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A vegetable farm planning model for primary producers Short, C. Cameron 1977

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A VEGETABLE FARM PLANNING MODEL FOR PRIMARY PRODUCERS by C. CAMERON SHORT THESIS SUBMITTED IN PARTIAL FULFILLMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Dept. of A g r i c u l t u r a l Economics) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July, 1976 © Charles Cameron Short, 1976 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t ha t t he L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depa r tment The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date ABSTRACT A VEGETABLE FARM PLANNING MODEL FOR PRIMARY PRODUCERS by C. Cameron Short The objective of the thesis was to construct a deterministic single year, farm planning model that would enable vegetable producers to select an optimal farm plan from among a l t e r n a t i v e crops and crop production methods so as to maximize farm income consistent with technological and resource constraints and other goals. The model was to be r e a d i l y adaptable to a wide range of commercial vegetable farmers i n Canada but s u f f i c i e n t l y f l e x i b l e to be adaptable to the p a r t i c u l a r s i t u a t i o n of a s p e c i f i c farm. A multiperiod l i n e a r programming model was b u i l t and validated through i t s ap p l i c a t i o n to a large commercial vegetable farm. The relevant theory of the firm was reviewed with sp e c i a l attention made to the theory's a p p l i c a t i o n to vegetable farms. The structure of a l i n e a r programming problem was discussed and related to the theory of the firm and vegetable farms. Special emphasis was placed on the problem of modeling the machinery used in vegetable production. The work of a g r i c u l t u r a l engineers was examined to determine the technological r e l a t i o n -ships involved i n machine operation. Other crop budgeting models which involved the construction of s i m i l a r planning models f o r a d i f f e r e n t sector of the a g r i c u l t u r a l community, e s p e c i a l l y the Purdue Crop Budgeting Models were reviewed. The model constructed was able to deal with machinery constraints by building a number of machine operating a c t i v i t i e s and t r a c t o r transfers so that the time constraint f o r a p a r t i c u -l a r job would consist of any subset of the predefined set of time periods. Standard c o e f f i c i e n t s were prepared based on engineering formulae f o r f u e l consumption and r e p a i r and main-tenance costs for t r a c t o r s . A l l inputs i n the model except repair and maintenance costs were i n physical u n i t s . This made i t necessary to b u i l d several d i f f e r e n t types of purchasing or renting a c t i v i t i e s but f a c i l i t a t e s the i n t e r p r e t a t i o n of data and the use of the model i n a large number of d i f f e r e n t s i t u a t i o n s . The model was va l i d a t e d through i t s a p p l i c a t i o n to a large commercial vegetable farm i n B r i t i s h Columbia. The model was run i n simulation mode by forc i n g the model to follow the farm's 1974 crop plan and a l t e r i n g y i e l d s and pric e s to y i e l d s and prices that a c t u a l l y occured i n that year. In thi"s manner the r e l i a b i l i t y of the cost c o e f f i c i e n t s of the input data and the r e l a t i o n s h i p s between resources could be evaluated and compared with the r e s u l t s recorded i n the farm's CANFARM records. The model was run i n optimization mode with expected 1976 prices and y i e l d s to demonstrate the use of the model i n sele c t i n g an optimal farm plan. A t o t a l of six plans were prepared based on alternate market and r i s k constraints and y i e l d s . These were compared with the plan selected by the i v . farmer without the aid of the model. A de t a i l e d report on one of the farm plans v/as also prepared. V . ACKNOWLEDGEMENTS I would l i k e to express appreciation to my family and e s p e c i a l l y my wife, Joyce, for the support given during the preparation and writing of t h i s t h e s i s . My thesis advisor, Dr. Earl Jenson, and other members of my thesis committee offered d i r e c t i o n and numerous