national Bureau of Standards

Library, N.W. Bldg

JUL 2 2 1960 Reference book not to be

taken from orary.

PB 161555

^ecUnical ^lote 54

DETERMINATION OF A GENERAL INDEX

OF EFFORT IN SORTING MAIL

BY CONVENTIONAL METHODS

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March.

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NATIONAL BUREAU OF STANDARDS

technical *7l©te

54

JUNE 1960

DETERMINATION OF A GENERAL INDEX

OF EFFORT IN SORTING MAIL BY

CONVENTIONAL METHODS

Seymour Henig

This work was sponsored by the Office of Research and

Engineering, of the U. S. Post Office Department.

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature. They are for sale by the Office of Technical Services, U. S. Department of Commerce, Washington 25, D. C.

DISTRIBUTED BY

UNITED STATES DEPARTMENT OF COMMERCE

OFFICE OF TECHNICAL SERVICES

WASHINGTON 25, D. C.

Price 50 cents

DETERMINATION OF A GENERAL INDEX OF EFFORT

IN SORTING MAIL BY CONVENTIONAL METHODS

Seymour Henig

The conventional method of sorting letters in stages is

described. It is shown, through reference to available

statistics, that about 90% of letters originating within

the areas served by several large post offices will be

involved in no more than five stages to be completely

sorted to a carrier, firm or section of boxes. A method

is presented for the accounting of each stage's individual

letter readings which are defined as the units of measurement for the index of sorting effort. It is found that

the upper bound average number of readings per letter

for three large post offices varies from 3.16 to 2.98 and

that these bounds are applicable to 96.2 to 92.4% of the

local originating first class letters. It is anticipated

that the values of such indexes for all large post offices

will be consistently close to the range already determined.

1. Introduction

Our adventure into a program of consultation to the Post Office Department

on the problem of letter sorting led us directly into the need for a number

of well-founded generalizations. One of these generalizations concerns the

average number of times that letters must be sorted between source and destination.

In order to choose a system for development from a number of sorting

mechanization proposals, it is desirable to find and compare their significant factors of cost. In machine systems which require human reading at

the input end of sorting, it is easily observed that this labor cost is the

most significant factor. For a given volume of mail sorted by conventional

methods, the total input effort increases almost exclusively with the average

number of sortings per letter. In systems where other factors (such as capital investment, human output and supporting effort, and space cost) are substantially equal, decisions can be based solely on input effort differences.

Conversely, where the input efforts of systems are found to have little variation, decisions can be based on the comparison of the other factors.

Many inquiries were made among postal officials and employees concerning

this average number of sortings, but the information that was turned up pertained rather to the number of times that it was possible to sort some of

the letters. Furthermore, only inadequate statistics were at first available

in regard to the mail volumes to each category of a post office's sorting.

With a knowledge of conventional postal sorting methods and the availability of more complete and reliable statistics, it has become possible to

close in on this average number of sortings per letter.

- 1 -
A study of current methods indicates that most letters may pass

through one to three sorting stages at both the "shipping" and "receiving" post offices. Besides this, there are letters that may be sorted

several times in transit either on vehicles or at intermediate stations,

or both.

The multiple stages appear to be warranted in the larger post

offices which are required to separate their mail to large numbers

of categories. These categories (of the outgoing stages) consist

of other post offices and transit routes. It can be seen that letters

which are separated directly to another post office, and are packaged

for shipment to it, require no further sorting enroute. It is significant that, among three large post offices for which outgoing separation statistics were evolved from sampling counts LlJj approximately

90% of all the letters are in 1000 to 2000 categories of such post

office "directs". The remaining 10% of the letters might be addressed

to any of our country's balance of 36-37,000 post offices. Because

each of these are shipped zero to a few letters per day, groups of

these minor post offices are resolved into less than 300 (or so)

transit route and state residue categories at the "shipping" office.

A determination of the sorting effort involved for 90% of the

letters originating at large post offices should be useful although

not fully comprehensive.

