This observed result is consistent with the growth function simulated with a CV of 20% for weights as the baseline of high variation. While nowhere near the complexity of the real world, the model will suffice to give some grainy video of the economic tradeoffs.

Simulating the Economic Impact of Variation

The primary economic impact of variation is the impact on revenue of the variation. This occurs through the combination of weight (pounds of pork sold), and price affected by packer premiums or discounts for weights and leanness of the pigs.

Figure 5 shows a representative packer grid. This is a surface plot that represents the revenue tradeoff in three dimensions — weight, backfat and premium level or price. To the left side, lightweight pigs are discounted; to the right side, heavy pigs are discounted. At the front edge of the box, pigs are discounted because of low backfat, and to the back of the box, pigs are discounted because of high backfat. The base hog price used is a $40/cwt., live equivalent price, and different values would affect absolute levels, but relative changes would be consistent.

The steps indicate where a premium/discount changes based on weight or backfat measures. You can market a pig anywhere on the surface or tread of the step and get the same price. The highest plateau is the highest possible value for a pig. Assuming costs are constant, ideally you would like to have all pigs priced at this plateau.

Figure 6 shows the high-variance pigs (CV = 20%) marketed through the packer grid, but not including feed costs or sort premiums. Notice how small the highest plateau is. Only 26% of the pigs meet the highest-revenue objective. Other pigs are discounted either because of weight or backfat measures. This is compared to Figure 7, which are the medium-variation pigs (CV = 10%). Not only are there more pigs on the plateau (37%), but 1.3% of pigs are now at the lowest possible price, whereas 2.7% of the higher-variance pigs are at the lowest value of $16.40/cwt.

Figures 8 and 9 take the analysis one step further to include feed costs. Feed costs are based on feed intake and growth described earlier and a corn price of $3.55/bu. and a soybean meal price of $275/ton.

Again, higher feed prices will affect the level of costs, but not the relative impacts of variation. These figures are shown as gross profit over feed costs/head. The distinguishing feature of these charts is the dark blue peak, which signifies pigs that are very near their “full value.”

At the lower left of Figure 8, a large number of high-variation pigs that are low weight and low backfat are actually sold at a loss. From an economic perspective, these pigs should simply be culled as not covering variable costs. With mid-variation (CV = 10%, Figure 9), there are no pigs sold at a loss; therefore, all pigs should be retained.

Now let's look at what's happening over time and levels of variation. Figures 10 and 11 show the gross profit over feed costs of marketing at the “optimum profit day/weight” for the medium- and high-variation examples. As a comparison to the surface charts, this chart is a slice of one day of a surface chart, and the day chosen is the day that the pigs, on average, have their highest value.

Figure 10 shows the value of each of the pigs marketed on Day 157 in a high-variance case (CV = 20%). Earlier, this was suggested as the variation one might observe in an unsorted barn or truckload sampled from that barn.

The pigs are marketed at an average weight of 258 lb. with an average value of $55.97/head. However, many pigs are marketed below this value and even in negative territory. The “full-valued pig” is marketed at 292 lb. and at a value of $86.37/head. The full-valued pig is the absolute best to hope for; it assumes no variation in weights, time or quality. But the difference between the full-valued pig and the average market pig is $30.40/head!

Achieving that optimum level for every pig is clearly not cost-effective. The only way I can imagine it is by selling each pig individually when it reaches that optimum — clearly beyond any reasonable management alternative. However, it does demonstrate the value of the “hole-in-one,” and we can improve by moving incrementally toward this full-value pig. Figure 11 demonstrates this.

Pigs in Figure 11 are drawn from a distribution of pigs with mid-variation (CV = 10%). This reduction in variation is similar to what is observed with sorting practices. The optimal date of marketing increases (164 vs. 157 days), average market weights are higher (271 vs. 258 lb.), and the average profitability increases ($68.37 vs. $55.97/head).