Rounding on Landing Reports Explained and Illustrated

Weights for landing reports and fish ticket may have fractions of pounds, but IFQ reports only allow weights that are whole pounds. However, it is necessary for the totals reported on Fish Tickets to match total IFQ debits.  This page documents the mechanism that eLandings uses to round fractional pounds and maintain matching total weights.

Rounding calculations become very complex in situations with stacked permits and distribution of catch across multiple stat areas. The eLandings system applies a number of business rules and constraints to ensure that pounds are not created or lost in the rounding process and that rounding introduces minimal statistical bias. However, due to the complexity of the underlying data (landing reports with stacked permits and stat area worksheets), multiple calculations with effects on rounding (allocation among multiple CFEC permits, distribution across stat areas, and allocation among multiple IFQ reports), it isn't always possible to predict the exact effect of rounding. It is possible to dissect particular examples and understand rounding in retrospect, and that is the purpose of this page.

Programmer documentation of rounding explains the software's internal mechanisms. This page explains rounding in customer terms.

A simple example with 1 permit and catch evenly distributed over 4 stat areas (even number of sold catch)

When the amount of sold pounds is an even number, the catch is applied evenly among stat areas (see Example 4).  

In this case effort was evenly distributed among four stat areas, and the catch is evenly distributed, with each stat area getting 1 pound.  Each stat area can be expected to get 1 pound when generating IFQ reports.

A simple example with 1 permit and catch evenly distributed over 4 stat areas (odd number of sold catch)

Consider a report with 1 permit and catch of one species distributed over 4 statistical areas. (For eLandings staff, we have a /wiki/spaces/ft/pages/4391021, Example 1, and the result can be viewed in eLandingsTest when logged in as AMACKEREL.)

In this case the effort was evenly distributed among the four stat areas, so the catch is evenly distributed, with each stat area getting 1.25 pounds. When generating IFQ reports, the pounds are rounded to whole numbers, so each stat area could be expected to get 1 pound, but, that leaves 1 pound uncounted. One stat area must receive an adjustment of +1 pounds to generate the correct total IFQ debit. In this simple example, eLandings must choose which stat area gets the adjustment, and in cases where the choice appears arbitrary, eLandings will make the adjustment to the line with the lowest numbered stat area.

Adjustments can be positive or negative

The initial sum of rounded whole values can be larger than the original total, or smaller.  If the initial sum of rounded whole values exceeds the original total, the correction applied can be negative.  (For eLandings staff, we have a /wiki/spaces/ft/pages/4391273, and the result can be viewed in eLandingsTest when logged in as AMACKEREL.)

In this case the effort was evenly distributed among the four stat areas, so the catch is evenly distributed, with each stat area getting 25,001.75 pounds of catch, and 26.25 pounds of deadloss. When generating IFQ reports, the pounds are rounded to whole numbers, so each stat area gets 25,002 pounds of catch, and 26 pounds of deadloss; but, adjustments are required to generate the correct total IFQ debit. As above, in cases where the choice appears arbitrary, eLandings will make the adjustments to the line with the lowest numbered stat area. Adjustments can be positive or negative, and in this case, the catch adjustment is -1 pound, while the deadloss adjustment is +1 pound.  Example 2 shows this adjustment.  (In contrast, Example 5 shows how one more sold pound is adjusted to the lowest stat area and one less deadloss pound is adjusted to the lowest stat area and Example 6 shows how one less pound is adjusted to both sold pounds and deadloss pounds.)

Adjustments are applied to the largest values when possible

When the distribution of catch is not uniform (that is, some stat areas get a higher percentage of the catch), eLandings attempts to apply any necessary adjustments to the largest catch lines. This is statistically preferable because an small adjustment to a large number introduces less bias than a small adjustment to a small number. (For eLandings staff, we have a /wiki/spaces/ft/pages/4391081, and the result can be viewed in eLandingsTest when logged in as AMACKEREL.)

In this case the effort was unevenly distributed among the four stat areas, so the catch is unevenly distributed. When generating IFQ reports, the pounds are rounded to whole numbers, but those whole numbers don't add up to the total of 1001, so an adjustment is required to generate the correct total IFQ debit. In this case eLandings will make the adjustments to the line with the largest catch value. Adjustments can be positive or negative, and in this case, a catch adjustment of +1 pound is applied to the stat area with the largest catch value.  Example 3 shows this adjustment.

