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Process Flow Measures

MM – OMSession 2a

Henry Yuliando

MM – OMSession 2a

Henry Yuliando

The essence of process flow including :1. Flow time ; indicates the time needed to

convert inputs into outputs and includes any time spent by a flow unit waiting for processing activities to be performed.

2. Flow rate ; the number of flow units that flow through a specific point in the process per unit of time. Ri

(t) and Ro(t)

3. Inventory ; is the total number of flow units present within process boundaries.

Process

Ri,1(t)

Ri,2(t) Ro

(t)

Input and Output Flow Rates for a Process with Two Entry Points

The inflow rate of passengers at a security checkpoint at Vancouver Airport changes over time. Recall that for each of the three flights, about half the 200 passengers for each flight arrive between 50 and 30 minutes before flight departure. So far for each of the three flights departing at 10 a.m.

About 100 passengers arrive between 9:10 and 9:30 a.m., a 20-minute interval. This means that a total of 300 passengers arrive during this time period for three flights, giving an inflow rate of roughly 15 passengers per minute. The remaining 300 passengers for the three flights arrive between 8:40 and 9:10 a.m. (about 80 to 50 minute before departure) and between 9.30 and 9:40 a.m. (about 30 to 20 minute before departure).

That is the remaining 300 passengers arrive during a total time period of 40 minutes, giving an inflow rate of 7.5 passengers per minute, which is half the inflow rate during the peak time period from 9:10 to 9:30 a.m. The outflow rate of the checkpoint, however, is limited by the X-ray scanner, which cannot process more than 18 bags per minute or, with an average of 1.5 bags per passenger, 12 passenger per minute.

Time 8:40 a.m.8:40 – 9:10

a.m.9:10 – 9:30

a.m.9:30 –

9:43:20 a.m.9:43:20 – 10:10 a.m.

Inflow rate Ri

Outflow rate Ro

Buildup Rate R

Ending Inventory

(number of passengers

in line)

0

7.5/min.

7.5/min.

0

0

15/min.

12/min.

3/min.

7.5/min.

12/min.

4.5/min.

7.5/min.

7.5/min.

0

0

• Outflow rate capacity 12 passengers/min.

• At peak period 9:10 to 9:30 a.m., the inflow rate 15 passengers/min. so that a queue (inventory) starts building at R = 3 passengers/min.

• At 9:30, the inventory has grown = R x (9:30-9:10) = 60 passengers.

• After 9:30 a.m. X-ray scanner keeps processing at full rate 12 passengers/min., while the inflow rate 7.5 passengers/min., so that the passenger queue is being depleted at a rate of 4.5 passengers/min.

• Thus, 60-passenger queue is eliminated after 60/4.5 = 13.33 minutes, or at 9:43:20 the queue is empty again.

•.Example video

Inflow rates with staggered departures for Vancouver Airport security checkpoint….

(unit / minute)Time

(start of period)8:40 8:50 9:00 9:10 9:20 9:30 9:40 9:50 10:00 10:10 10:20 10:30

Inflow rate for flights arriving on the hour, Ri,1

2.5 2.5 2.5 5 5 2.5 2.5 2.5 2.5 5 5 2.5

Inflow rate for flights arriving 20 minutes past the hour, Ri,2

5 2.5 2.5 2.5 2.5 5 5 2.5 2.5 2.5 2.5 5

Inflow rate for flights arriving 40 minutes past the hour, Ri,3

2.5 5 5 2.5 2.5 2.5 2.5 5 5 2.5 2.5 2.5

Total inflow rate Ri

10 10 10 10 10 10 10 10 10 10 10 10

The inventory includes all flow units within process boundaries (in – on – off process) valid for manufacturing, services, financial, or even information process.

The inventory dynamics are driven by the difference between inflow and outflow rates.

The instantaneous inventory accumulation (buildup) rate, R(t)

as the difference between instantaneous inflow rate and outflow rate.

R(t) = Ri(t) – Ro(t)

Within a time interval (t1, t2), inventory change = buildup rate x

length of time interval. For R constant = I(t2) – I(t1) = R(t) x (t2-t1)

A stable process is one, in which in the long run, the average

inflow rate is the same as the average outflow rate.

(ex : inflow 600 passenger per hour; outflow 12 passengers per

minute or equal 720 passengers per hour; means that in the

long rung the average outflow rate is 600 passengers per hour)

Average flow rate or throughput is the average number of

flow units that flow through (into and out of) the process per

unit of time. Denoted as R.

