Computer formulation observations and caveats

Journal of Applied Poultry Research

Volumn 5, Issue 2, 1996, Pages 116-125

  Roush, William B ^a   Cravener, Terril ^a   Zhang, Fushan ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Feed formulation; Linear programming; Stochastic programming

Indexed keywords

EID: 0030515039     PISSN: 10566171     EISSN: None     Source Type: Journal    
DOI: 10.1093/japr/5.2.116     Document Type: Article

References (20)

1. Render, B. and R.M. Stair, 1982. Quantitative Analysis for Management. Allyn and Bacon, Inc., Boston, MA.
2. Van De Panne, C. and W. Popp, 1963. Minimum cost cattle feed under probabilistic protein constraints. Management Sci. 9(3):405-430.
3. 2 ≥ 15 This method more accurately handles the nonlinear nutrient variation. An intuitive analogy for the way the constraints are handled is to compare: √9 + √16 = 7 (1) and √9 + 16 = 5 (2) The linear program with a margin of safety corrects the nutrients by adjusting with individual square root values (Equation 1) and the stochastic nonlinear adjustment is accomplished by a square root of the summation (Equation 2). Equation 1 over-corrects the values.
4. Shulze, J.V. and F.H. Benotf, 1981. Statistical evaluation of ingredient variation and procedures for determining number of samples needed for laboratory analysis. Pages 134-146 in: Proc. 1981 Georgia Nutr. Conf., Atlanta, GA.
5. Nott, H. and G.F. Combs, 1967. Data processing of ingredient composition data. Feedstuffs 14:21.
6. D'Alfonso, T.H., W.B. Roush, and J.A. Ventura, 1992. Least cost poultry rations with nutrient variability: A comparison of linear programming with a margin of safety and stochastic programming models. Poultry Sci. 72:620-627.
7. Roush, W.B. and T.L. Cravener, 1995. Soybeans in formulated poultry rations. Pages 44-49 in: Pennsylvania Crops Conf., Carlisle, PA.
8. Assumptions and adjustments: A normal distribution is assumed for stochastic nonlinear programming and implied for linear programming adjusted for a margin of safety, though the latter is in error because of the basic assumption of certainty for linear programming. Kirby et al. [14] indicated that not all nutrients in ingredients are normally distributed. This finding contradicted the findings of Duncan [15, 16]. Duncan [16] pointed out that for practical purposes, naturally occurring factors are normally distributed. Non-normal distributions are most likely due to man-made composites of several distributions of ingredients from different sources. Proper sampling can overcome the problem of a non-normal distribution. The Central Limit Theorem, a powerful theorem from statistics [10], indicates that the distribution of sample means from a non-normal population approaches the normal distribution as the sample size increases. Each sample mean is assumed to be the mean of several subsamples. Another assumption is that a good database is available with mean and standard deviation values for the nutrients in ingredients. With some nutrients such as amino acids, direct analysis regarding mean and variance data may not be readily available. Simple and multiple regression equations have been published for the estimation of amino acids in ingredients based on protein percent and proximate analysis of the ingredient [17]. The equations can be further enhanced for stochastic non-linear programming by including the standard deviation. For example, Degussa [18] includes the mean value and Coefficient of Variation, from which the standard deviation can be calculated [19]. For large sample sizes, this is sufficient estimation of the standard deviation for the amino acid [20]. Bioavailability and digestibility values can be used to adjust nutrient mean and standard deviation values. For example, if the bioavailability of phosphorus is 0.3 in alfalfa, then the mean and standard deviation values can be adjusted by 0.3 to reflect the bioavailable phosphorus. The same is true of amino acid digestibility values [17]. The mean and standard deviation values are multiplied by appropriate digestibility values. The adjustment is made on the standard deviation and not the variance. Adjustment of the variance requires the squaring of the adjustment value before multiplication [19].
9. Roush, W.B., R.H. Stock, T.L. Cravener, and T.H. D'Alfonso, 1994. Using chance-constrained programming for animal feed formulation at Agway. (Operations Research Society of America/The Institute of Management Sciences) Interfaces 24:53-58.
10. Klemele, M.J. and S.R. Schmidt, 1993. Basic Statistics - Tools for Continuous Improvement. 3rd Edition. Air Academy Press, Colorado Springs, CO.
11. value = 23.46-23/0.5729 0.8029 From Table D-1 in [10] the probability is 0.7967 or 0.80 (80%).
12. Rahman, S.A. and F.E. Bender, 1971. Linear programming approximation of least-cost feed mixes with probability restrictions. Amer. J. Agric. Econ. 53(4):612-618.
13. Cravener, T.L., W.B. Roush, and T.H. D'Alfonso, 1994. Laying hen production responses to least cost rations formulated with stochastic programming or linear programming with a margin of safety. Poultry Sci. 74:1290-1295.
14. Kirby, S.R., G.M. Pesti, and J.H. Dorfman, 1993. An investigation of the distribution of protein content of samples of corn, meat and bone meal, and soybean meal. Poultry Sci. 72:2294-2298.
15. Duncan, M.S., 1973. Nutrient variation: Effect on quality control and animal performance. Doctoral Dissertation. Kansas State University, Manhattan, KS.
16. Duncan, M.S., 1994. Silk Purses and Sows' Ears. Production Management Systems, Wilkesboro, NC.
17. National Research Council, 1994. Nutrient Requirements of Domestic Animals. Nutrient Requirements of Poultry. 9th Edition. Natl. Acad. Sci., Washington, DC.
18. Degussa, 1990. The Amino Acid Composition of Feedstuffs. Degussa Corporation, Allendale, NJ.
19. Roush, W.B., 1994. Stochastic nonlinear programming: A new generation of feed formulation. Pages 273-285 in: 55th Minnesota Nutr. Conf. and Roche Tech. Symposium, Bloomington, MN.
20. Neter, J., W. Wassennan, and M.H. Kutner, 1990. Applied Linear Statistical Models. 3rd Edition. Irwin, Boston, MA.