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--- input_allocation [2020/02/11 09:44] – [Input Allocation] matsz
+++ input_allocation [2020/02/24 08:53] – [Input allocation for feed] matsz
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 All of the econometric coefficients were required to be transformed into an ‘activity level’ form, due to the fact that this is the definition used in the CAPRI model. Before this could be done, it seemed necessary to fill up the matrix of estimated coefficients because some estimates were missing and others were negative. In order to this we constructed a number of coefficients that were weighted averages among certain groups. These mean coefficients were the following.
+  - //Mean coefficients of activity groups//. Each activity was allocated to a certain group (e.g. soft wheat belonged to cereals). For each group we built weighted averages among the positive estimates within a group using the estimated t statistics as weights. This coefficient only existed if there was at least one positive estimate inside that group and was then used to replace the gaps inside the coefficient matrix. If that mean coefficient was not available, due to no positive estimate inside a group at all, the next type of mean coefficients became relevant:
+  - //Mean coefficients for an activity among European regions//. This second type of mean coefficients calculates weighted averages among three types of regional clusters. These clusters are Northern European States, Southern European states and all European regions. Again, the estimated t statistics were used as aggregation weights. Unfortunately, this type of averages did not fill all gaps in the coefficient matrix as there were some activities that had no positive estimate over the entire EU. For those the third type of mean coefficients was calculated.
+  - //Mean coefficients for activity groups among regional clusters//. Here we calculated for the three regional clusters the averages of the first type of mean coefficients. As even the latter are synthetic, we gave each mean of them the same weight. Fortunately there was only a small probability that this coefficient did not exist for one of the groups as this was only the case if no coefficient inside a group over the entire EU had a positive estimate, which was not the case.
+Following these rules we finally got a matrix of estimated and synthetic calculated input coefficients for both, the ‘per activity level’ and the ‘per production’ unit definition((In addition, a similar procedure (using slightly different groups) was applied to constructing coefficients for the ‘Other’ activities (e.g. OCER, OFRU, OVEG), which had been omitted from the econometric estimations. They are given the average group coefficient, unless there is none; then they are given the average northern or southern European coefficient as appropriate.)). For the synthetic one there was no estimated standard error available but we wanted to use those later on. So we assumed them –to reflect that these coefficients have only weak foundation– to have a t statistic of 0.5.
+The ‘per level’ definition was only taken over if the coefficient was really estimated or if no per production unit definition did exist. To transfer the latter into per activity level definition, we multiplied them with the average yield (1985 2001) of the respective activity. The resulting coefficients and their standard errors were then used a HPD approach as a //first set of priors//((The previously described completions are implemented in file gams\input\fill_inp_matrix.gms. Adjustments were made for scaling issues with regard to eggs for certain countries, and grass for Finland. In addition, when ‘CAFR’,’CAFF’ and ‘HEIR’ did not have econometric data, they assumed the coefficients and standard errors of ‘CAMR’, ‘CAMF’ and ‘HEIF’ respectively (CAPRI activity code definitions in the Annex).)).
+Missing econometric estimates and compatibility with EAA figures were not the only reasons that made a reconciliation of estimated inputs coefficients necessary. Moreover, the economic sense of the estimates could not be guaranteed and the definition of inputs in the estimation differed from the one used in CAPRI. Therefore we decided to include further prior information on input coefficients in agriculture. The //second set of priors// in the input reconciliation was therefore based on data from the EAA. Total costs of a certain input within an activity in a European Member State was calculated by multiplying the total expenditures on that input with the proportion of the total expected revenue of that activity to that of all activities using the input. Total expected revenue in this case was the production value (including market value and premiums) of the respective activity. If this resulted in a certain coefficient being calculated as zero due to missing data, then this coefficient would be replaced by one from a similar activity e.g. a zero coefficient for ‘MAIF’ would be replaced by the coefficient for ‘GRAS’
+This kind of prior information tries to give the results a kind of economic sense. For the same reason the //third type of priors// was created based on standard gross margins for agricultural activities received from EUROSTAT. Those existed for nearly all activities. The set from 1994 was used, since this was the most complete available. Relative rather than absolute differences were important, given the requirement to conform to EAA values((Contrary to the econometric estimated priors, the two other types were different in different years, since the reconciliation had to be done for each year in the database. The second prior type is year specific by nature, as the EAA values differ between years. In case of standard gross margins, unfortunately, we had them only for one year (1994). So we decided to ‘drive them over time’ using the proportion of expected revenue of an activity in a certain year to that in the year 1994. Furthermore it may be mentioned that for plant protection coefficients a fourth set of priors from an industry source has been used and that energy inputs also received a special treatment in the key file gams\input\dist_inputs.gms.)).
