Balancing rations using computer Formulating least cost rations – The most commonly used computer programming technique to do this is called linear programming (LP) – The program contains equations to predict animal requirements and supply of nutrients needed to meet requirements – On the amounts of nutrients such as energy, protein, etc. minimum and maximum limits can be used. – We also can set minimum and maximum constraints on the amount of ingredients like rapeseed meal, barley, wheat etc. – Set the objective function, which is in this case a linear equation with which the linear programming minimizes the price of the ration – Then the computer finds the optimum combination of feeds that provides the nutrients that meets the constraint set. – The optimized diet should be re-evaluated if needed
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Balancing rations using computer Formulating least cost rations –The most commonly used computer programming technique to do this is called linear programming.
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Balancing rations using computer
Formulating least cost rations
– The most commonly used computer programming technique to do this is called linear programming (LP)
– The program contains equations to predict animal requirements and supply of nutrients needed to meet requirements
– On the amounts of nutrients such as energy, protein, etc. minimum and maximum limits can be used.
– We also can set minimum and maximum constraints on the amount of ingredients like rapeseed meal, barley, wheat etc.
– Set the objective function, which is in this case a linear equation with which the linear programming minimizes the price of the ration
– Then the computer finds the optimum combination of feeds that provides the nutrients that meets the constraint set.
– The optimized diet should be re-evaluated if needed
The mathematical model of linear programming
linear matrix:• a11X1 + a12X2 + …..a1nXn < => r1
• a21X1 + a22X2 + …..a2nXn < => r2
• a31X1 + a32X2 + …..a3nXn < => r3
• . . . .• am1X1 + am2X2 + …..amnXn < => rm
the objective function:• P1X1 + P2X2 + P3X3 + …. PnXn = MIN or MAX
where: • X1 + X2 + X3 … = the ratio of feedstuffs
• a11 - amn = coefficients (energy, protein, Ca, P etc. contents of feedstuffs)
• r1 - rm = constraints (requirement values like energy, protein etc.)
• < > = relations
• P = the value of the objective function (in this case the minimum price of the ration)• P1 - Pn = the prices of feedstuffs
Requirement values are the nutrient contents of the compound diets