At the "receiving" or incoming part of a post office, sorting

for local delivery is performed on letters arriving from out-of-town

as well as on a substantial portion of the output from its own "shipping" or outgoing section. Here again, several thousand categories,

carriers and large firms, may be required. For these categories,

the large city offices need no more than two stages of sorting for

most of the mail, but carriers must also collocate their mail.

The outgoing and incoming sorting is generally performed at the

city's main post office while the final stage, the collocation of letters

according to the carriers' walks, is performed at their stations.

This final stage of sorting is special because of the manner and the

place where it is now done. Practically all letters leave the outgoing

section of a post office after up to three stages of sorting, and 90%

of these letters are subject, additionally, to no transit sorting

and no more than two incoming stages when carrier collocation is discounted. Therefore, without the final stage, 90% of the letters originating within the area served by a large post office will not go

through more than five sorting stages.

Figure in brackets indicates the reference at the end of this paper,

- 2 -
2. Category Allocation Among Stages

For the maximum conservation of sorting effort, the larger volume

directs are usually separated in the earlier stages. The completion

of some of the separation categories in a stage of sorting reduces

the volume of letters for the succeeding stage.

In general, the first outgoing stage (primary) consists of (l)

secondary categories and (2) post office directs; the second outgoing

stage (secondaries) consists of (l) post office directs and (2) tertiary categories or state residues; the third outgoing stage (tertiaries) consists substantially of (l) post office directs and (2)

transit routes. Likewise, the first incoming stage (primary) con- sists of (l) station (branch post office) categories, (2) firm directs

and (3) main office boxes; the second incoming stage (secondaries)

consists of (l) firm directs, (2) station boxes and (3) carriers.

Of the above types of categories, post office directs, transit

routes, state residues, firm directs, boxes and carriers are completed

separations with respect to the sorting office.

3. Index of Effort

The sorting effort expended in eaeh stage is related to the total

volume of letters minus that part of the volume which bypassed the

stage or was completed in previous stages. The average effort (or

operator time) expended per letter at each sorting is known to vary

with the complexity of each sorting scheme (part of a stage), but

the common operation to each letter in each stage is a single reading of the address. The number of readings in a stage is identical

with the number of letters sorted in a stage. A reading, as defined

here, is divorced from the variability of each sorting effort and so provides us with a standard unit of measurement.

The bypassed part of the volume is derived by the patron's separation into two or more of his post office's sorting categories. The

largest and simplest of these categories is the mail for local delivery. When the patron puts such mail into a letter drop designated

"local", this mail is directed to the incoming primary and, therefore,

bypasses the normal first stage, the outgoing primary. The potentiality of bypass for this category is equal to its proportion of 40

to 60 percent of the local originating mail.

For the local delivery mail which is received by a post office

from out-of-town, it is easily imagined that some difficulty wight

be encountered in tracing the previous sorting effort performed on letters which could have originated at any one of 38,000 other post

offices.

- 3 -
With the preceding "background, it is now possible to derive an upper bound estimate on the average number of readings per letter

involved in reaching a carrier, a firm or a section of boxes for 90%

of a post office's local originating mail. This estimate is considered

to be an upper bound, because we will assume that two readings per letter

are required at all out-of-town post offices, although we know that many

of the smaller ones need only one reading per letter, and we can account

for all the other readings in this S0% with much greater accuracy.

Average Readings Per Letter

Total Letter Readings in System

Letters in System

Sum of Stage Letter Volumes

Letters in System

Sum of Stage Fractions of Sampled Entire

_ Local Originating First Class Letters

Corrected First Class Letter System Fraction

4. Example

For an example of this accounting, let us use the statistics of distribution LlJ for one of the post offices where sample counts were made.

The pertinent data from these statistics are shown in Figure 1 for the

San Francisco (California) Post Office. Let us also assume that patron

separation of local delivery and out-of-town mail has developed to the

point that 20% may bypass the outgoing stages to directly enter the incoming primary. A second assumption is the availability of sorting machines

with separation capabilities of 100 categories each. However, the possible

benefits of this separation capability were not taken into consideration for

incoming primaries of either the source or destination post offices.