+Given the three types of prior information explained above –estimated input coefficients, data from EAA and standard gross margins , a HPD estimator has been used to reconcile the prior information on input coefficients. Accounting constraints ensure (see in “dist_input.gms”) first that gross margins for an activity is the difference between expected revenue per activity level of that activity and the sum over all inputs used in that activity and second that the sum over all activities of their activity levels multiplied with an input gives the total expenditures on that input given by the EAA. The estimation is carried out in GAMS within and run for each year in the database. Some bounds are further set to avoid estimates running into implausible ranges.
+The Highest Posterior Density estimation yields monetary input coefficients for the fertiliser types (Nitrate, Phosphate, Potassium), seeds, plant protection, feeds, pharmaceutical inputs, repairs, agricultural service input, energy and other inputs. While some of these can be directly used in the CAPRI model, we need special treatments for others –e.g. fertilisers, because they are used in physical units inside the model, and feeds, since they are much more disaggregated.
+====Input allocation for young animals and the herd flow model ====
+Figure below shows the different cattle activities and the related young animal products used in the model. Milk cows (DCOL, DCOH) and suckler cows (SCOW) produce male and female calves (YCAM, YCAF). The relation between male and female calves is estimated ex post in the COCO framework. These calves are assumed to weigh 50 kg at birth (see gams\feed\feed_decl.gms) and to be born on the 1st of January. They enter immediately the raising processes for male and female calves (CAMR, CAFR) which produce young heifers (YHEI, 300 kg live weight) and young bulls (YBUL, 335 kg). The raising processing are assumed to take one year, so that calves born in t enter the processes for male adult fattening (BULL, BULH), heifers fattening (HEIL, HEIH) or heifers raising (HEIR) on the 1st January of the next year t+1. The heifers raising process produces then the young cows which can be used for replacement or herd size increasing on the first of January of t+2. The table below the diagram shows a numerical example (for DK, 1999-2001) for these relationships.
+**Figure 5: The cattle chain**
+{{:figure_5.png?600|}}
+Accordingly, each raising and fattening process takes exactly one young animal on the input side. The raising processes produce exactly one animal on the output side which is one year older. The output of calves per cow, piglets per sow, lambs per mother sheep or mother goat is derived ex post, e.g. simultaneously from the number of cows in t-1, the number of slaughtered bulls and heifers and replaced in t+1 which determine the level of the raising processes in t and number of slaughtered calves in t. The herd flow models for pig, sheep and goat and poultry are similar, but less complex, as all interactions happen in the same year, and no specific raising processes are introduced.
