chapter05-feed-mix

chapter05-feed-mix - Feeding Problem Basic Concept This...

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Feeding Problem Basic Concept This problem involves composing a minimum cost diet from a set of available ingredients while maintaining nutritional characteristics within certain bounds. Objective:Minimize total diet costs Variables: how much of each feedstuff is used in the diet Restrictions: Non negative feedstuff Minimum requirements by nutrient CH 05-Feeding-1
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Maximum requirements by nutrient Total volume of the diet CH 05-Feeding-2
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This problem requires two types of indices: Type of feed ingredients available from which the diet can be composed ingredientj = {corn, soybeans, salt, etc.} Type of nutritional characteristics which must fall within certain limits nutrient = {protein, calories, etc.} CH 05-Feeding-3
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Feeding Problem Basic Concept Variable -- Feed ingredientj amount of feedstuff ingredient j fed to animal Objective – total cost We want to minimize total diet costs across all the feedstuffs so we need an expression for feedstuff costs. Let us define a data item giving the per-unit cost of ingredients as cost ingredientj . Our objective then becomes to minimize the sum of the diet costs over all feed ingredients CH 05-Feeding-4
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Minimize ingredientj cost ingredientj Feed ingredientj CH 05-Feeding-5
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Basic Concept Feed ingredientj represent the decision variables Additional parameters representing how much of each nutrient is present in each feedstuff as well as the dietary minimum and maximum requirements for that nutrient are needed. Let 1). a nutrient,ingredientj be the amount of the nutrient present in one unit of the j th feed ingredient (technical coefficients) 2). UL nutrient and LL nutrient be the maximum and minimum amount of the nutrient in the diet (RHS) Then the nutrient constraints are formed by summing the nutrients generated from each feedstuff and requiring these to exceed the dietary minimum and/or be less than the maximum. CH 05-Feeding-6
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chapter05-feed-mix - Feeding Problem Basic Concept This...

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