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The Economics Of Ingredient Allocation

Introduction
Ingredient Allocation is a term used to describe a method of formulation or ingredient evaluation that is based on multiple formulation. This paper seeks to describe the principles of multiple product formulation and then will show two exercises. The first will be to show how multiple formulations can be used to save ingredient cost, and then to demonstrate the comparison of two ingredients against each other on a n economic and technical basis.

Single Product Optimization
In order to understand the workings of Multiple Product Optimization (MPO), we should first look at the basic Single Product Optimization (SPO). Both techniques use the same method of calculation, Linear Programming or LP, to achieve an optimal solution. There are some basic functions common to all SPO systems:

Ingredient Data - The ingredient database contains all the nutrient data for the ingredients in the feedmill and also those that the feedmill may wish to evaluate. One of the roles of the nutritionist is to search for alternative ingredients even though they may not be currently available.

Price Data - The ingredients should all have prices. Operationally these may be the stock or replacement prices. Test ingredients may use guide prices or even very high prices to prevent them from being used. These high prices are used to generate shadow prices.

Formula Specifications - Formula specifications contain two components; the nutrient specifications and the ingredient specifications. These take the form of minimum and maximum limits in both sections.

Examples of these are given in the Tables 1, 2 and 3.

Given these three data, the LP can be used to calculate a solution. The solution, if feasible, is a combination of ingredients that meets the nutrient limits at the lowest or ¡ã¡Þleast cost¡ã¡À. We have to u the term ¡ã¡Þleast cost¡ã¡À with some caution as it can imply that the feed is too cheap, however, it shou be remembered that the selection of the ingredients and their limits makes a major contribution to the quality of the feed. The term ¡ã¡Þoptimize¡ã¡À is preferred as this implies that the feed will have the be cost for a required situation and desired quality. Table 4 shows the ingredient solution resulting from optimizing the feed specified in Table 3.

The first three columns are ingredient name, percent of mix and ingredient cost per kg (from the ingredient file). The next two columns are information generated by the LP relating to ingredient price. In Table 4, the price of corn changes from 6.30 to less than 6.18 (the Low Range Price) then the formula will change. If the price exceeds 7.79 (the high range price) then the formula will change. This applies only if the other ingredient prices do not change. Thus the ranging prices give an indication of the price stability of the feed.

Originally when LP was applied to feed formulation problems, this was very useful information as an experienced formulator could spot potential problems. It would also enable the nutritionist to make judgments from print outs of solutions. The application of this was to be able to make accurate changes to the specification or prices before calculating the feed again. This was important as feeds could take several minutes to re-optimize so changes had to be selected with care. Now that both the programs and particularly the computer hardware are faster, the ranging values are not so important  to the user. It is much simpler to use a parametric analysis where the feed is tested over a pre-set range of prices to see the impact on ingredient composition and feed cost.

The restriction cost indicates the cost of imposing an ingredient limit. For example, rice bran has an ingredient cost of (R)C0.120. This means that each 1 percent of increase in the maximum limit of ric bran will save 0.120 Baht per Kg. The units in which these restrictions costs are expressed will vary between systems, so reference to your user manual may be needed before making any deductions regarding the restriction price. As with ranging price there are some limitations to the value of the data. The cost of restriction is only valid and linear up until the next break point (that is where the  cost/unit changes as the inclusion changes). We cannot assume that the relationship of (R)C0.12 Bah per Kg holds true over a wide range. So again the best approach is to run a parametric analysis on the formula to see the reaction of feed cost to rice bran inclusion over a wide range.

The last two columns show the minimum and maximum limits of each ingredient. Note that the usage of these is slightly different between ingredients. Some ingredients such as fat will have minimum values as well as maximum due to physical constraints on production, others such as rice bran will have maximum constraints. These constraints are very subjective, and depend on the experience of the nutritionist, QC department and production staff.