These benefits will be determinable when incoming distribution statistics

become available.

There was also no consideration made for a very minor fraction of the

mail which presently goes through an additional sorting stage in the outgoing or incoming sections of some post offices. It is anticipated that

this practice can be eliminated by the use of the greater separation

capability of machine sorting over that of manual.

Step 1 of Figure 2 illustrates the method of extrapolating to an outgoing primary of a desired separation capability from the statistical

distribution data. This step yields the fraction which can be expected

to be completed in the first outgoing stage and consequently the balance

remaining for the second stage.

Step 2 of Figure 2 illustrates the fractions of the entire local

originating mail which are worked through the five stages pertinent

to the post office directs of the three significant outgoing stages.

- 4 -
STAGE LEGEND:

No. SYMBOL NAME

1 fb OUTGOING PRIMARY

2 So OUTGOING SECONDARY

3 To OUTGOING TERTIARY

4L PL INCOMING PRIMARY LOCAL

5L Sl INCOMING SECONDARY DELIVERY

4d Pd INCOMING PRIMARY DESTINATION DELIVERY 5d so INCOMING SECONDARY

1.000

.900 <

Sjboo

*

(t.600 o

_l<

O.500 3

UJ

(T.400

UJ 300 7

0.200b

I-o

<

£.100

OUTGOING DISTRIBUTION STATISTICS

OF THE FIRST CUSS LETTER MAIL

FOR THE SAN FRANCISCO (CALIFORNIA) POST OFFICE

\CUMULATIVE PLOT OF THE 200 LARGEST FINAL OUTGOING

SORTING COMPONENTS IN WHICH Di IS LOCAL DELIVERY MAIL, D5 AND D> ARE STATES { WHOSE OUTGOING SECONDARY

STAGE IS PERFORMED EN ROUTE ) AND THE REMAINDER

ARE POST OFFICE DIRECTS (NO SORTING EN ROUTE).

IN ADDITION THE FOLLOWING FRACTIONS ARE RECORDED:

FRACTION SYMBOL TYPE ASSUMED

DERIVATION ASSUMEDDISPOSITION .03200 EA AIRMAIL Po LEAVES I st CL SYSTEM

.00201 Ef FOREIGN Po LEAVES I st- CL SYSTEM

.03564 Eu UNCANCELED Po REWORKED ONCE

.00426 En NIXIE Po REWORKED TWICE .00753 Em MISSORTED So REWORKED TWICE

.0136 To TERTIARY So To

50 100 150 DESTINATION (D, To Dgoo'N ORDER OF DECLINING FRACTION)

FIGURE 1. PERTINENT DATA FROM POST OFFICE MAIL STATISTICS [1]

200

STEP 2. STEP 1.

2 3 4L 5L 4 5 STAGE OF SORTING

81 FINAL SEPARATIONS

ALLOCATION OF ITEMS IN A

100 SEPARATION OUTGOING PRIMARY

FOR ABOVE POST OFFICE

50 100 150 DESTINATION OR SEPARATION

200

FIGURE 2. ILLUSTRATION OF ANALYSIS OF MAIL FRACTION TO SORTING STAGE
The summary accounting of the stage fractions of the sampled

entire local originating first class letters is as follows:

Note: Symbols are consistent with those in Figures 1 and 2.

Stage No. 1 P + E

U

+ E

N

+ E

M

.8G0 + .03564 + .00426 + .00753

.847

Stage No. 2 S + D,- + D, + E„ + E

5 10 N M

.228 + .012 + .008 + .00426 + .00753

.260

,014

Stage lie. 3

014

Stage Nc. 4 P + ?

