200

400

I(t)

1 2 3 Week

Under the discrete assumption:

The average inventory over weeks 0 to 3 is 300

Under the continuous assumption:

The average inventory? ??????

12/27/2011

16

31

Little’s Law

31

Average Inventory I [units]

Average throughput rate R

[units/hr]

... ...

Average Flow Time T [hrs]

... ... ...

• Establishes a relationship between average inventory, average throughput rate, and average flow time

32

Little’s Law

• Throughput rate: 1 car/min

• 900 cars in the system

• Flow time?

32

I = R * T 900 cars = 1 car/min * 900 min

12/27/2011

17

33

Example 1

• Patients waiting for an organ transplant are placed on a list until a suitable organ is available. We can think of this as a process. Why?

33

Patients matched to donated organs

INPUT

Patients in need of a transplant

OUTPUTS

Patients leaving the list hopefully with a

successful transplant

34

Example 1 –cont’d

Question (a) • On average, there are

300 people waiting for an organ transplant

• On average, patients wait on the list for 3 years

• How many transplants are performed per year?

34

300 patients ?? / year

3 years in system (T)

I = R * T

Inventory I = 300 patients Flow Time T = 3 years Throughput Rate per year R = I/T = 100 patients / year

12/27/2011

18

35

Example 1

35

Question (b) • On average, there are 300

people waiting for an organ transplant

• On average, 100 transplants are performed per year

• Assume that no patients die during the wait

• How long do patients stay on the list?

300 patients 100/year

??? years in system

I = R * T

Inventory I = 300 patients Throughput R= 100 patients/year Flow Time T = I/R = 3 years

36

Example 2

• You are managing the construction of a new container terminal at the Port of Vancouver. You expect to “process” 1000 containers/day, and you have promised customers that containers will spend no more than 1 day waiting to be shipped.

36

INPUT

Containers to be shipped

OUTPUT

Containers Loaded to a ship

12/27/2011

19

37

Example 2

Question (b) • Suppose the yard is expanded to hold 2000

containers • Since container traffic is growing rapidly soon, you

will soon process 2000 containers/day • You are asked to make improvement to the terminal

to handle 2000 containers/day • But there is no more room to expand the yard

• What changes can you make in order to process 2000 containers/day?

37

38

Insights from Little’s Law

• Throughput rate, flow time, and inventory are related

• Depending on the situation, a manager can influence any one of these measures by controlling the other two – You cannot independently choose flow time,

throughput and inventory levels!

– Once two are chosen, the third is determined

– For example, if the flow time is fixed, the only way to reduce inventory is to increase throughput

38

12/27/2011

20

39

Insights from Little’s Law

• How would you reduce wait time for patients on the transplant waiting list?

– Increase throughput rate (per year)

– Decrease number of people on the list (inventory)

• How would you increase throughput rate of containers at the port? R= I/T

– Decrease flow time (T)

– Increase “inventory” (I)

39

40

Inventory Turnover

• Inventory Turnover (or turns) = [Cost of goods sold] / [Average inventory investment] = [$ value of cost of output] / [$ value of average inventory] = R / I = 1 / T

• Why are higher inventory turns good?

• How to increase inventory turns, i.e., how to turn “stock” into “flow”?

• The flow time (i.e., T) when expressed in days is also referred to days in inventory

40

12/27/2011

21

41

Days of Inventory & Inventory Turnover

41

Inventory [$]

Cost of goods sold [$/year] (Throughput)

Days of Inventory [days] (Flow time)

365 Ave. Inventory

Cost of goods sold (Throughput) =

This measures the velocity of moving inventory.

Inventory

Days of Inventory

Inventory Turnover (per year)

= Cost of goods sold (Throughput)

42

The Importance of Inventory Turnover and Increasing Inventory Turns

42

Inventory Turnover Increasing Inventory Turns (Velocity)

Dell 5-8 times more than competitors

Dell’s business model

Toyota Spare parts inventory 10 times faster than competitors

Just-in-time

Wal-Mart Year 2002: 7.5 Turns (Kmart was slightly less than 5)

Cross docking

Progressive Insurance

Claims processed in hours instead of days

Immediate response claims handling

12/27/2011

22

43

Lessons • Capacity rate versus throughput rate (Utilization)

• Input and output rates vary over time resulting in – Excess capacity

– Inventory build-ups

• Inventory build-up diagrams are useful tools, but – Average can be misleading (hides variability); need to

study carefully

• Little’s Law helps make the connection between average flow measures : Throughput time (T) = I (ave. Inventory) / R (Throughput rate per period)

43

process analysis ii

Documents