Table 5 shows the data on rejected ingredients. Some of these have been rejected due to availability such as Meat and Bone Meal 45%. Others, such as Soybean Meal 48% have been rejected on price. The Low Range Price then shows the price at which the ingredient can be accepted into this formula. This price is often referred to as the Shadow Price or Entry Price.

Again this is useful information, but it has limitations of which we have to be aware. Firstly, the shadow prices will vary between formulas. Indeed where prices are competitive, some formulas may use an ingredient whereas others will reject it. The other limitation is that while this indicates the threshold price, the quantity of the ingredient may not be sufficient to warrant purchasing it.

With all of this price and restriction cost data there is the other advantage that as soon as a price of one ingredient changes significantly, the comparable price information will also change. Thus the shadow prices would have to be re-evaluated, which would be very time consuming. Unfortunately, in a large feedmill, the amount of time required may be prohibitive which underscores the need for multiple formulation where the operation is fully integrated and considerably faster.

Similar data is also generated for the Nutrient Data as shown in Table 6. The minimum and maximum nutrient values have all been met and where the nutrients are restricted, there is a restriction cost. The unit of restriction here is per 100 kgs feed per unit of change. As with ingredient data, it is better to use the parametric analysis to take a closer look at these constraints as wider ranges of nutrient can be examined dynamically.

It should be remembered that any ¡ã¡Þtightening¡ã¡À of a limit will lead to an increase in cost of the fee Tightening means either lowering an active maximum constraint or increasing an active minimum constraint. The same principle applies to MPO where applying tighter limits will increase the cost of the overall solution.

Before running MPO, all the formulas should be optimized and feasible. Some MPO systems will highlight any formulas in the set that are infeasible, but correcting them at this stage can be time consuming, so it is best done first.

In the MPO examples that follow, we will be running the sample feeds listed in Table 7. Table 8 shows the ingredients that will ideally be needed to manufacture these feeds.

Multiple Product Optimization
The original use for MPO was to restrict the usage of ingredients that were not available at the full amount required. As an example, we might limit the amount of 4124 Meat and Bone Meal 52% to 100 tons. We can see the effects in Table 9a, b, c and 10. Table 9a shows the usage of ingredients from the MPO solution to the SPO solution without restriction.

As well as the minimum and maximum ingredient limits there is a column showing the Penalty (Table 9b). This is the restriction cost of limiting the usage of 4214 Meat and Bone 52% DD. The unit is in per ton of restriction. This however only applies at the particular quantity shown above. At other levels of restriction, the effect may be less.

As we allow more Meat and Bone Meal to be used, the penalty decreases. This is partly explained by the difference in value in different formulas. As mentioned earlier, the ranging data will be different for each feed, and this response reflects a summary of those ranging values. A contributing factor is that as an ingredient becomes more scarce, it acquires more value. This is a well-known economic effect, shown here in practice.

The concept of value is important. It is not the offer price of the ingredient, but the true value of the ingredient to the feedmill. For example in Table 9b, we can conclude that the value of 160 tonnes of meat and bone meal is 14,000 (its costs) +1460.11 (its penalty) = 15,460.11. Thus if we can successfully bid lower than the value of 15,460.11 we have secured a profit to the feedmill. If we were able to buy it at 15,000, then the profit on each tonne bought would be 460.11 baht.

This is the first instance where we highlight the important concept that ingredient price and quantity are closely interlinked. In fact they are inseparable when calculating the value of a commodity.

Table 10 shows the effect of the restriction on the formula price. It is important to note that the effect of restriction is not equally shared across all formulas. We can see that the layer feeds and duck feeds are unaffected by the restriction whereas there is a varying effect in the others. The feed cost of broiler grower in particular is increased by 51.15 baht. Again, this points to the different value of commodities in different feeds. This is going to affect the pricing of some of the feeds, so the nutritionist may wish to limit the swing in the usage of MBM in the broiler grower to balance out the cost increase. Another consideration that is not often practiced is to strategically sell less of the feed that suffers the most from the ingredient restriction. This will increase the allocation of ingredients for other feeds.