+** Table 7: Example for the relation inside the cattle chain (Denmark, 1999-2001)**
+^ ^		^1999	^2000	^2001^
+|**Male calves used in t and born in t**||
+|DCOWLEVL	|Number of dairy cows|	667,03|	654,08|	631,92|
+|DCOWYCAM	|Number of male calves born per 1000 dairy cows|	420,72	|438,62	|438,26|
+|//Number of males calves born from dairy cows//	| |	280,63|	286,89|	276,95|
+|SCOWLEVL	|Number of suckler cows	|127,36	|126,91	|124,85|
+|SCOWYCAM	|Number of male calves born per 1000 suckler cows|	420,72|	411,83|	401,61|
+|//Number of male calves born from suckler cows//|		|53,58	|52,27	|50,14|
+|//Number of all male calves born//|		|334,22	|339,16	|327,09|
+|GROFYCAM	|Number of male calves produced	|334,21	|339,16	|327,09|
+|CAMFLEVL	|Number of male calves fattened	|81,32	|72,57	|49,18|
+|CAMRLEVL	|Activity level of the male calves raising process|	252,89|	266,59|	277,91|
+|Sum of processes using male calves	|	|334,21|	339,16|	327,09|
+|GROFYCAM	|Number of male calves used	|334,21	|339,16	|327,09|
+|**Female calves used in t and born in t**||
+|DCOWLEVL	|Number of dairy cows	|667,03	|654,08|	631,92|
+|DCOWYCAF	|Number of female calves born per 1000 dairy cows|	404,15|	421,58|	412,86|
+|//Number of female calves born from dairy cows//|	|	269,58|	275,75|	260,89|
+|SCOWLEVL	|Number of suckler cows	|127,36	|126,91	|124,85|
+|SCOWYCAF	|Number of male calves born per 1000 suckler cows	|404,15|	398,04|	387,21|
+|//Number of female calves born from suckler cows//|		|51,47|	50,52	|48,34|
+|//Number of all female calves born//|		|321,05	|326,26	|309,24|
+|GROFYCAF	|Number of female calves produced	|321,05	|326,27|	309,24|
+|CAFFLEVL	|Number of female calves fattened	|26,64	|28,74|	18,39|
+|CAFRLEVL	|Activity level of the female calves raising process|	294,41	|297,53	|290,85|
+|Female calves used in t and born in t	|	|321,05|	326,27|	309,24|
+|GROFYCAF	|Number of female calves used	|321,05	|326,27	|309,24|
+|**Young bulls used in t and young bulls produced in t**||
+|BULFLEVL|	Activity level of the bull fattening process|	262,94|	252,89|	266,59|
+|GROFIBUL|	Number of young bulls used	|262,94	|252,89|	266,59|
+|GROFYBUL|	Number of young bulls raised from calvs	|252,89|	266,59	|277,91|
+|CAMRLEVL|	Activity level of the male calves raising process	|252,89|	266,59|	277,91|
+|**Heifers used in t and heifers produced in t**||
+|HEIFLEVL|	Activity level of the heifers fattening process	|64,36	|67,25|	68,12|
+|HEIRLEVL|	Activity level of the heifers raising process	|235,45|	227,16|	229,4|
+|Sum of heifer processes|		|299,81| 294,41|	297,52|
+|GROFIHEI	|Number of heifers used	|299,81	|294,41	|297,53|
+|GROFYHEI	|Number of heifers raised from calves	|294,41|	297,53	|290,85|
+|CAFRLEVL	|Activity level of the female calves raising process	|294,41	|297,53|	290,85|
+|**Cows used in t and heifers produced in t**||
+|DCOWLEVL	|Number of dairy cows	|667,03|	654,08|	631,92|
+|DCOWICOW	|Number of young cows needed per 1000 dairy cows	|332,01	|332,5|	327,52|
+|//Sum of young cows needed for the dairy cow herd//|		|221,46	|217,48|	206,97|
+|DCOWSLGH	|Slaugthered dairy cows	|221,47	|217,48	|206,11|
+|SCOWLEVL	|Number of suckler cows	|127,36	|126,91	|124,85|
+|SCOWICOW	|Number of young cows needed per 1000 suckler cows	|332,01	|332,48	|327,52|
+|//Sum of young cows needed for the suckler cow herd//|		|42,28	|42,20|	40,89|
+|SCOWSLGH	|Slaugthered suckler cows	|42,29	|42,19	|40,72|
+|//Sum of slaughtered cows//|		|263,76	|259,67	|246,83|
+|GROFICOW	|Number of young cows used	|263,75	|259,67|	247,86|
+|Stock change in dairy cows	|(DCOWLEVL(t+1)-DCOWLEVL(t)	|-12,95	|-22,16	|
+|Stock change in suckler cows	|(SCOWLEVL(t+1)-SCOWLEVL(t)	|-0,45	|-2,06	|
+|//Sum of stock changes in cows	//	| |-13,4	|-24,22	|
+|//Sum of slaughtered cows and stock change//|		|	|235,45|
+|GROFYCOW|	Numer of heifers raised to young cows|	235,45	|227,16	|229,4|
+|HEIRLEVL|	Activity level of the heifers raising process	|235,45	|227,16	|229,4|
+The table above is taken from the COCO data base. In some cases, regional statistical data or estimates for number of young animals per adult are available, but in most cases, all input and output coefficients relating to young animals are identical at regional and national level. Nevertheless, experiences with simulations during the first CAPRI project phase revealed that a fixed relationship between meat output and young animal need as expressed with on bull fattening process overestimates the rigidity of the technology in the cattle chain, where producers may react with changes in final weights to relative changes in output prices (meat) in relation to input prices (feed, young animals). A higher price for young animals will tend to increase final weights, as feed has become comparatively cheaper and vice versa. In order to introduce more flexibility in the system, the dairy cow, heifer and bull fattening processes are split up each in two processed as shown in the following table.
