Balancing rations using computer Formulating least cost rations –The most commonly used computer...
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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
Transcript of Balancing rations using computer Formulating least cost rations –The most commonly used computer...
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
growing diet for broiler chicks• AMEn = 13,38 MJ/kg (min)• Crude protein = 200 g/kg (min)• Crude fibre = 40 g/kg (max)• Ca = 9 g/kg (min) • available P = 3,5 g/kg (min)• Lysine = 10 g/kg (min)• Methionine = 3,8 g/kg (min)• Methionine + cystine = 7,2 g/kg (min)
AMEnMJ/kg
C. prot.g/kg.
C. fibreg/kg
Cag/kg
avail. P
g/kg
LYSg/kg
METg/kg
M+Cg/kg
PriceFt/kg
corn 14,02 85 22 0,2 1,1 2,6 1,7 3,6 32
animal fat 29,66 - - - - - - - 35
extr. soybean meal (44%)
9,33 440 70 2,9 2,1 28,3 6,1 13,1 60
meat meal 8,3 534 24 79,4 40,3 30,7 8,0 14,0 68
L-LYS - - - - - 800 - - 530
DL MET - - - - - - 950 950 580
limestone - - - 360 - - - - 15
Hostaphos - - - 90 175 - - - 49
Feedstuff table