.385 + .581

166

Stage No. 5 S, + S

jj JJ .385 + .581

966

Sum of Stage Fractions of Sampled Entire

Local Originating First Class Letters 3.053

It should "be noted that the airmail and foreign mail items in the

table of Figure 1 are considered to leave the first class sorting system

after the outgoing primary in which all of the foreign and most of the

- 6

-
airmail should be withdrawn. This is believed to be a fair assumption,

because no sampling was made of the final separations in either the

foreign or airmail sorting systems, and because the volume indicated

by the fraction for each of these types probably represents only part

of each total; the part which normally missed being segregated at the

culling or facing operations. The entire local originating firstclass mail (as sampled), which for simple outgoing accounting is con- sidered unity, therefore is corrected to allow for this loss to the

system in the more general problem.

Corrected First Class Letter System Fraction

= 1 - (Airmail Fraction + Foreign Mail Fraction)

= 1 - CEA

+ E

F

)

= 1 - (.03200 + .00201) = .966

It should also be noted that the system does not lose the other

error categories among which the uncancelled mail predominates but

which includes the missorted and the nisie (defective address; some- times grouped with postage due) mail. Practically all of this mail

is resolved into a transmittable separation after rework.

Then

Average Readings Per Letter = 3.053 _ 3.16

.966

5. Applicability of Index

We have repeatedly indicated 90% as an estimate of the post office

direct separation categories of the outgoing mail. This figure was

based on a summation of those fractions of the sampled entire local

originating first class letters. In order to be consistent with our determination of average readings per letter, these post office directs

relative to the letters in the system will be:

% Post Office Directs

-[-

Corrected First Class Letter System Fraction

-(States Residue Fraction + Transit Route Fraction)

j_ Corrected First Class Letter System Fraction

From the Original Data [ l]

States Residue Fraction = .0434

Transit Route Fraction = .0027

- 7 -

(100)
Then

% Post Office Directs = [

- 966 " ( -°434+ - 0027 ) 1 (100) = 95.2

L .966 J

6. Indexes for Other Post Offices

The sample count outgoing distribution statistics are available

also for the Los Angeles (California) and Baltimore (Maryland) Post

Offices [1]. From these data, we have made similar accountings.

The Los Angeles Post Office makes an outgoing primary separation for

one of its large local zones to effect an easy economy in eliminating

that much work from its incoming primary. The Baltimore Post Office

effects such an economy to an even greater extent and, besides, has

advanced patron separation to a point where it actually exceeds the

value of 20% which was assumed for the other two post offices. Aside

from taking into consideration their already practiced economies and

their individual distribution data, the method of accounting is the

same for Los Angeles and Baltimore as the example shown for San Francisco.

A summary table follows:

% of Their First Class Receive Less Than (No.)

System Letters Average Readings/Letter

San Francisco 95.2 3.16

Los Angeles 96.2 3.16

Baltimore 92.4 2.98

7. Discussion

From this table, it may be seen, that there exists a very high and

fairly consistent percentage of letters which requires no intermediate

sorting between source and destination post offices and that, for these

letters, the upper bound average number of readings under the given con- ditions is consistently in the vicinity of three.

It appears reasonable to expect that the results of such an accounting

for any large post office could not significantly vary. If this consistency

is indeed common to all post offices which warrant at least one sorting

machine, then we have determined a useful index for all the sorting effort

to be performed on those letters which may be processed by such machines.

More specifically, it appears that over 90% of the letters processed

in post offices equipped with sorting machines will pass through such

machines an average of less than 3.2 times and will require no other

- &
sorting in order to reach a firm, a section of boxes or a carrier.

It will be possible to reduce this upper bound average readings

per letter to a truer index when specific machines with higher separation capabilities are taken into consideration; when machine separation

capability benefits are applied to incoming mail; and when an estimate

can be made for those proportions of mail for out-of-town destinations

which require one and two stages of sorting.

8. Reference

LlJ IT. C. Sever o and A. E". Newman, Distribution of mail by destination

at the San Francisco, Los Angeles and Baltimore Post Offices, NBS

Tech. Note 27 (1958) P3 151386. (Order by PB number from the

Office of Technical Services, U. S. Department of Commerce, Washington 25, D. C.)

U.S. DEPARTMENT OF COMMERCK

Frederick H. Mueller, Secretary NATIONAL BUREAU OF STANDARDS

A. V. Aslin, Director XjJnJT*:

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