suggestions which lead to substantial improvements i n the f i n a l product. The operator of the case farm also improved the thesis with his advice. Members of the Department of A g r i c u l t u r a l Economics at The University of B r i t i s h Columbia were also h e l p f u l with t h e i r support and suggestions. Dr. John Graham, Roger McNeil, and Barry Coyle deserve s p e c i a l mention i n t h i s respect. The Department and CANFARM provided funding which made the work possible. I would also l i k e to thank Jenny Roberts f o r changing a much revised manuscript in t o i t s present form. v i . TABLE OF CONTENTS CHAPTER PAGE 1 INTRODUCTION 1 1.1 BACKGROUND PERSPECTIVE 1 1.2 NATURE AND SCOPE OF THE PROBLEM 3 1.2.1 Factors A f f e c t i n g Production Decisions 3 1.2.2 F i n a n c i a l and Marketing Decisions 6 1.2.3 The Planning Period 7 1.3 OBJECTIVES OF THE STUDY 8 1.4 METHODS ADOPTED FOR ACHIEVING OBJECTIVES 10 1.4.1 The F i r s t Sub-Objective 10 1.4.2 The Second Sub-Objective 12 1.4.3 The Third Sub-Objective 14 1.4.4 The Fourth Sub-Objective 15 1.5 ORGANIZATION 16 2 THEORETICAL MODEL OF THE FIRM 18 2.1 THE THEORY OF THE FIRM 20 2.2 QUANTITATIVE MODELING METHODS 23 2.3 PRACTICAL CONSIDERATIONS THAT MODITY THE THEORETICAL MODEL . 26 2.3.1 Relationship between the Theory of the Firm and Vegetable Farms 26 2.3.2 The Structure of the Linear Programming Problem and Its Implication f o r the Theory of the Firm 28 3 THE DEVELOPMENT OF THE EMPIRICAL MODEL 34 3.1 CROP BUDGETING: THE PURDUE MODELS 36 3.2 ALTERNATIVE SCHEDULING MODELS 40 v i i . CHAPTER PAGE 3.3 SPECIAL FEATURES OF THE MACHINE SCHEDULING BLOCK SELECTED 46 3.4 SUMMARY OF THE COMPLETE FARM PLANNING MODEL INCORPORATING THE MACHINE SELECTION BLOCK - 49 4 DETAILED PRESENTATION OF THE EMPIRICAL MODEL 53 4.1 SOURCES OF DATA 55 4.2 PRESENTATION OF THE MODEL 58 4.2.1 O b j e c t i v e F u n c t i o n 58 4.2.2 R e s o u r c e s and C o n s t r a i n t s 62 4.3 MAJOR A C T I V I T I E S IN THE MODEL 64 4.3.1 L a b o u r H i r i n g i n t h e Model 64 4.3.2 R e s o u r c e P u r c h a s i n g and H i r i n g A c t i v i t i e s 66 4.3.3 F i x e d C o s t s 72 4.4 SUMMARY 73 5 APPLICATIONS OF THE EMPIRICAL MODEL TO A CASE FARM 75 5.1 SELECTION OF THE CASE FARM 77 5.2 PICTURE OF THE FARM PLANNING MODEL 81 5.3 EMPIRICAL RESULTS OF MODEL VERIFIC A T I O N 85 5.3.1 P r o c e d u r e f o r S i m u l a t i n g 1974 Fa r m P l a n 85 5.3.2 R e s u l t s f o r V e r i f i c a t i o n 88 5.4 RESULTS OF USING THE MODEL TO DERIVE THE OPTIMAL FARM. PLAN 96 6 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY 103 6.1 SUMMARY OF THE THESIS 103 6.2 CONCLUSIONS 107 v i i i . PAGE 6.3 SUGGESTIONS FOR FURTHER RESEARCH 110 6.3.1 F u r t h e r Developments o f the P r e s e n t Model 110 6.3.2 T e c h n o l o g i c a l S t u d i e s Needed I l l 6.3.3 E x p a n d i n g the Model t o More Complex Farm P l a n n i n g Problems ....... 113 REFERENCES 118 APPENDIX A THE IMPORTANCE AND PERFORMANCE OF THE VEGETABLE INDUSTRY IN BRITISH COLUMBIA AND CANADA 123 B THE CALCULATION OF REPAIR AND MAINTENANCE COSTS B . l REPAIR AND MAINTENANCE COSTS 130 B.2 REPAIR AND MAINTENANCE COST COEFFICIENTS IN THE MODEL 136 C FUEL CONSUMPTION COEFFICIENTS 139 D FIELD CAPACITY AND POV/ER REQUIREMENTS .. 148 E GLOSSARY OF ENGINEERING TERMS 156 F VALIDATION OF THE LOGIC OF THE MODEL 160 G THE OPTIMAL FARM PLAN G . l THE NATURE OF THE FARM REPORT 168 G.2 THE FINANCIAL RECORDS 172 G.3 THE PHYSICAL RECORDS 189 LIST OF TABLES TABLE PAGE 2.1 Modeling Methods Compared 24 4.1 Summary of Data Required by Type and Source 56 4.2 Summary of Data Required and Sources by Section of the Model 57 5.1 Income Statement: Actual 1974 Farm Plan 86 5.2 Income Statement: 1974 Simulation Farm Plan 87 5.3 A Comparison of Actual 1974 Costs with Major Items of Variable Costs i n the Simulated Farm Plan 91 5.4 Income Statement: 1976 Optimal 'Plan A' 97 5.5 A Comparison of A l t e r n a t i v e 'Optimal' Plans 101 A . l Importance of the Vegetable Industry i n Canada and B r i t i s h Combia: Area 1970-74 124 A.2 Importance of the Vegetable Industry i n Canada and B r i t i s h Columbia: Farm Value of Production 1970-74 124 A.3 Importance of the Vegetable Industry, i n Canada and B r i t i s h Columbia: The Number of Farms Reporting Vegetable Production 1961, 1966 and 1971 125 A.4 Relative Importance of Selected Vegetables i n the B r i t i s h Columbia A g r i c u l t u r a l Industry: Averages 1970-74 125 A.6 Average Farm Size i n B r i t i s h Columbia, Canada, and Washington State f o r Census Years 1960-72 127 A. 7 Per Acre Farm Value of Production in B r i t i s h Columbia, Canada, United States and Washington State: Averages 1970-74 128 B. l ASAE Formulae f o r Repair and Maintenance Costs .. 