Optimizing Dietary Net Energy for Maximum Profitability in Optimizing Dietary Net Energy for Maximum Profitability in Growing-Finishing Pigs Growing-Finishing Pigs

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Introduction
Feed accounts for up to 75% of pork production cost, with energy alone representing 50% or more of the total cost. 4,5The knowledge of energy metabolism is essential to predict, optimize, and formulate diets to achieve expected performance.Typically, the DE (digestible energy) and the ME (metabolizable energy) systems are the most common in the US. 5 However, the concentration of dietary NE provides the most accurate estimate of the amount of energy available to the pig. 6Acknowledging the difficulties of Swine Day 2017 measuring NE and limited availability of NE estimates in dietary ingredients, Nitikanchana et al. (2015)  7 developed and validated regression equations to predict growth rate and feed efficiency of growing-finishing pigs the NE system.These equations provide a useful estimate for growth performance of pigs fed different dietary NE concentrations.Taking into consideration the financial implications of the energy density of the diet, the objective of this study was to develop a tool to estimate the dietary NE concentration that yields maximum profitability for growing-finishing pigs.

Model Description
The NE optimization tool is a Microsoft Excel®-based model.This tool is intended for use by swine nutritionists as a method to contrast current dietary NE concentrations to recommended values that yield maximum profitability.The model is divided into 3 sections: 1) model inputs, with economics, production, and dietary criteria; 2) model calculations and optimization, for growth performance and carcass yield predictions, and profitability indicators; and 3) model outputs with recommended dietary NE concentrations, predicted growth performance, carcass yield, and profitability indicators contrasting current with the estimated ideal dietary NE concentrations.

User Input Page
Economics and System Performance For calculation of growth performance and profitability, the user is required to enter the following inputs: current ADG (lb), F/G, and carcass yield (%), pork carcass price ($/lb), feeder pig cost ($/pig), facility cost ($/pig/d), and other cost (e.g., veterinary supplies, insurance, etc.).For the growth curve, the user can utilize default values or input a custom growth curve.In addition, the profit determination criteria can be customized by selecting the economic evaluation based on a live-or carcass-basis and marketing pigs on either a fixed time or fixed weight basis.

Nutritional Program Specifics
In this section, the number of dietary phases is selected (currently the model allows the selection of 4 to 6 phases) along with the BW range per phase.In addition, current, minimum, and maximum NE (kcal/lb) concentrations are specified by the user in each dietary phase.Inputs for minimum and maximum NE will be obtained by diet formulation.With these three NE inputs, the model will calculate 5 equidistant NE values, maintaining the minimum, maximum as well as the current NE value used.Afterward, the user needs to input the feed cost ($/ton) for diets at each NE value in all phases and the percentage of neutral detergent fiber (NDF) associated to each concentration of dietary NE for diet phases 3 and greater.(this equation includes BW, dietary NE, and the quadratic term of BW as regressors) and 2) equation with dietary SID Lys at suboptimal values (this equation includes BW, dietary NE, and SID Lys).In the inputs section, the user is required to select if their diets are adequate in SID Lys or not.If diets are deficient, the user needs to input the SID Lys associated to each value of dietary NE in each dietary phase.

Building the Calculations for Performance and Economics
To calculate ADG, the user provides a current system overall ADG, which is partitioned to a current calculated ADG in each dietary phase with the use of a regression equation developed from a reference population (Table 1).Furthermore, ADG is calculated with the inputs provided by the user (BW and dietary NE in each dietary phase).The difference between both, current and calculated ADG, are added or subtracted to predict ADG, which represents an adjustment to the intercept for the calculated ADG results.
To calculate G:F, the model utilizes estimations performed by Beaulieu8 et al., which suggested a 1:1 ratio between feed efficiency and dietary energy concentration.The model utilizes this ratio to calculate the influence of dietary NE on F/G.Comparable to the procedures to calculate predicted ADG, the user provides an overall F/G, and these values are partitioned to a current F/G (as G:F) in each dietary phase with the use of a growth curve from the reference population (Table 1).

