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Universiw International INFORMATION TO USERS This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograph and reproduce this document, the quality of the reproduction is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction. 1. The sign or “target” for pages apparently lacking from the document photographed is “ Missing Page(s)” . I f it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity. 2. When an image on the film is obliterated with a round black mark, it is an indication of either blurred copy because of movement during exposure, duplicate copy, or copyrighted materials that should not have been filmed. For blurred pages, a good image o f the page can be found in the adjacent frame. I f copyrighted materials were deleted, a target note w ill appear listing the pages in the adjacent frame. 3. When a map, drawing or chart, etc., is part of the material being photographed, a definite method of “sectioning” the material has been followed. It is customary to begin film ing at 1 .e upper le ft hand comer o f a large sheet and to continue from left to right in equal sections w ith small overlaps. I f necessary, sectioning is continued again-beginning below the first row and continuing on until complete. 4. For illustrations that cannot be satisfactorily reproduced by xerographic means, photographic prints can be purchased at additional cost and inserted into your xerographic copy. These prints are available upon request from the Dissertations Customer Services Department. 5. Some pages in any document may have indistinct print. In all cases the best available copy has been filmed. UniversiW M ioO Tlnns International 300 N. Zeeb Road Ann Arbor, Ml 48106 8510638 St-Pierre, Normand Roger MINIMUM COST REQUIREMENTS FROM A RESPONSE FUNCTION AND INCORPORATION OF UNCERTAINTY IN COMPOSITION OF FEEDS INTO CHANCE-CONSTRAINED PROGRAMMING MODELS OF LIVESTOCK RATIONS The Ohio State University Ph.D. 1985 University Microfilms I nternâtionel 300 N. zeeb Road, Ann Arbor, Ml 48106 PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V 1. Glossy photographs or pages. 2. Colored illustrations, paper or print _______ 3. Photographs with dark background _____ 4. Illustrations are poor copy _______ 5. Pages with black marks, not original copy ^ 6. Print shows through as there is text on both sides of p a g e . 7. Indistinct, broken or small print on several pages ^ 8. Print exceeds margin requirements ______ 9. Tightly bound copy with print lost in spine ________ 10. Computer printout pages with indistinct print 11. Page(s) _____________lacking when material received, and not available from school or author. 12. Page(s) _____________seem to be missing in numbering only as text follows. 13. Two pages numbered . Text follows. 14. Curling and wrinkled pages _ 15. Dissertation contains pages with print at a slant, filmed as received _ 16. Other University Microfilms International MINIMUM COST REQUIREMENTS FROM A RESPONSE FUNCTION AND INCORPORATION OF UNCERTAINTY IN COMPOSITION OF FEEDS INTO CHANCE-CONSTRAINED PROGRAMMING MODELS OF LIVESTOCK RATIONS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Normand Roger St-Pierre, B.S., M.S. ***** The Ohio State University 1985 Reading Committee: Approved By W.R. Harvey C.S . Thra en F .R. Walker ,1. / ^ , H.R. Conrad -WiïHîV.lt J.'> Advis er Department of Dairy Science Copyright by Normand Roger St-Pierre 1985 "Truth is so large a target that nobody can wholly miss hitting it, but at the same time, nobody can hit all of it with one throw". Aristotle (384-330 BC) "Science not founded on exact experience and mathematics are either deception or madness - a banner of charlatans, blown full by the wind, after which the foolish rabble flocks". Lenordo Da Vinci (1452-1519) - ii - ACKNOWLEDGEMENT The author wants to express his sincere appreciation to Dr. W.R. Harvey for being such a devoted adviser during the time this research was conducted. His motto 'think' should always inspire me. Many thanks to Drs. H.R. Conrad, F.R. Walker and C.S. Thraen for their time in reviewing this manuscript. Dr. Conrad has been and will always be a model of excellence to me. Dr. Walker was very instrumental in my formation in mathematical programming. Dr. Thraen's interest in joining expertise from our two respective departments has been a keypoint in the initiation of this research. Special thanks to my parents, brothers and sisters for their constant support. My parents have always emphasized the importance of education. Now, I finally understand why. And thanks to all my fellow graduate students, especial­ ly Paul Ferguson and Bill Weiss. Their friendship will be remembe red. Dee, there is no words good enough for you. This dis­ sertation is a partial result of your patience and under- stending. - iii - VITA October 1, 1955 . Born - Montreal, Canada 19 78 .............. B.Sc., Université Laval, Quebec city, Canada 1980 .............. M.Sc., Université Laval, Quebec city, Canada 1979-1981 . Animal nutritionist. Cooperative Federe de Quebec, Montreal, Canada 1981- ............ Research scientist, Agriculture- Canada, Lennoxville, Canada PUBLICATIONS St-Pierre, N.R. 1980. Effets du gel et du stade de maturi­ té sur la valeur alimentaire de l'ensilage de mais pour la vache laitiere. M.Sc. Thesis, Université Laval, Quebec city, Canada, april 1980. St-Pierre, N.R., R. Bouchard, G.J. S t-Laurent, C . Vinet and G.L. Roy. 1983. Effects of stage of maturity and frost on nutritive value of corn silage for lactating dairy cows. J. Dairy Sci. 66 : 1466-1473. St-Pierre, N.R., R. Bouchard, G.J. S t-Laurent, C . Vinet and G.L. Roy. Performance of dairy cows fed corn silage affec­ ted by frost and evaluation of corn silage energy values. J. Dairy Sci. (submitted, accepted). St-Pierre, N.R., R. Bouchard, G.J. S t-Laurent and G.L Roy. Relationship between chemical composition of corn and In vitro dry matter digestibility. Can. J. Anim. Sci. (submitted). - IV - St-Pierre, N.R., R. Bouchard and J.G. St-Laurent. 1980. Effect of frost on the nutritive value of corn silage fed to lactating dairy cows. J. Dairy Sci. 63(suppl) : 151. St-Pierre, N.R., R. Bouchard and G.J. St-Laurent. 1980. Performance of dairy cows fed corn silage affected by frost and evaluation of corn silage energy values. J. Dairy Sci. 63(suppl): 151(abstract) . St-Pierre, N.R., C.S. Thraen and W.R. Harvey. 1984. Energy-protein substitution in the growth of feeder calves; evaluation of alternative models. J. Anim Sci 59(supple- ment 1): 413 (abstract). St-Pierre, N.R., C.S. Thraen and W.R. Harvey. Impact of energy-protein substitution on growth of feeder calves : a biological and economic analysis. Ohio Agric. Res. Bull, (submitted, accepted). St-Pierre, N.R., C.S. Thraen and W.R. Harvey. Nutrient energy/protein substitution in feeder cattle; a study in applied production economics. Amer. J. Agric. Econ. (submi t ted). FIELDS OF STUDY Major Field: Management Studies in Dairy Science and Management. Professors R.M. Porter, D.E. Pritchard, N.S. Fech- he imer. Studies in Statistical Methods. Professors W.R. Harvey, D. Kikuchi, H.N. Nagaraja, J.S. Verducci, T.A. Willke, D.A. Wolfe. Studies in Animal Breeding and Population Genetics. Professors W.R. Harvey, F.R. Allaire, M.E. Davies, K .M. Irvin. Studies in Mathematics, Systems Simulation and Optimiza­ tion. Professors A. Cronheim, G . Papalios, J.P. Klein, F.R. Walker Studies in Agricultural Economics. Professors D.D. Southgathe, T.T. Stout, C.S. Thraen - V - TABLE OF CONTENTS ACKNOWLEDGEMENTS ........................................... ill VITAE .............................................................iv LIST OF TABLES................................................ vili LIST OF F I G U R E S ............................ xii Chapt er page I. INTRODUCTION ........................................... 1 II. ENERGY-PROTEIN RESPONSE FUNCTIONS FOR GROWTH . 6 INTRODUCTION ......................................... 6 FROM THE PHYSIOLOGY TO A PRODUCTION FUNCTION ...................................... 8 METHODOLOGY AND D A T A ................................13 A n i m a l s ............................................13 D i e t s .............................................. 13 Statistical methods and models .............. 16 Polynomial model........................... 16 Non-linear model........................... 18 Transcendental logarithmic production function................................18 C obb-Douglas.................................. 20 STATISTICAL RESULTS ..................... 20 INTERPRETATION .................................... 32 P h y s i c a l ......................................... 32 E c o n o m i c ......................................... 42 CONCLUSION............................................57 III. UNCERTAINTY IN COMPOSITION OF FEEDSTUFFS .... 59 INTRODUCTION ...................................... 59 LITERATURE REVIEW ............................... 63 Least-cost ration as a linear programming problem......................
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