131 B.2 Repair and Maintenance Costs per Hour as a Per Cent L i s t Price According to Broad Implement C l a s s i f i c a t i o n 133 X. TABLE PAGE B.3 R e p a i r and Maintenance Costs per Hour as a Per Cent of L i s t P r i c e A c c o r d i n g to Machine Type .. 134 B. 4 Average Repair and Maintenance C o s t s per Hour as a Per Cent of L i s t P r i c e f o r Two Wheel .Drive T r a c t o r s 136 C l Frequency D i s t r i b u t i o n of T r a c t o r S i z e i n Maximum P-TO Horsepower at the Rated Engine Speed of T r a c t o r s Tested i n the Nebraska T e s t s . 142 C. 2 F u e l Consumption f o r G a s o l i n e T r a c t o r s A c c o r d i n g to T r a c t o r S i z e and Load 145 C. 3 F u e l Consumption f o r D i e s e l T r a c t o r s A c c o r d i n g to T r a c t o r S i z e and Load 146 D. l Machinery Performance Data 150 D.2 E f f e c t of S o i l Type on T r a c t i v e E f f i c i e n c y R a t i o 154 F . l V e r i f i c a t i o n of F e a s i b i l i t y o f Farm Plan 162 F.2 V e r i f i c a t i o n of P r o d u c t i o n and S a l e s i n the Model 163 F.3 V e r i f i c a t i o n of Purchased Inputs 164 F.4 V e r i f i c a t i o n of Labour i n the Model 165 F. 5 V e r i f i c a t i o n of the T r a c t o r S e l e c t i o n Block 166 G. l The Main C a t e g o r i e s of the Farm Record System ... 171 G.2 Income Statement: 1976 Optimal 'Plan A' 173 G.3 Cash Flow Statement: 1976 Optimal 'Plan A» 175 G.4 E n t e r p r i s e Statement: 63 Acres of L a t e P o t a t o e s 1976 Optimal 'Plan A' 178 G.5 E n t e r p r i s e Statement: 20 Acres of E a r l y P o t a t o e s 1976 Optimal 'Plan A' 179 G.6 E n t e r p r i s e Statement: 30 Acres of Beans 1976 Optimal 'Plan A' 180 G.7 E n t e r p r i s e Statement: 15 Acres of Late Peas 1976 Optimal 'Plan A' 181 x i . TABLE PAGE G.8 E n t e r p r i s e Statement: 30 Acres of E a r l y Peas 1976 Optimal 'Plan A' • ••• 182 G.9 E n t e r p r i s e Statement: 108 Acres of B a r l e y 1976 Optimal 'Plan A» 183 G.10 E n t e r p r i s e Statement: 20 Acres of Sugar Beets 1976 Optimal 'Plan A» 184 G . l l E n t e r p r i s e Statement: 5 Acres of T u r n i p s 1976 Optimal 'Plan A' •. - 185 G.12 E n t e r p r i s e Statement: 20 Acres of Cabbage 1976 Optimal 'Plan A' ... 186 G.13 E n t e r p r i s e Statement: 5 Acres of S t r a w b e r r i e s 1976 Optimal 'Plan A' 187 G.14 E n t e r p r i s e Statement: 2 Acres of R a s p b e r r i e s 1976 Optimal 'Plan A' 188 G.15 U t i l i z a t i o n Report f o r Land: 1976 Optimal 'Plan A' 190 G.16 Crop F e a s i b i l i t y : 1976 Optimal 'Plan A' 191 G.17 Labour U t i l i z a t i o n : 1976 Optimal 'Plan A' 192 G.18 U t i l i z a t i o n Report f o r T r a c t o r s : 1976 Optimal •Plan A' 193 G.19 U t i l i z a t i o n Report f o r Implements: 1976 Optimal 'Plan A' 194 x i i . LIST OF FIGURES FIGURE , PAGE 1.1 Resource Flow i n the Farm Firm 4 1.2 Organizational Flow Chart of the Major Steps taken towards S a t i s f y i n g the Objectives of the Thesis . .. 1 1 2.1 A Comparison of the Theoretical Input-Output Relationship and the Linear Programming Approximation 32 3.1 Land Preparation i n the Purdue Model 38 3.2 Method One of Programming the Machinery 41 3.3 Method Two of Programming the Machinery 43 3.4 Method Three of Programming the Machinery 45 3.5 Resource Flow i n the Empirical Model 50 4.1 Picture of the Complete Matrix 59 4.2 Key to Figures I l l u s t r a t i n g Sections of the Complete Matrix 6 ^ 4.3 The Labour Section of the Model 6 5 4.4 The Fuel Purchasing A c t i v i t i e s of the Model .... 67 4.5 The Land Rental A c t i v i t i e s of the Model 67 4.6 The Purchased Input Buying A c t i v i t i e s 70 4.7 The Cash Block of the Model 70 4.8 The Tractor Transfer Block Together with Rows and Columns f o r Repair and Maintenance Cost C a l c u l a t i o n s 71 4.9 Schemata of the Method Used f o r Fixed Costs .... 