+**Table 8: Split up of cattle chain processes in different intensities**
+^ ^Low intensity/final weight	^High intensity/final weight^
+|Dairy cows (DCOW)	|DCOL: 60% milk yield of average, variable inputs besides feed an young animals at 60% of average	|DCOH: 140% milk yield of average, variable inputs besides feed an young animals at 140% of average|
+|Bull fattening (BULF)	|BULL: 20% lower meat output, variable inputs besides feed an young animals at 80% of average	|BULH: 20% higher meat output, variable inputs besides feed an young animals at 120% of average|
+|Heifers fattening (HEIF)|	HEIL: 20% lower meat output, variable inputs besides feed an young animals at 80% of average	|HEIH: 20% higher meat output, variable inputs besides feed an young animals at 120% of average|
+====Input allocation for feed====
+The input allocation for feed describes how much kg of certain feed categories (cereals, rich protein, rich energy, feed based on dairy products, other feed) or single feeding stuff (fodder maize, grass, fodder from arable land, straw, milk for feeding) are used per animal activity level((The reader should notice again that the activity definition for fattening processes are slaughtered plus exported minus imported animals and not stable places.)).
+The input allocation for feed takes into account nutrient requirements of animals, building upon requirement functions. The input coefficients for feeding stuff shall hence ensure that energy, protein requirements, etc. cover the nutrient needs of the animals. Further on, ex post, they should be in line with regional fodder production and total feed demand statistics at national level, the latter stemming from market balances. And last but not least, the input coefficients together with feed prices should lead to reasonable feed cost for the activities.
+===Estimation of fodder prices===
+Since the last revision of the EAA, own produced fodder (grass, silage etc.) is valued in the EAA. Individual estimates are given for fodder maize and fodder root crops, but no break down is given for fodder on arable land and fodder produced as grassland as presented in the CAPRI data base. The difference between grass and arable land is introduced, as conversion of grass to arable land is forbidden under cross compliance conditions so that marginal values of grassland and arable land may be different.
+The price attached to fodder should reflect both its nutritional content and the production costs at regional level. The entropy based estimation process tries to integrate both aspects.
+The following equations are integrated in the estimator. Firstly, the regional prices for ‘grass’, ‘fodder on arable land’ and ‘straw’ (fint) multiplied with the fed quantities at regional level must exhaust the vale reported in the economic accounts, so that the EAA revenues attached to fodder are kept unchanged:
+\begin{equation}
+\sum_{r,fint}\overline{FEDUSE}_{r,fint}PFOD_{r,fint} = \overline{EAAP}_{OFAR,MS}+\overline{EAAP}_{GRAS,MS}
+\end{equation}
+Secondly, the Gross Value Added of the fodder activities is defined as the difference between main revenues (from main fodder yield), other revenues, and total input costs based on the input allocation for crops described above.
+\begin{equation}
+GVAM_{r,fint} = \overline{YIELD}_{r,fint}PFOD_{r,fint}+\overline{OREV}_{r,fint}-\overline{TOIN}_{r,fint}
+\end{equation}
+Other revenues may be from the nutrient value in crop residues. Next, an HDP objective is added which penalises deviations from the a priori mode.