Adjustments can happen in multiple discrete steps

Rounding is a stepwise process, and to understand the results it is sometimes necessary to understand each step of the process. This example illustrates the steps involved with multiple IFQ permits (without maxout pounds), multiple stat areas, and multiple line items. (For eLandings staff, we have a /wiki/spaces/ft/pages/4390937, and the result can be viewed in eLandingsTest when logged in as AMACKEREL.)

When IFQ reports are generated, the stat area worksheet causes sold catch and deadloss to be distributed over two stat areas, with 75 pounds to stat area 575731 and 25 pounds to stat area 575732.  The sold pounds and deadloss pounds are then evenly distributed among the two IFQ permits, rounding down because 75 and 25 are not evenly divisible by two, giving IFQ report items with 37 and 12 pounds respectively. 

Next, whole-number amounts from fish ticket summaries are compared with the corresponding amounts on the IFQ reports (75 compared with 37+37, and 25 compared with 12+12), and one pound adjustments are applied to IFQ reports until they match Fish Ticket totals.  Adjustments are applied to IFQ report items with maxout pounds first; within those with maxout pounds the smallest first; within those by IFQ Permit: next IFQ permit items with area/fishery; within those by area/fishery; within those by IFQ permit: then IFQ permit items with neither max out pounds or area/fishery by IFQ permit.  In this case no IFQ report items have maxout or area/fishery, so the smallest (990051) IFQ permit gets the adjustment pounds in every case. 

Finally, IFQ reports are "leveled", and in this case, since one report got four positive rounding-related adjustments, while the other report got none, leveling requires that 2 pounds be moved from 990051's report to 990052's report.  Leveling adjustments are made in 1 pound increments; there are two adjustments of 1 pound each from the sold items on 990051's report to the corresponding sold items on 990052's report.  The end result of the leveling is that 990051's report retains both rounding adjustments on its deadloss items, while 990052's report effectively acquires both rounding adjustments on its sold items. 

Net result can be difficult to predict

This example illustrates an unexpected result with multiple IFQ permits (without maxout pounds), multiple stat areas, and multiple line items. (For eLandings staff, we have a /wiki/spaces/ft/pages/4390938, and the result can be viewed in eLandingsTest when logged in as AMACKEREL.)

When IFQ reports are generated, the stat area worksheet causes sold catch and deadloss to be distributed over two stat areas, with 76 pounds to stat area 575731 and 25 pounds to stat area 575732. (The stat area with the larger percent gets the extra pound.) The sold pounds and deadloss pounds are then evenly distributed among the two IFQ permits. Stat area 575731 has 76 pounds, evenly divisible by 2 yielding 38 pounds. Stat area 575732 has 25 pounds which rounds down to 12 pounds.

Next, whole number amounts from fish ticket summaries are compared with the corresponding amounts on the IFQ reports (76 compared with 38+38, and 25 compared with 12+12), and one pound adjustments are applied to IFQ reports until they match Fish Ticket totals. Adjustments are applied to IFQ report items with maxout pounds first; within those with maxout pounds the smallest first; within those by IFQ Permit: next IFQ permit items with area/fishery; within those by area/fishery; within those by IFQ permit: then IFQ permit items with neither max out pounds or area/fishery by IFQ permit. In this case no IFQ report items have maxout or area/fishery, so the item with the smallest (990051) IFQ permit gets the one pound adjustment on both sold and deadloss items.

Finally, IFQ reports are "leveled", and in this case, since one report got two positive rounding-related adjustments (adjustments for stat area 575732 on both catch and deadloss), while the other report got none... one adjustment of 1 pound from the stat area 575731 (the stat area with the largest percent) sold item on 990051's report to the stat area 575731 sold item on 990052's report "levels" the reports while retaining the match between fish ticket pounds and IFQ pounds. The end result of the leveling is that 990051's report loses one pound from a stat area 575731 catch item, while 990052's report acquires one pound on its stat area 575731 sold item.