72 5.1 Flow Diagram Showing the C l a s s i f i c a t i o n of Resources and Time Periods f o r Each Resource and the Use of Resources on the Case Farm .... 84 B.l T o t a l Accumulated Repair and Maintenance Costs i n Per Cent of L i s t Price as a Function of Age for a Two Wheel Drive Tractor 132 x i i i . FIGURE PAGE B.2 R e p a i r and -Maintenance Costs per Hour i n Per Cent of L i s t P r i c e as a F u n c t i o n of Age: ASAE Formulae Compared wi t h L i f e -time Average as an Approximation 135 B. 3 R e p a i r and Maintenance C o s t s per Hour i n Per Cent of L i s t P r i c e as a F u n c t i o n of Age: ASAE Formulae f o r Two Wheel D r i v e T r a c t o r Compared with Approximations of the Formulae used i n the Model 137 C. l F u e l E f f i c i e n c y of a Duetz D10006 and a Deutz D5506 T r a c t o r from Nebraska T e s t s Reports ...,.„.-. 141 C.2 F o r t r a n Program Used to Produce Ta b l e C.2 and Table C.3 147 CHAPTER 1 INTRODUCTION 1.1 Background Perspective In 1971 the vegetable industry i n B r i t i s h Columbia was of d i r e c t concern to more than 1400 farmers and t h e i r f a m i l i e s who are engaged i n the production of vegetables. Relative to such large sectors as dairy, beef, and tree f r u i t s , however, the vegetable industry i s a small part of primary a g r i c u l t u r e accounting for 2.1% of t o t a l cropped acres and 6.0% of the t o t a l value of farm production i n that year (see Appendix A). Canada follows the B r i t i s h Columbia pattern quite c l o s e l y except that the vegetable industry i s s l i g h t l y less important i n r e l a t i o n to the a g r i c u l t u r a l industry of the nation. The vegetable industry i t s e l f i s very diverse encompas-sing a large number of very d i f f e r e n t types of crops, crop production systems, and marketing and other i n s t i t u t i o n a l arrangements. With the exception of potatoes, no s i n g l e vegetable stands out within the industry. In B r i t i s h Columbia potatoes accounted f o r approximately half the land in vegetables and of the farm value of vegetables produced during the period 1970-74. A l l other vegetables account for less than 7% of farm income and, with the exception of peas for processing, less than 7% of the land. There are considerable differences i n the performance of the vegetable industry i n d i f f e r e n t parts of Canada and the 2 United States. If average y i e l d s are used as an i n d i c a t o r of performance, Washington State obtains higher y i e l d s i n general than does B r i t i s h . Columbia, B r i t i s h Columbia does better than the United States, and the United States does better than Canada as a whole. To r e a l l y understand the dif f e r e n c e in average y i e l d s an examination has to be made of the sp e c i a l circumstances i n which each vegetable i s produced i n each region. Y i e l d s may be d i f f e r e n t because of the d i f f e r e n t q u a l i t i e s of the crops produced i n which case average value of production per acre may provide a better basis f o r compari-son. There may be sp e c i a l economies of scale of which American producers are able to take advantage but the Canadian producers are not, for some i n s t i t u t i o n a l reason. I t has often been suggested that American producers have a natural advantage owing to c l i m a t i c and other natural f a c t o r s . What-ever the cause of the d i f f e r e n c e i n performance, the sphere i n which the i n d i v i d u a l farm family can act to improve i t s performance i s by improving i t s managerial a b i l i t y . In thi s t h e s i s , an attempt i s made to improve the managerial environ-ment i n which vegetable producers make planning decisions so that they may be better able to achieve farm goals. 