Feed Cost, SID Lys, and NDF Prediction Equations
For the calculated NE values not provided by the user, feed cost, SID Lys, and NDF for energy, are predicted using a set of regression equations that were developed using the least squares estimates method from the Linest function of Microsoft Excel.According to Briand and Carter,9 the Linest function is an alternative to the use of least squares estimator formulas to obtain the best fit under a predefined criterion, and allows combinations with multiple functions to calculate statistics for other linear models.
For the feed cost prediction, Linest calculates the slope and intercept from the feed cost associated to each NE value provided by the user.In each dietary phase, a set of five linear regression equations are calculated by combining pairs of consecutive feed cost and associated NE values.The rationale supporting these calculations is to provide exact estimates of feed cost, and consequently more accurate economic estimates.
For the NDF prediction, Linest calculates a set of three linear regression equations (linear, quadratic, and cubic) and the equation with the best fit is selected to estimate NDF.The regression equations are calculated by selecting the NDF and associated NE values in each dietary phase from the inputs provided by the user.The equation fit is determined by the adjusted coefficient of determination, intended to account for the number of predictors in the model (Table 2).

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Comparable to the procedures to calculate predicted NDF, Linest calculates a set of three linear regression equations, and the model with the best fit is selected for estimation of SID Lys.

Regression Equations to Predict Carcass Yield
This model uses carcass yield prediction equations developed by Soto10 et al., which provides an estimate of the effects of dietary NDF on carcass yield.

Building the Linear Programming Model for Optimization in Excel
A non-linear mathematical programming (NLP) model was designed to select the optimum values of dietary NE that yields the maximum profitability for growing-finishing pigs.In Microsoft Excel Solver, NLP problems are solved with the generalized reduced gradient (GRG) algorithm.In this model, the objective function is income over total cost (IOTC) on a live-or carcass-basis and is maximized by the optimal value of NE in each dietary phase.
In the model, once economic, system performance, weight ranges, and dietary inputs are entered, the GRG algorithm begins the routine at any feasible solution (starting point).Then through multiple iterations across the feasible region, it searches for a solution that provides the value of NE that satisfies the greatest profitability (IOTC) defined in the objective function.When no further possibility for profitability improvement exists, the current solution becomes local optima in relation to nearby points.However, a global optimal solution represents the best possible solution for the objective function. 11o land in the global optima, the model has the GRG in the Solver set up with the Multistart option, which selects several starting points throughout the feasible region, which produces multiple local optima solutions; therefore, increasing the chance of arriving to the global optima solution.The mathematical structure and economic calculations of the model are described in Tables 3 and 4.

Scenario Building
An example using this model is presented in Tables 5, 6, 7, and 8.In this example, a six-phase feeding program based on corn-soybean meal and dried distillers grains with solubles (DDGS) was used.To generate the NE range, a series of 5 diets per phase were formulated to include 0, 10, 20, 30, and 40% DDGS.In our simulation, the base feeding program used for comparisons had 20% DDGS added throughout all dietary phases.The resulting NE values from the 20% DDGS diets in this simulation were: 1,104, 1,122, 1,130, 1,145, 1,150, and 1,140 Kcal/lb for phases 1, 2, 3, 4, 5, and 6, respectively (Table 5).From phases 3 to 6, resulting NDF values had an average of 13% for diets with a 20% DDGS inclusion.The results of calculations for 5 equidistant NE values and respective NDF values are presented in Table 5.

Dynamic Scenario Variables Definition
To further evaluate the model performance, dried distillers grains with solubles (DDGS) pricing was modified from low-cost ($90.00/ton) to high-priced ($150.00/ton).Similarly, carcass pricing was also modified from moderate-priced ($0.65/lb) to high-priced ($0.85/lb).For calculation of feed cost the pricing of main ingredients used was: corn $3.48/bu, soybean meal $290.60/ton, and L-Lys $0.69/lb.Resulting feed costs are presented in Table 5.

