Backward scheduling: the tightest document is not always the slowest one

Type your own internal date and each document walks backward from it: time to produce, time to travel, time for you to read it, time to put it right. The date its request has to leave falls out of that, and so does the margin. On the sheet this page opens with, the smallest margin sits on the shortest chain.

Live result

Commercial invoice has the least margin on this sheet, and its request can leave no later than 27 March.

your internal date1 April
margin left on it1 working day
documents on the sheet6

The shortest chain runs out first, and the plan behind it decides when the request leaves.

S=D-L

where

S

is 27 Mar,

D

1 Apr, and

L

3 working days.

m=S-P

where

m

is the margin in working days and

P

26 Mar. · pack front 13 Mar, 13 working days out

Your internal date

Try a plan

Your internal date

Your planning date, against which every margin is measured.

Non working days

One working week applies to the whole chain.

The document in focus

These day counts are an example. Replace them with your own.

Document

Productionworking days

The time between the request arriving and the document existing.

Transitworking days

The document's courier time to your desk.

Your reviewworking days

The time you take to read the document before sending it.

Correction allowanceworking days

Time reserved for a correction round trip.

You plan to ask on

Commercial invoice: Ask by 27 Mar · 1 working day spare
Transport document: Ask by 23 Mar · 2 working days spare
Packing list: Ask by 27 Mar · 3 working days spare
Legalised invoice copy: Ask by 13 Mar · 3 working days spare
Certificate of origin: Ask by 18 Mar · 4 working days spare
Inspection certificate: Ask by 13 Mar · 6 working days spare

The table above is authoritative for the current inputs and stays in least margin order.

Six documents working back to one date

Why the shortest chain runs out first

A chain length belongs to a document, while a margin belongs to a plan, and nothing links the two automatically.

Long chains attract early requests while short chains are often left late.

The correction allowance therefore stays separate from production so its protection remains visible.

What a margin is not

A margin is the working days between a planned request and the last date the typed chain permits. It is not a rule period, contractual float or time anybody owes you.

The smallest margin names the tightest document but not necessarily the one controlling the outcome. The date is only as accurate as the typed duration estimates.

Correction allowance, Commercial invoice

working days

Fromworking days

Toworking days

In steps ofworking days

It does not check the values in between.

Across the values sampled, the document with the least margin stays Commercial invoice from 1 working day to 12 working days, the highest value sampled. The nearest value where it changes is 0 working days, where it becomes Transport document.

The answer	Commercial invoice
Values sampled	0 working days to 12 working days, 13 values, step 1 working day
Holds from	1 working day
Holds to	12 working days, highest sampled
Nearest value that changes it	0 working days
The answer there	Transport document

What an unchanged region does and does not prove is set out in a short lesson.

The sweep samples only the values you entered. Between samples the answer is not checked, so read the boundary as observed, not proven.

Here is the maths

The formula, in words

One document is four spans laid end to end, and every one of them is counted in working days. The time to produce it, the time for it to reach your desk, the time you take to read it, and the time held back for the round trip if it comes back wrong. Added together they are the chain. Subtracted from your internal date, walking backward over working days only, they give the last date the request can leave.
The margin is the distance between two dates and belongs to your plan. It is the working days between the date you wrote down that you would ask and the last date the chain leaves room for. It is not a rule period and it is not float in any contractual sense. Where the planned date falls later than the last safe date the margin is reported as a negative number rather than clamped to zero, because the state a sheet like this exists to surface is exactly that one.
Chain length and margin are computed from different things and do not have to agree. A chain is a property of a document and of whoever issues it. A margin is a property of a plan, and a plan is written by whoever was worried. On the sheet this page opens with, the ranking by chain and the ranking by margin are close to reversed.
The pack runs in parallel, so it is never a sum. Six chains totalling forty nine working days occupy thirteen working days of calendar, because six requests are in the post at the same time. The number that matters is the earliest of the six last safe dates, and it is the only figure on the sheet that describes the pack rather than a document.

A worked example

The calendar. 1 March is a Sunday in this scenario. Saturdays and Sundays are the non working days on the default setting. No public holiday exists on this page.

The internal date. 1 April, a Wednesday, as typed. It is the visitor's own date. Nothing on this page proposes it and nothing checks it.

Walking backward. Counting working days back from Wednesday 1 April gives the ladder every latest safe date is read off.

back	date
1	31 Mar Tue
2	30 Mar Mon
3	27 Mar Fri
4	26 Mar Thu
5	25 Mar Wed
6	24 Mar Tue
7	23 Mar Mon
8	20 Mar Fri
9	19 Mar Thu
10	18 Mar Wed
11	17 Mar Tue
12	16 Mar Mon
13	13 Mar Fri
14	12 Mar Thu
15	11 Mar Wed
16	10 Mar Tue
17	9 Mar Mon
18	6 Mar Fri
19	5 Mar Thu

The six chains, and where each request has to leave.