3 1.2 NATURE AND SCOPE OF THE PROBLEM The framework for planning decisions f o r the vegetable farm manager i s i l l u s t r a t e d i n Figure 1.1 which has been adapted from Bauer (1972, p. 15 ). The farm manager has ava i l a b l e a number of s p e c i f i c resources which are e i t h e r acquired on the fact o r markets or are a flow of s p e c i f i c c a p i t a l inputs which have been purchased on c a p i t a l markets. Through the technological r e l a t i o n s h i p s of the production process he i s able to transform the resources into f i n a l products which are sold on the product markets. Decision points where decisions have to be made r e l a t i n g to the ac q u i s i t i o n of resources, the use of the resources i n the production process, the f i n a l products which are to be produced, the d i s p o s i t i o n of f i n a l products, and the managing of the firm's f i n a n c i a l resources are i n d i c a t e d . The diagram i l l u s t r a t e s three broad types of decisions which have to be made. F i r s t of a l l , there are the produc-t i o n decisions about what to produce and what method of production to use. I t i s t h i s type of decision that i s the cen t r a l focus of t h i s study. 1.2.1 Factors A f f e c t i n g Production Decisions There are several f a c t o r s which combine to make t h i s type of d e c i s i o n very complex f o r the vegetable producer. Vegetables may be perennial, b i e n n i a l , or annual. M u l t i p l e cropping may be f e a s i b l e but at the same time, some crops may be incompatible so that rotations must also be accurately s p e c i f i e d . Furthermore, some vegetable crops produce j o i n t Factor Markets Technological Relationships Product Markets t xO jlO_ xo r JKfiL xO xO xO Land Labour and Management Machinery Buildings Supplies and Services Overhead Cash ScO Family with-drawals : taxes xO xO xO xO xO xO xO input-input input-output output-output Ox Ox Ox Potatoes Carrots Peas etc. Family and group transfers FIGURE 1.1 RESOURCE FLOW IN THE FARM FIRM Legend: Decision points Accounting points Product flow Cash flow x 0 x 5 products. A l l of these v a r i a b l e s considerably increase the scope of the problem. Another f a c t o r that increases the scope of the problem i s the wide range of technological systems that may be used to produce vegetables* These range from greenhouses and market gardens through to large commercial vegetable farms. Each of these systems may be extensively mechanized or r e l y on large amounts of hired labour i n c r i t i c a l time periods. I r r i g a t i o n and drainage systems may or may not be used. I t was not thought possible to examine the s p e c i a l concerns of a l l possible types of technological systems. This study i s relevant to medium and large scale commercial vegetable producers regardless of whether they employ a machine intensive or a labour intensive system. The concentration i s i n the use of farm machinery i n f i e l d operations but the study i s not s p e c i f i c to farms which employ a p a r t i c u l a r technological system or degree of machine or labour i n t e n s i t y . Management decisions on vegetable farms are also made more complex by the wide range of locations i n which vegetables may be produced. The p a r t i c u l a r c l i m a t i c and s o i l conditions w i l l have an e f f e c t on the decisions made by each farm manager. An e f f o r t was made to avoid making the study s p e c i f i c to a region so that i t i s relevant to vegetable production i n a l l areas of the country. The d i v e r s i t y of vegetables, technological systems and locations delineate the wide range of s i t u a t i o n s i n which the vegetable producer i s making decisions and considerably 6 e n l a r g e s the scope o f the problem. The a c t u a l p r o d u c t i o n r e l a t i o n s h i p s which are r e l e v a n t t o a p a r t i c u l a r farm o p e r a t o r are concerned w i t h the c u r r e n t i n p u t s , such as purchased goods and s e r v i c e s and w i t h the f l o w o f s e r v i c e s from l a b o u r and i n p u t s such as machines, b u i l d i n g s and l a n d . I t i s e s s e n t i a l f o r r a t i o n a l d e c i s i o n making t h a t the r e l a t i o n s h i p s between these i n p u t s a r e understood and t h a t they are e v a l u a t e d i n terms o f r e l e v a n t c o n s t r a i n t s on t h e i r s u p p l y and o f the p a r t i c u l a r o p e r a t o r s knowledge and a b i l i t y . I t i s n e c e s s a r y to see t h a t the f l o w o f these i n p u t s i s measured per u n i t of time so t h a t the c o n s t r a i n t s on the r e s o u r c e s have to take i n t o account the t i m e l i n e s s o f the use of these r e s o u r c e s . 