The effect of limiting MBM in this case is to raise the average feed price from 8413.78 to 8434.27 baht per ton or an increase in cost per ton of 20.49. This does indicate that it is preferable to buy the ingredients needed. It also suggests that MPO is going to increase the cost of the feed. It should be remembered that MPO will give the cheapest solution to a particular problem.

The solution above contains an example of a very common hidden cost. In the base formulas, the use of meat and bone meal has been manually restricted by putting maxima in the formula specifications that are lower than the maxima that would be technically acceptable. All of the feeds have maximum of 3% where 5% might be used. Table 10 shows the effect of raising the limits in each formula specification and then using the MPO to allocate the ingredient to the most economic formulas.

We can see in this case that the re-allocation has saved 3.91 baht per ton or 38,000 baht on a single commodity. This is analogous to the costs incurred when manual formulation is practiced in case of optimization. In order for these savings to be valid, then technical limits need to be observed closely, but the above changes would be quite acceptable. It is useful to occasionally review limits (if MPO is an option) to make sure that maxima designed to restrict total usage rather than formula usage has not accumulated in the database.

Ingredient Allocation is a critical tool in pricing ingredients. A good example of this is the comparison of 43% SBM to 48% SBM. There are several methods used such as pro-fat pricing comparison of protein values, but these do not take into account the overall contribution of the SBM 48% to a full range of nutrients needed in the feed including ME, Protein, amino acids and density. When we compare values of the two ingredients using MPO additional factors such as available tonnage and product mix can be taken into account.

It is useful to review the single formula shadow prices of SBM 48% in these formulas from SPO. These data show the variable value of SBM 48% in different feeds. This is one reason for the effect of different product mixes on comparative value. Table 12 lists the shadow prices of SBM 48% in different feeds. This is one reason for the effect of different product mixes on comparative value. Table 12 lists the shadow prices of SBM 48% when compared to SBM 43% at 12 baht per kg. There is a range of values from 12.50 up to 13.80 baht per kg so the shadow price is by no means constant. If the enterprise concentrated on making these duck feeds then the value of SBM 48% would be relatively low when compared to a broiler producer.

Table 13 shows the quantities demanded at different levels of SBM 48 price with the same acceptance ranges indicated by the shadow prices of 12.50 to 13.80 baht per kg, however there is no single point at which we can say that SBM 48 is definitively economic. At 12.80 baht per kg, it is the preferred source in terms of volume. The data from this table is graphed in Figure 1 to show the demand curve of this set of formulations for the different types of soybean meal. This highlights that there is no distinctive formula that would give a relative price in order to decide which of the soybean meals to purchase. If we were to base the price comparison on protein the relative price of SBM 48 would be 13.39 baht. On a lysine basis, the competitive price of SBM 48 would be 13.85 and on an energy basis it would be 12.50.

We can also use the allocation technique to equalize the total prices of the formulations when either SBM 43 or SBM 48 is available. The base price of the formulation is 8,413 baht per tonne when SBM 43 is used and the price of SBM 48 required to equal this over the whole product range is 12.99 baht. It should be stressed that the ingredients being compared here are assumed to have equal amino acid digestibilities. It is important that the evaluations of this type also take account of the origin of the meal and its processing conditions.

Conclusion
Ingredient Allocation is a useful exercise in not only producing economic feeds, but also for accurate comparison of feed ingredients. The advantage in normal feed formulation is that MPO can give the best answer to situations when ingredients are in short supply when compared to manual allocation of scarce raw materials. Ingredient Allocation is a better tool for ingredient pricing when compared to less dynamic studies on shadow prices. The presentation of the MPO problem in state of the art formulation programs is such that rapid economic tests can be made to identify the profitable ingredients taking into account the product types and tonnage in the feedmill. In addition, the MPO systems allow the buyer or nutritionist to determine threshold quantities as well as prices for competitive purchases.

Tags · Economics · Ingredient Allocation · Feed Ingredients · Feed Formulation · Feed Formulation · Ingredient Evaluation

17.02.2008. 13:03