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Allocation rules: six hundred units arrived, two locations still short

Type each location's demand, stock and declared cover, then the quantity that arrived and the sharing rule. On 600 units across three locations, 2 stay short, and no location is ranked.

Live result

At 600 units, 2 locations stay below their declared cover.
  • locations on the sheet3
The first name follows the row order you typed, and it is not a ranking.
At 600 units, 2 locations stay below their declared cover.The first name follows the row order you typed, and it is not a ranking.

The exact shortfall staircase

Locations below declared cover by arriving quantityThe staircase checks 61 quantities from 0 through 12,000 in exact steps of 200. At the typed quantity, 2 locations remain below declared cover from the 3 locations typed, and B is first in row order.Locations short

Try an allocation

600

This is the one dominant control. It moves on the exact 200 unit grid from 0 through 12,000.

Allocation rule

Edit the locations

Location 1
Location 2
Location 3

The computable witness

Locations still below cover
2
First short location in typed row order
B
Units unused by this arithmetic
0
Rule applied
Equal days

The first name follows the row order you typed. It is not a ranking.

Adjacent checked changes

First change above
1,400
First change below
400

The boundary where this stopsThis applies the rule typed to the stock typed. It allocates and ships nothing, does not judge fairness, and knows nothing about demand not entered.

Compressed answer bands

0 to 400
Locations still below cover3
First short location in typed row orderA
600 to 1,200
Locations still below cover2
First short location in typed row orderB
1,400 to 12,000
Locations still below cover0
First short location in typed row orderNone

Arriving quantity in units

It does not check the values in between.

How the answer sits across the values sampledA rail of the 61 values sampled, from 0 to 12,000 in steps of 200. Across the values sampled, the short location count and the first short name in typed row order stays 2, B from 600 to 1,200. The nearest value where it changes is 400, where it becomes 3, A.first change400first change1,400600on the page

Across the values sampled, the short location count and the first short name in typed row order stays 2, B from 600 to 1,200. The nearest value where it changes is 400, where it becomes 3, A.

Across the values sampled, the short location count and the first short name in typed row order stays 2, B from 600 to 1,200. The nearest value where it changes is 400, where it becomes 3, A.
The answer2, B
Values sampled0 to 12,000, 61 values, step 200
Holds from600
Holds to1,200
Nearest value that changes it400
The answer there3, A

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

Declared cover at one location is its demand rate multiplied by its cover days. The proportional rule gives each location the same share of arrival as its share of total demand. The equal days rule raises the lowest post allocation days of cover together, stops each location at its own cover, and leaves any excess unused.
Ci=diciC_i=d_i c_i
where CiC_i is declared cover in units, did_i demand per day, and cic_i cover days.
ai=Qdi∑jdja_i=Q\frac{d_i}{\sum_j d_j}
where aia_i is the proportional allocation, QQ arrival units, and jj each location in the total.
bi=dimax⁡(0,min⁡(λ,ci)−sidi)b_i=d_i\max\left(0,\min(\lambda,c_i)-\frac{s_i}{d_i}\right)
where bib_i is the equal days allocation, λ\lambda the common cover level in days, and sis_i stock on hand.
∑ibi=min⁡(Q,∑imax⁡(0,Ci−si))\sum_i b_i=\min\left(Q,\sum_i\max(0,C_i-s_i)\right)

A worked example

  1. Three locations each use 100 units a day, start with 0 stock and declare cover of 2, 6 and 6 days. The arriving quantity is 600 units and the rule is equal days.
  2. The first location needs 200 units to reach its 2 day cover. The remaining 400 units raise the other 2 locations to 2 days each.
  3. Two locations remain below their declared 6 day cover. The first short name is B because B is the second row and comes before C in the typed order.

What this does not model

The proportional rule does not reassign a share after one location reaches cover. The equal days rule does not use units beyond all declared cover.

Demand not entered, transit timing, pack constraints, minimum drops and service consequences are outside the arithmetic.

The count and first name do not rank locations, judge fairness or form a cut list.

What the sweep holds fixed

Only arrival moves. Every location row and the selected rule stay fixed while all 61 quantities from 0 through 12,000 are checked in steps of 200. Identical tracked answers are compressed into bands without interpolation.

Source basis

The two declared rules use standard proportional allocation and water filling arithmetic from public distribution and inventory mathematics. No private source wording is reproduced, and the selected rule comes only from the control on this page.

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

A request for cut candidates is refused. The result reports a count and the first short name in typed row order for traceability only, and it does not select, rank or deprioritise a location.

Related

Allocation shortfall record

Allocation rules: six hundred units arrived, two locations still short

Accepted allocation

Allocation rule
Equal days
Arriving quantity
600
Location A
100, 0, 2
Location B
100, 0, 6
Location C
100, 0, 6

Results

Locations still below cover
2
First short location
B
Unused units
0
Answer band
0 to 400, 3, A
Answer band
600 to 1,200, 2, B
Answer band
1,400 to 12,000, 0, None

Record fields

Calculation version
1.0.0
Boundary
This applies the rule typed to the stock typed. It allocates and ships nothing, does not judge fairness, and knows nothing about demand not entered.

A request for cut candidates is refused. The result reports a count and the first short name in typed row order for traceability only, and it does not select, rank or deprioritise a location.

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