1.2.2 F i n a n c i a l and M a r k e t i n g D e c i s i o n s A second broad a r e a o f farm management t h a t i s e v i d e n t i s i n the a r e a of marketing. The farmer i s o p e r a t i n g on both the f a c t o r markets and on the p r o d u c t markets. For the purpose of t h i s study two a s p e c t s of h i s behaviour on these markets are c o n s i d e r e d : p r i c e s t h a t he can expect t o o b t a i n o r pay, and c o n s t r a i n t s on h i s p u r c h a s i n g o r s e l l i n g a c t i v i t i e s . The t h i r d broad a r e a o f concern i s i n the a r e a o f f i n a n -c i a l management. A n e c e s s a r y i m p l i c a t i o n o f f i n a n c i a l manage-ment i s t h a t f i n a n c i a l r e c o r d s have t o be k e p t . A c c o u n t i n g p o i n t s where t h i s type o f i n f o r m a t i o n s h o u l d be r e c o r d e d are i n d i c a t e d i n F i g u r e 1.1. The e f f e c t o f f i n a n c i a l w i t h d r a w a l s and t r a n s f e r s must a l s o be taken i n t o c o n s i d e r a t i o n . The i important a r e a of c a p i t a l b u dgeting l a r g e l y a s s o c i a t e d w i t h 7 f i n a n c i a l management i s not included as t h i s i s considered beyond the scope of the study. The decisions that are the subject of t h i s thesis are those which optimize decisions i n the s t a t i c sense rather than those that take in t o account the dynamic growth p o s i t i o n of the farm. 1.2.3 The Planning Period For the purposes of t h i s study the normal planning period i s considered to be one year. There are two main reasons for t h i s . Most vegetables are annuals produced over the period of one year. Even i n cases where multiple cropping i s f e a s i b l e or perennials and b i e n n i a l s are a f a c t o r the period of a year provides a complete set of c l i m a t i c and b i o l o g i c a l conditions which can be considered by the farm manager. The i n s t i t u t i o n a l s e t t i n g of the vegetable farm i s also based on a year. A complete set of f i n a n c i a l records i s required every twelve months f o r taxation purposes. Loan repayments and other dealing with f i n a n c i a l intermediaries are also frequently based on the year. 8 1.3 OBJECTIVES OF THE STUDY The o b j e c t i v e of the study was to develop a computerized farm planning model fo r those farmers whose resources, technical knowledge, experience and markets l i m i t t h e i r choice of what to produce from a f i n i t e l i s t of vegetables; who are l i m i t e d i n t h e i r options of how to produce to the bundle of c a p i t a l inputs they presently own and current inputs they can purchase or h i r e . The model should be r e a d i l y adaptable to a wide range of commercial vegetable farms producing a wide v a r i e t y of vegetables i n various l o c a t i o n s and using e i t h e r labour i n t e n s i v e or machine intensive tech-nology. The model should r e a l i s t i c a l l y cope with the d i v e r s i t y of current inputs and the flow of c a p i t a l inputs i n a frame-work that r e f l e c t s the timeliness of the use of these inputs. The model to be b u i l t i s to be a d e t e r m i n i s t i c , s i n g l e year, farm planning model that w i l l enable producers to s e l e c t crops and crop production methods from among a l t e r n a t i v e s a v a i l a b l e so as to form an optimal farm plan with the maximum l e v e l of income consistent with the farm manager's technological and resource c o n s t r a i n t s and h i s other goals. The o b j e c t i v e may be separated i n t o several sub-objectives that are necessary to be able to complete the o v e r a l l o b j e c t i v e : 1. To i d e n t i f y problems encountered by vegetable producers i n formulating a farm plan and technological information a v a i l a b l e that i s relevant to r a t i o n a l l y making planning decisions; To construct a model that w i l l s e l e c t optimal farm plans f o r vegetable producers; To v e r i f y the model through i t s a p p l i c a t i o n to a case farm; To demonstrate the use of the model i n developing an optimal farm plan f o r the case farm. 10 1.4 METHODS ADOPTED FOR ACHIEVING OBJECTIVES 1.4.1 The F i r s t Sub-Objective The f i r s t sub-objective involved i d e n t i f y i n g the problems f a c i n g primary producers and the areas of d e c i s i o n making that i t would be po s s i b l e to incorporate i n t o a farm planning model. This sub-objective i s the f i r s t step i n the o v e r a l l o b j e c t i v e of the thes i s as i n d i c a t e d i n Figure 1 . 