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--- input_allocation [2020/02/13 11:18] – [Input allocation for young animals and the herd flow model] matsz
+++ input_allocation [2020/02/24 08:53] – [Input allocation for feed] matsz
@@ Line 130: / Line 130: @@
 \begin{equation}
-\sum_{r,fint}\bar{FEDUSE}_{r,fint}PFOD_{r,fint} = \bar{EAAP}_{OFAR,MS}+\bar{EAAP}_{GRAS,MS}
+\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