+The a priori mode for the prices of ‘grass’ and ‘other fodder on arable land’ are the EAAP values divided by total production volume which is by definition equal to feed use. The price of straw for feed use is expected to be at 1 % of the grass price.
+Supports for Gross Value Added per activity are centred around 150 % of the value of total inputs as allocated by the rules and algorithm described above, with wide bounds.
+Wide supports for the Gross Value Added of the fodder activities mirror the problem of finding good internal prices but also the dubious data quality both of fodder output as reported in statistics and the value attached to it in the EAA. The wide supports allow for negative Gross Value Added, which may certainly occur in certain years depending on realised yields. In order to exclude such estimation outcomes as far as possible an additional constraint is introduced:
+FIXME
+\begin{equation}
+GVAM_{r,fint} \ge \overline{TOIN}_{r,fint}\overline {gvafac} \text PLATZHALTER EQUATION 37
+\end{equation}
+The parameter \(gvafac\) is initialised with zero so that first a solution is tried where all activities have positive GVAs. If infeasibilities arise, the factor is stepwise increased until feasibility is achieved, to ensure that estimated fodder prices are giving the minimal number of activities with negative Gross Value Addeds.
+===Calibration of the feed allocation ===
+The allocation of feed to animal activities has been changed several times (like the fertiliser allocation). The most recent version has been developed ((This section draws upon a corresponding Star 2 deliverable and coding which are due in major parts to CAPRI expert Markus Kempen. As Markus was not involved in this documentation, he is released from any responsibility for remaining errors. A more detailed version of this section is offered as [[https://www.capri-model.org/dokuwiki/lib/exe/fetch.php?media=docu_feed_calib.pdf]].)) in the Stable Release 2 (in the following: “Star2”) project which will become also the standard version in the CAPRI trunk at the next opportunity.
+**General concept**
+In the “pre-Star2”((It has to be acknowledged that the specificaiton described in this section is not activated by default in CAPRI task “build regional database” whereas it is active in CAPRI task “Calibrate supply models”. This setting will be changed shortly.))  implementation, based on the CAPRI model procedures, the objective in the data consolidation in tasks “build regional database” (capreg base year) and “baseline calibration supply” (capmod, baseline mode) is to cover the daily needs per animal with the available feed stuff (considering the daily feed intake capacity). In CAPRI most parameters determining the actual requirements of animals can be derived from statistics, e.g. milk yield, final live weight, daily gain, Apart from the uncertainty of statistical data, the calculated requirements can be seen as the “true” requirements in a country or region, as the differences between different animal nutrition literature sources are usually small. Nonetheless uncertainty in the data derived parameters can often lead to an over- or underestimation of the requirements in a range of 5-20% from the computed average need. This uncertainty may be taken into account when specifying the objective function for the required allocation model in a high posterior density (hpd) approach where the uncertainty on feeding requirements is expressed in terms of a standard deviation. This basic approach also underlies the “pre-star2” feed allocation.
+The pre-star2 feed calibration approach also considered two economic indicators that depend on the feed allocation:
+  * Feed costs and
+  * Gross margins, in particular the avoidance of negative gross margins ((Note that this refers to gross margins of animal activties, not to the gross margins of fodder activities which have been addressed in the previous section.))
+These two criteria have been abandoned because technical plausibility was considered more important for the feed allocation than the derived value items. It may be argued that uncertainty in feed prices should not be transferred to the physical coefficients which is a consequence when considering both in the objective. Furthermore, the pmp approach of CAPRI has proven able to cope with negative margins even though it is admitted that they may not be entirely plausible.
+In the pre-star2 CAPRI approach minimum and maximum bounds on specified feeding stuffs are specified to ensure technical plausibility, but to prevent infeasibilities they left considerable degrees of freedom. Additional hard constraints were for lysin and fiber contents of feed. However, a detailed analysis revealed that the purpose of these restrictions to ensure plausible feed ratios, for example regarding the relation of concentrate feed and roughage, was often missed. It has been decided therefore to skip these constraints.