2 The f i r s t sub-objective has been s a t i s f i e d through conversations with growers, u n i v e r s i t y experts, and others interested and informed about the problems of vegetable producers. This sub-objective i s n a t u r a l l y an on-going one that i s c o n t i n u a l l y being updated throughout the work done towards the completion of the t h e s i s . The major economic problems f a c i n g vegetable producers have been i d e n t i f i e d as a problem of. crop s e l e c t i o n and resource a l l o c a t i o n . How many acres of each crop should be produced and what combination of inputs or resources should be used to produce each crop? Crops are to be selected according to t h e i r p r o f i t a b i l i t y on the farm subject to technological r e l a t i o n s h i p s and resource c o n s t r a i n t s . Because of the d i v e r s i t y pf vegetables, regions, and i n d i v i d u a l p r a c t i c e s and because the basic ' t e s t i n g 1 has not been done to define systematic b i o l o g i c a l r e l a t i o n s h i p s i n most cases, i t was f e l t necessary to leave the d e f i n i t i o n of these r e l a t i o n s to the d i s c r e t i o n of the farmer. Consequently the d i r e c t i o n of research has focused on the r e l a t i o n s h i p s that the farmer can be expected to provide. Evaluations of Sub-Objective 1 Sub-Objective 2 Step I Problem Statement (Chapter 1) r Step I I Theoretical Model (Chapter 2) < Empirical Model of the Step I I I Vegetable Farm (ChaDters 3 and 4) Sub-Objectives 3 and 4 Step Farm IV Data 1 Step V I I - S u m m a r y l • and Conclusions :hapter 6) 0 . W T T T Suggestions f o r Further Step v i i i R e s e a r c h (chapter 6) FIGURE 1.2 ORGANIZATIONAL FLOW CHART SHOWING MAJOR STEPS TAKEN TOWARDS SATISFYING THE OBJECTIVES OF THE THESIS Step V Applied Farm Planning Model (Chapter 5 ) Step Farm VI Reports 12 resource c o n s t r a i n t s i n a r e a l i s t i c time frame i s seen as a major problem about which considerable information may be obtained relevant to the i n d i v i d u a l grower. The scheduling of machine operations with an accurate evaluation of machine and labour resources a v a i l a b l e over the time period budgeted f o r the operation and the p r e d i c t i o n of associated costs i s the area of c e n t r a l concern. I t has been the technological information about machine performance and cost that has been investigated i n a most d e t a i l e d manner. The model has been developed to evaluate these types of c o n s t r a i n t s and c a l c u l a t e these types of costs i n d e t a i l . The b i o l o g i c a l r e l a t i o n s h i p s are i n c i d e n t a l to the main work done on the model. I n t u i t i v e l y t h i s can be seen as a r a t i o n a l approach; there are such a large number of vegetables and regions each with a great v a r i e t y of s p e c i f i c b i o l o g i c a l requirements but the technological r e l a t i o n s h i p s between the machinery used to produce them, i s common to a l l . 1.4.2 The Second Sub-Objective There are two steps that have been i d e n t i f i e d as necessary f o r the completion of the second sub-objective: the development of a t h e o r e t i c a l model of the vegetable firm and the construction of a q u a n t i t a t i v e empirical model (steps II and III r e s p e c t i v e l y i n Figure 1.2). The t h e o r e t i c a l model given i s the theory of the f i r m . The theory of the fi r m i s modified by s p e c i a l considerations of the s i t u a t i o n of vegetable farm and of the q u a n t i t a t i v e model used. The model b u i l t i s a multiperiod l i n e a r programming 13 model. The model assumes that a l l c o e f f i c i e n t s are known with complete c e r t a i n t y and that the farm operator has the s i n g l e goal of maximizing h i s gross margins. These l a s t two c h a r a c t e r i z a t i o n s of the model can be relaxed to some extent i n the s p e c i f i c a t i o n of l i m i t s on resources and a c t i v i t i e s within the model but these are not e x p l i c i t l y incorporated i n t o the model. An