Scenario Results
Considering a scenario with low-priced DDGS and moderate carcass, the model solution suggested that NE should be decreased, thus forcing in 40% DDGS.This decrease is only observed from phases 1 to 5. In phase 6, the model yielded no modification from the current energy value.The recommended NE values worsened ADG, feed efficiency, and carcass yield, nonetheless, the recommend NE values under the conditions of this scenario improved IOTC by $3.75/pig.Interestingly, by only changing the scenario to a high carcass price, the model solution suggested a similar NE decrease in phases 1 to 5 to the previously explained scenario.However, in phase 6 the model suggested the highest energy value, thus switching to a corn-soybean meal-based diet, and improving carcass yield.With the use of the recommend NE values under the conditions of this scenario, IOTC improved by $3.76/pig over the current system performance.
Considering a scenario with high-priced DDGS and moderated carcass price, the model solution still suggested that NE should be decreased; however, the extent of this decrease is lower compared to the scenarios described above, particularly for phases 1 and 3.For phases 2 and 4, the recommend NE values remain the lowest, forcing the 40% DDGS diet.For phases 5 and 6, the recommended NE values are increased, particularly for phase 6.The recommended NE values slightly worsened feed efficiency, yet carcass yield was improved.With the use of the recommend NE values under the conditions of this scenario, IOTC improved by $1.26/pig.With a more favorable scenario for carcass price, NE is moderately reduced for phases 1 and 3.For phase 2 the recommended NE value remained the lowest.For phase 4, the model yielded no modification.Like the previous scenario, the recommended NE values are increased for phases 5 and 6, particularly for phase 6.With the use of the recommend NE values under the conditions of this scenario, IOTC improved by $1.56/pig.The model described in this paper can be used to predict the value of dietary NE that yields the greatest economic return to the production system.To evaluate the performance of the model, an example is presented considering different economic scenarios created by modifying DDGS and carcass pricing.  1 Model calculated 5 equidistant NE levels by phase, keeping minimum, maximum, and currently used NE levels as defined by the user. 2 The feeding program had an inclusion of 20% dried distillers grains with solubles (DDGS) in all dietary phases. 3Main ingredients pricing: corn $3.48/bu, soybean meal $290.60/ton,L-Lys $0.69/lb. 4Current levels of NE defined by user. 5Neutral detergent fiber defined by user for dietary phase 3 and greater.
Growth performance prediction equations and SID Lys adequacyThis model utilizes the ADG prediction equations developed by Nitikanchana 7 et al.Their publication provides two equations: 1) equation with adequate dietary SID Lys Swine Day 2017

Table 1 .
1egression equation to partition ADG and G:F by dietary phase from overall growth performance inputs1

Table 2 .
1ample set of regression equations for SID Lys and NDF by dietary phase for data provided by the user1 1The equation selected for the prediction is the one with the highest adjusted coefficient of determination.

Table 3 .
General linear programming model

Table 4 .
Input equations used in model development

Table 5 .
Resulting NE levels and respective feed cost and NDF

Table 6 .
1,2,3mended net energy levels (kcal/lb) compared with user defined levels in a six-phase feeding program with varying scenarios for distillers dried grains with solubles and carcass pricing on a fixed time marketing basis1,2,3

Table 7 .
1,2,3,4 performance with recommended net energy levels compared with user defined levels in a six-phase feeding program with varying scenarios for distillers dried grains with solubles and carcass pricing on a fixed time marketing basis1,2,3,4

Table 8 .
1,2,3mics of user defined net energy levels with recommended levels in a six-phase feeding program with varying scenarios for distillers dried grains with solubles and carcass pricing on a fixed time marketing basis1,2,3