Document	prod	tran	rev	corr	chain	ask by	plan to ask	margin
Commercial invoice	1	0	1	1	3	27 Mar Fri	26 Mar Thu	1
Packing list	1	0	1	1	3	27 Mar Fri	24 Mar Tue	3
Transport document	3	1	1	2	7	23 Mar Mon	19 Mar Thu	2
Certificate of origin	4	2	1	3	10	18 Mar Wed	12 Mar Thu	4
Inspection certificate	6	2	2	3	13	13 Mar Fri	5 Mar Thu	6
Legalised invoice copy	5	3	1	4	13	13 Mar Fri	10 Mar Tue	3

One row read out loud. The commercial invoice takes one working day to produce, no transit because it never leaves the building, one working day for somebody to read it, and one held back in case it comes back wrong. Three working days. Three working days back from Wednesday 1 April is Friday 27 March. The plan says ask on Thursday 26 March. Between those two dates there is exactly one working day, and that is the whole margin on the document nobody was worried about.

The rank inversion, stated. Sorted by chain, longest first: inspection 13, legalised copy 13, certificate of origin 10, transport 7, invoice 3, packing list 3. Sorted by margin, smallest first: invoice 1, transport 2, packing list 3, legalised copy 3, certificate of origin 4, inspection 6. The document at the top of the first list is at the bottom of the second. The chain is a fact about the document. The margin is a fact about the plan. They were never the same question.

The front of the workback. The earliest of the six latest safe dates is Friday 13 March, shared by the inspection certificate and the legalised copy. That is thirteen working days before the internal date, and thirteen working days here span nineteen calendar days: 13 March to 1 April. Six of those nineteen are Saturdays and Sundays. Six days of the pack's runway are days on which nobody was going to do anything.

The number that explains why the sheet is a sheet. The six chains add to forty nine working days of document time. The pack takes thirteen. The difference is not efficiency, it is parallelism: six requests are in the post at once. This is also why the workback is computed per document and never as a total, and why a single lead time for the pack would be the wrong number by thirty six working days.

The check that makes it stick. Switch the non working days from Saturday and Sunday to Friday and Saturday. Four of the six latest safe request dates move and two do not. Not one of the six margins changes.

Document	Sat and Sun	Fri and Sat	margin
Commercial invoice, chain 3	27 Mar Fri	29 Mar Sun	1
Packing list, chain 3	27 Mar Fri	29 Mar Sun	3
Transport document, chain 7	23 Mar Mon	23 Mar Mon	2
Certificate of origin, chain 10	18 Mar Wed	18 Mar Wed	4
Inspection certificate, chain 13	13 Mar Fri	15 Mar Sun	6
Legalised invoice copy, chain 13	13 Mar Fri	15 Mar Sun	3

Five working days is seven calendar days under either convention, so the two counts stay in step and only part company where a chain ends on a Friday or a Sunday. The convention decides which dates are closed. It does not decide how much room you have.

The three chips, and what each one proves.

Document	default	inspection $\times 2$	no correction	date out a week
Commercial invoice	1	1	2	6
Transport document	2	2	4	7
Packing list	3	3	4	8
Legalised invoice copy	3	3	7	8
Certificate of origin	4	4	7	9
Inspection certificate	6	0	9	11
least margin sits on	Commercial invoice	Inspection certificate	Commercial invoice	Commercial invoice

Chip 1 doubles the inspection certificate's production from six working days to twelve, taking its chain from thirteen to nineteen and its margin from six to zero. The slowest document becomes the tightest only after its production doubles, and at that point it has no room at all. Chip 2 removes every correction allowance, which grows every margin and leaves the tightest document exactly where it was: the correction allowance is not what makes the invoice tight, the planned request date is. Chip 3 moves the internal date out five working days, which adds five to all six margins and changes nothing about their order, because the order is a property of the plan and not of the deadline.

Check it yourself

Switch the non working days to Friday and Saturday. Four of the six latest safe dates move and two stay, and none of the six margins changes. Five working days span seven calendar days in both conventions, so the two counts move together and separate only where the chain ends on a Friday or a Sunday. The convention decides which dates are closed. It does not decide how much room you have.

What this does not model

Any period or framework date set by somebody else; whether a late request earns anything, which is a question about the words in a contract; how anybody will treat a document; a public holiday of any kind, in any place; two different working weeks on one sheet, which is what a chain crossing two places actually needs, and which would also break the single margin ranking this page reports; a document whose chain shares a person with another document's chain, where the binding constraint is the person and not the smallest figure; more than one correction round; a correction round that cannot begin until somebody says what is wrong, which is real elapsed time this sheet folds into its correction span rather than counting; the pooling of correction time at the end of the pack instead of per document, which is what the critical chain literature argues for and the opposite of what this sheet does; a request that goes out and is never answered; documents beyond six; the derivation of any date from any particular document, which decides what a real chain would count from; and the accuracy of any day count typed into it, all of which are estimates until the issuer has been asked.