For the case of Vancouver Airport, it is known that from 8:40

to 9:10 a.m., the inventory or queue is zero. From 9:10

through 9:43 a.m., the inventory builds up linearly to a

maximum size of 60. Thus the average inventory during that

period is 60/2 = 30.

Finally, the inventory is zero again is from 9:43 to 10:10 a.m.,

when the cycle repeats with the next inventory buildup. Thus,

the average queue size is the time-weighted average:

I = (33 min x 30 passengers + 27 min x 0 passengers)/60 min

= 17.5 passengers

Further, average inventory over time is denoted by I.

Average flow time (T) is as the average (of the flow times) across

all flow units that exit the process during a specific span of time.

Little`s Law : average inventory equals throughput times average

flow time, or I = R x T.

To determine the average time spent by a passenger in a checkpoint

queue, is that

T = I/R = 17.5 passengers/10 passengers per minute =

= 1.75 minutes pax/minute

where R = 600 passengers per hour or 10 passengers per minute.

Process I : HOM financial services provides financing to qualified creditors. It receives about 1,000 applications per month and makes accept/reject decisions based on an extensive review of each applications.

Assume a 30-day working month. Up to present, HFS process each application individually. On

average, 20% of all applications received approval. Based on an audit, it revealed that HFS on average had about

500 applications in process at various stages of the approval/rejection procedure.

In response to customer complaints about the time taken to process each application, HFS called for a measure to improve its performance.

It was suggested that (Process II) :

An Initial Review Team should be set up to preprocess according to strict but fairly mechanical guidelines.

Each application would fall into one of three categories: A (looks excellent), B (needs more detailed evaluation), and C (reject summarily). A and B applications would be forwarded to different specialist subgroups.

Each subgroup would then evaluate the applications in its domain and make accept/reject decisions.

Process II was implemented on an experimental basis. HFS found that on average, 25% of all applications were A

category, 25% B, and 50% C. Typically about 70% of all A applications and 10% of all B applications were approved on review. (Recall that all C applications were rejected). It was also noticed that 200 applications were with the Initial Review Team undergoing preprocessing. Just 25, however, were with the Subgroup A Team undergoing the next stage of processing and about 150 with the Subgroup B Team.

Under Process I : Throughput R = 1,000 applications/month

Average inventory I = 500 applications

Average flow time T = I/R = 0.5 months = 15 days.

Initial ReviewIIR = 200

Subgroup AReviewII = 25

Subgroup BReviewII = 150

Accepted

Rejected

1000/month 25%

25%

50% 90%

10%

30%

70% 200/month

800/month

Throughput R = 1000 applications/month

Average inventory I = 200 + 150 + 25 = 375 applications.

Average flow time T = I/R = 0.375 months = 11.25 days.

Detailed analysis and calculate the average flow time of each type group under

process II can be done. As seen on the above figure, there are 200 applications

with the Initial Review Team (average inventory). The performance is that

Throughput = 1000 applications/month

and

Average inventory = 200 applications

then

Average flow time TIR = IIR/RIR = 200/1000 months

= 0.2 months = 6 days

For subgroup A process, there are 25 applications. Since 25% of all incoming applications are categorized as type A, on average, 250 of the 1000 applications received per month are categorized as type A. Therefore,

Throughput RA = 250 applications/month

Average inventory IA = 25 applications

then

Average flow time TA = IA/RA = 25/250 months = 0.1 months = 3 days

Similarly, for subgroup B process, there are 25% of incoming applications are 250, and 150 applications with subgroup B. That is,

Throughput R B = 250 applications/month

Average inventory IB = 150 applications

then

Average flow time TA = IA/RA = 150/250 months = 0.6 months = 18 days

And for subgroup C process, since this application type leave immediately means that the average inventory are 0.

Recall that both subgroup process must through Initial Review Team process first which is taking 6 days process, thus the average flow time of each type application under process II: Type A applications spend, on average, 9 days in the process. Type B applications spend, on average, 24 days in the process. Type C applications spend, on average, 6 days in the process.

To find the average flow time across all applications under process II it using the weighted average across three application types.