+The revised feed allocation methodology includes several new additional terms in its objective to capture technical plausibility beyond the animal requirements in terms of energy and protein and technical reproducibility of the calibration approach. These will be explained in more detail in the following sections.
+**Equations**
+An overview of the equations used in the old and new feed allocation procedure is given in Table below. The objective function has changed significantly and more details on this will be discussed below. The equations ensuring consistency among production and consumption of feed, as well consistency across regional levels are unchanged.
+**Table 9: Equations used in old and new feed allocation routine**
+^equation^^ ^ ^
+^old^new^description ^comment ^
+|hpdFeed_|hpdFeed_|objective function|changed significantly (see following section)|
+|FEDUSE_|FEDUSE_|Balance for feeding stuff regional| needed to achieve consistency between produced feed and feed input to all animals and among regional layers|
+|FEDUSEA_|FEDUSEA_|Aggregation to regional feed input coefficient to aggregate one |:::|
+|FEDUSES_|FEDUSES_|Fixation for feeding stuff regional in calibration| :::|
+|REQSE_|REQSE_|Requirements of animals written as equality|for energy ENNE and crude protein CRPR |
+|REQSN_| |Requirements of animals written as in-equality |other requirements (lysine, dry matter and fibre)|
+|MINSHR_|		|Maximum feed shares|Constraints on single feed stuff not used as hard bounds in new version |
+|MAXSHR_|		|Minimum feed shares|Constraints on single feed stuff not used as hard bounds in new version |
+|CST_|CST_|Definition of feed cost from feed input coefficients and prices|Feed cost in new version only for monitoring, not in objective or constraints|
+|MEANDEV_|		|Definition of average deviation from requirements for all herds|oversupply by animal type was pulled against the mean oversupply.|
+| |NutContFeed_	|Nutrition content in the feed aggregates supplied to an animal category|nutrient content (per kg dry matter) is part of the objective|
+| |FEDAGGR_ |aggregate to roughage, concentarte feed, etc|Defines feed aggregates from single bulks FEED|
+| |FeedAggrShare_ |Calculate share of feed aggregates (roughage, concentrates, other)|shares of roughage and concentrate feed enter objective|
+| |MeanFeedTotal_ |Calculates total feed intake in DM per animal|Part of revised objective function|
+The four additional equations developed in the new feed allocation procedure are described in more detail in the following.
+__NutContFeed_ __
+{{::code_p_71.png?600|}}
+For nutrient content (energy, crude protein) in the total feed mix or in concentrate feed recommendations are frequently given in the animal nutrition literature. The equation NutContFeed_ calculates this based on the estimated feed input coefficients and the data on nutrient content and dry matter per feeding stuff. A small number is added to the denominator to avoid division by zero (e.g. while gams is searching for a feasible solution)
+__FedAggr_ __
+{{:code_p_72.png?600|}}
+An aggregation of specific feeding stuff to aggregates (roughage, concentrates) is done since prior shares as well as minimum and maximum shares are more often found in the literature for aggregates than for single feedstuffs. The mapping is shown in Table below. It has been specified basically by putting into the “other” category all “special” items. Therefore, straw is a component of this “other” category rather than “roughage”.
+**Table 10: Mapping feeding stuff to feed aggregates**
+^ ^FGRA^FMAI^FOFA^FROO^FCOM^FSGM^FSTR^FCER^FPRO^FENE^FMIL^FOTH^
+^FeedRough|  X  |  X  |  X  |  X  | | | | | | | |
+^FeedCons| | | | | | | |  X  |  X  |  X  |  X  | |
+^FeedOth| | | | |  X  |  X  |  X  | | | | |  X  |
+^FeedTotal|  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |  X  |
+__ FeedAggrShare_ __
+{{:code_p_72_2.png?600|}}
+__ MeanFeedTotal_ __
+{{:code_p_72_3.png?600|}}
+One of the aggregates calculated is the total feed intake per animal. It is expected that, inspite of regional differences in fodder supply, this total feed intake is mostly a genetic characteristic of animals and hence should not vary markedly across regions. To influence this distribution in the objective, the average across regions needs to be computed.