Equation trace

Add production, transit, review, and correction to obtain each document chain.
Walk that chain backward from the internal date using the selected working week.
Subtract the planned request date from the latest safe date to obtain margin.
Order valid rows from the least margin upward without changing the underlying document record.

Boundary

The internal date is a planning input rather than a rule period or right to time, one working week applies to every chain, public holidays are outside the model, and parallel requests are not added together.

Source anchors

Project Management Institute scheduling standards. Describes published scheduling practice used as context for backward planning.
International Chamber of Commerce documentary credits overview. Identifies the documentary credit framework that makes the actual required documents source specific.

Calculation version

1.0.0

The whole record prints. Your browser can save it as a PDF instead of printing it.

This page counts working days backward from a date you typed and reports how much of your own plan is left in front of each request. That date is yours: it is not a rule period, it is not a deadline set by any framework, and no rule period appears anywhere on this page or on the sheet it prints. Which documents a shipment needs, and how long each of them takes, comes from the contract and the credit in front of you; the six on the default sheet are an example to overwrite and every day count on them is invented for this page. The method is described from the documentary credit literature and from published scheduling practice, and no text from any of those sources appears here: the mechanisms are described in this page's own words and the sources are named where they are used. Nothing here reports how anybody will treat a document or says anyone is owed time.

Claim preparation: assemble a packet and hear what a reviewer asksPick the evidence, do the arithmetic, and a reviewer walks the packet naming what is missing, what does not agree with something else in it, and what a real one would ask next. There is no mark at the end, because a reviewer does not give one.Interactive lesson · 6 min

DOCUMENT REQUEST WORKBACK

: YOUR INTERNAL DATE
1 April, a WednesdayYour own date. Every margin on this sheet is measured against it and against nothing else.
NON WORKING DAYS
Sat and SunOne working week, counted in one place.
THESE NUMBERS
These day counts are an example. Replace them with your own. The day counts below are the ones you typed. Replace them with figures from the people who issue these documents.
THE PACK
6 documents · first request leaves 13 Mar13 working days to the internal date19 calendar days, 6 of them non working49 working days of document time in total, because the requests run beside each other
THE WORKBACK
Documentask bymarginprodtranrevcorrchainCommercial invoice27 Mar110113Transport document23 Mar231127Packing list27 Mar310113Legalised invoice copy13 Mar3531413Certificate of origin18 Mar4421310Inspection certificate13 Mar6622313
margins and spans are working days, and rows are in margin order, tightest first
LEAST MARGIN
Commercial invoice, 1 working daythe shortest chain on the sheet

Sweep of Correction allowance, commercial invoice

The assumption: Correction allowance, commercial invoice
Values sampled: 0 to 12 working days, 13 values, step 1
The answer: Commercial invoice holds the least margin
Holds across: 1 to 12 working days
Nearest change: 0 working days, where it becomes Transport document
Reading the boundary: The sweep samples only the values you entered. Between samples the answer is not checked, so read the boundary as observed, not proven.

Field record

The table above is authoritative for the current inputs and stays in least margin order.: Commercial invoice: 27 Mar, 1; Transport document: 23 Mar, 2; Packing list: 27 Mar, 3; Legalised invoice copy: 13 Mar, 3; Certificate of origin: 18 Mar, 4; Inspection certificate: 13 Mar, 6
Equation trace: Add production, transit, review, and correction to obtain each document chain. Walk that chain backward from the internal date using the selected working week. Subtract the planned request date from the latest safe date to obtain margin. Order valid rows from the least margin upward without changing the underlying document record.
Boundary: The internal date is a planning input rather than a rule period or right to time, one working week applies to every chain, public holidays are outside the model, and parallel requests are not added together.
Source anchors: Project Management Institute scheduling standards; International Chamber of Commerce documentary credits overview
Calculation version: 1.0.0
The printed workback uses the same inputs, calculation, ordering, and margins shown on screen.: The printed workback uses the same inputs, calculation, ordering, and margins shown on screen.

: TO FILL IN
Documentissueroriginalsasked onpromisedarrivedCommercial invoiceTransport documentPacking listLegalised invoice copyCertificate of originInspection certificate
WHAT MOVED

Your internal date

The document in focus

Six documents working back to one date

Why the shortest chain runs out first

What a margin is not

Correction allowance, Commercial invoice

Here is the maths

The formula, in words

A worked example

Check it yourself

What this does not model

Equation trace

Boundary

Source anchors

Calculation version

Related

YOUR INTERNAL DATE

NON WORKING DAYS

THESE NUMBERS

THE PACK

THE WORKBACK

LEAST MARGIN

Sweep of Correction allowance, commercial invoice

Field record

TO FILL IN

WHAT MOVED