)6(500250250

500)186(

500250250

250)36(

500250250

250

)()()(

T

so

TTRRR

RTT

RRR

RTT

RRR

RT CIR

CBA

CBIR

CBA

BAIR

CBA

A

Under process II also, 70% of type A applications (175 out of 250 per month,

on average) are approved, as are 10% of type B applications (25 out of 250 per

month, on average). Thus the aggregate rate at which all applications are

approved equals 175+25 = 200 applications per month. Hence, average flow

time for approved applications can be calculated by:

days 875.10)186(200

25)36(

200

175

)(25175

25)(

25175

175

BIRAIRapproved TTTTT

Similarly, average flow time for rejected applications can

be calculated by:

days

343.11)6(800

500)186(

800

225)36(

800

75

)(50022575

500

)(50022575

225)(

50022575

75

IR

BIRAIRrejected

T

TTTTT

Analyzing Financial Flows Through Financial Statements

MBPF Consolidated Statements of Income and Retained Earnings 2010

Net saleCosts and expenses Cost of goods sold Selling, general and administration expenses Interest expense Depreciation Other (income) expenses Total costs and expensesIncome before taxesProvision for income taxesNet incomeRetained earnings, beginning of yearLess cash dividends declaredRetained earnings at end of yearNet income per common shareDividend per common share

250.0

175.847.24.05.62.1

234.715.37.08.3

31.02.1

37.20.830.21

Table 1

MBPF Consolidated Balance Sheet as of December 2010

Current assets Cash Short-term investments at cost (approximate market) Receivables, less allowances of $0.7 million Inventories Other current assets Total current assetsProperty, plant, and equipment (at cost) Land Building Machinery and equipment Construction in progress Subtotal Less accumulated depreciation Net property, plant, and equipmentInvestmentsPrepaind expenses and other deferred chargesOther assetsTotal assets(Selected) current liabilities Payables

2.13.0

27.950.64.1

87.7

2.115.350.16.7

74.225.049.24.11.94.0

146.9

11.9

Table 2

MBPF Inventories and Cost of Goods Details

Cost of goods sold Raw materials Fabrication (L&OH) Purchased parts Assembly (L&OH) TotalInventory Raw materials (roof) Fabrication WIP (roof) Purchased parts (base) Assembly WIP Finsihed goods Total

50.160.240.225.3

175.8

6.515.18.6

10.69.8

50.6

Table 3

...flow analysis

Throughput R = $175.8 million/year (Cost of goods sold- table 1) Average inventory I = $50.6 million (Inventories – table 2) Average flow time T = I/R = 50.6/175.8 year = 0.288 years = 14.97

15 weeks For the accounts-receivable (AR)

Throughput RAR = $250 million/year (Net sales – table 1)

Average inventory IAR = $27.9 million (Receivables – table 2)

Average flow time TAR = IAR / RAR = 0.112 years = 5.80 6 weeks

For the accounts-payable (AP) or purchasing = $50.1 + $40.2 = $90.3 million, average inventory in purchasing = $11.9 million TAP = IAP / RAP = 0.13 years= 6.9 weeks

Cash to cash cycle performance

Average lag = 15 + 6 =21 weeks is the cost-to-cash cycle (ROE)

Investment in the form of purchased parts and raw materials after 6.9 weeks, cash-to-cash cycle (Net Trade Cycle) = 21 – 6.9 = 14.1 weeks

Targeting improvement

The throughput rate through fabrication :

$50.1 million/year in raw materials

+ $60.2 million in labor and overhead

= $110.3 million/yearThe throughput through assembly area :

$110.3 million/years in roofs

+ $ 40.2 million/year in bases

+ $ 25.3 million/year in labor & overhead

= $175.8 million

$6.5Raw

materials (roofs)

$15.1Fabrication

(roofs)

$10.6Assembly

$8.6Purchased

parts (bases)

$9.8Finished goods

$50.1/yr

$40.2/yr

$60.2/yr $25.3/yr

$110.3/yr

$40.2/yr

$175.8/yr $175.8/yr

Flow times through MBPF

Raw Materials

Fabri-cation

Purchased Parts

AssemblyFinished Goods

Throughput R$/year$/week*Inventory I ($)Flow time T=I/R (weeks)*

50.1 0.966.5

6.75

110.32.1215.17.12

40.20.778.6

11.12

175.83.3810.63.14

175.83.389.8

2.90

*=rounding to 52 weeks per year

Purchased partsPurchased partsRaw

materialsRaw

materials

FabricationFabrication

Accounts receiveableAccounts

receiveable

0.770.96

2.12

3.38

5.0

Flow Rate R(million $/week)

11.12 6.75 7.12 3.14 2.90 5.80A

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bly

Fin

ishe

d go

ods

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