+**Objective function**
+The objective function is extensively revised compared to the pre-star2 versions. The criteria to be optimised are now:
+  - coverage of animal requirements with feed
+  - regional variation of certain feed input coefficients
+  - concentration of energy and protein in feed mix
+  - shares of feed aggregates (roughage, concentrates, other) in total feed mix
+  - feed input coefficients of all FEED bulks receive prior expectations
+The parameters in the objective function are partly means and imputed standard deviations AND so-called “soft” upper and lower limits. The “soft” limits increase the penalty significant when the solver picks values close to or even beyond them.
+__ Coverage of animal requirements with feed __
+{{:code_p_73.png?600|}}
+This part of the objective functions tries to minimize the difference between the requirements calculated from the feed input coefficients (v_animReq) and the expected (mean) requirements (p_animReq) coming from literature. Due to the weighting with number of animals (v_actLevl) and expected requirements (p_animReq) the optimal solution tends to distribute over or under supply of nutrients relatively even over all activities and regions. It has been decided to attach an exponent smaller one to these weights which strongly pulls them towards unity (see: [...] FIXME (doppelstern) .1). This tends to give more weight to “less important” animal types compared with untransformed weights.
+__Deviation of sub regional total feed intake from regional average__
+{{:code_p_73_2.png?600|}}
+As argued above, we expect that total feed intake in DRMA is mostly a genetic characteristic of animals and hence should not vary markedly across regions. Deviations of (sub-)regional feed intake from the associated regional average (NUTS1 or MS) are therefore penalised.
+__Deviations of sub regional feed input coefficients of non-ruminants from regional average__
+{{:code_p_73_3.png?600|}}
+As the comment explains, non-ruminants should have a rather standardised diet across regions.
+__Concentration of energy and protein in feed aggregates__
+{{:code_p_73_4.png?600|}}
+This part of the objective functions tries to minimize the difference between the nutrient content of feed aggregates (v_nutContFeed) and the expected nutrient (p_nutContFeed(…”MEAN”)) coming from literature or IFM-CAP. To avoid unreasonably large deviations from MEAN, lower and upper limits are introduced (MIN, MAX), where the penalty in the objective function increases significantly. The extra penalties rely on the GAMS built-in smooth approximation of the min operator (Chen-Mangasarian smoothing function ncpcm). The values for mean and upper and lower limits are presented in the table below.
+**Table 11: Expected nutrient content in total feed per animal category**
+^ ^^ Energy  ^^  Crude protein  ^^
+^^  MEAN  ^  MIN  ^  MAX  ^  MEAN  ^  MIN  ^  MAX  ^
+DCOL	6.7	6.4	7	0.155	0.14	0.17
+DCOH	6.8	6.6	7.2	0.155	0.14	0.17
+BULL	6.7	6.2	7	0.155	0.14	0.17
+BULH	6.8	6.4	7.2	0.155	0.14	0.17
+HEIL	6.3	5.8	7	0.155	0.14	0.17
+HEIH	6.8	6.2	7.2	0.155	0.14	0.17
+SCOW	6.4	6	7	0.155	0.14	0.17
+HEIR	6.4	6	7	0.155	0.14	0.17
+CAMF	6.6	6.6	7.2	0.155	0.14	0.17
+CAFF	6.6	6.6	7.2	0.155	0.14	0.17
+CAMR	6.6	6.6	7.2	0.155	0.14	0.17
+CAFR	6.6	6.6	7.2	0.155	0.14	0.17
+PIGF	8	7.8	8.2	0.155	0.14	0.17
+SOWS	8	7.8	8.2	0.155	0.14	0.17
+SHGM	6.3	5.8	7	0.155	0.14	0.17
+SHGF	6.3	5.8	7	0.155	0.14	0.17
+HENS	8	7.8	8.2	0.18	0.14	0.2
+POUF	8	7.8	8.2	0.18	0.14	0.2