e s s e n t i a l feature of the model i s that i t i s a multiperiod model with l i m i t s placed on most resources f o r a number of segments of the t o t a l planning period. The number of segments and the length of each v a r i e s according to the demands placed on those resources. A c e n t r a l part of the model allows the length of time i n which a s p e c i f i c job must be completed to be s p e c i f i e d i n d i v i d u a l l y i n terms of groups of the basic time segments. This q u a l i t y of the model enables evaluation of d i f f e r e n t farm plans i n a r e a l i s t i c time constraint framework. The model incorporates quite d e t a i l e d machinery data used to determine f u e l consumption, r e p a i r and maintenance costs, and c o n s t r a i n t s on machine time. Most of t h i s data, and a l l data concerning chemical use, c u l t u r a l p r a c t i c e s , and y i e l d response should i d e a l l y o r i g i n a t e on the farm to which the model i s being applied. Another feature of the model i s that i t can r e a d i l y accommodate v a r i a t i o n s i n v a r i a b l e inputs that are known. Considerable work i s required to b u i l d a crop into the model but when t h i s has been done a d d i t i o n a l v a r i a t i o n s i n para-14 meters and t h e i r consequences f o r y i e l d s can be evaluated by adding a few columns to the matrix. The model has also been constructed almost completely i n terms of p h y s i c a l u n i t s . For example, the approach taken to estimate r e p a i r and maintenance costs i s to b u i l d i n the hours of use of the machinery and c a l c u l a t e the cost of use on an hourly basis within the model rather than use only a sing l e c o e f f i c i e n t i n d o l l a r s . 1.4.3 The T h i r d Sub-Objective Three steps have been i d e n t i f i e d i n the completion of the t h i r d sub-objective, which are i n d i c a t e d as steps IV, V and VI i n Figure 1.2. The f i r s t step involved s p e c i f i c a t i o n of the data required by the empirical model and sources of the data. Once the data had been s p e c i f i e d a case farm was selected and the farm data recorded*. The selected case farm was r e l a t i v e l y complicated i n that a large number of technologi-c a l l y diverse crops are grown. The operators* CANFARM records and information c o l l e c t e d on several v i s i t s to the farm, and s p e c i a l machine c o e f f i c i e n t s o r i g i n a t i n g i n empirical studies done by a g r i c u l t u r a l engineers constitute the data base f o r the case farm. A farm planning model of the case farm was constructed and constrained to follow the case farm's 1974 farm plan. The s o l u t i o n found with t h i s 'simulation run' of the farm planning model i s used to v e r i f y the model. • Data c o l l e c t e d i s documented i n a separate paper "An Optimal Farm Plan f o r a Vegetable Farm." 15 The l o g i c of the model was evaluated by showing that a so l u t i o n to the model was consistent with resources u t i l i z e d and costs c a l c u l a t e d based on numerical analysis of the empirical model and the data. The v a l i d i t y of the c o e f f i c i e n t s used for the case farm and r e l i a b i l i t y of plans produced by the model were shown by comparing the costs predicted with the farm planning model with those recorded i n the CANFARM records of the farm. 1.4.4 The Fourth Sub-Objective F i n a l l y the model was used to produce an optimal 1976 farm plan f o r the farm. This was done to show that the model can indicate some important changes i n the farmer's plan so that he can better s a t i s f y h i s o b j e c t i v e s . Several farm plans were prepared and compared with the farm plan selected by the operator without the a d d i t i o n a l knowledge he would have had using the farm planning model. Detailed farm reports were prepared f o r one of the farm plans. 1.5 ORGANIZATION l b The organization of the thesis as i t r e l a t e s to the steps taken to achieve objective i s summarized i n Figure 1.2. The f i r s t sub-objective of problem i d e n t i f i c a t i o n i s documented i n t h i s chapter. The second sub-objective was separated i n t o two steps. The f i r s t step involved an examination of the standard theory of the firm and t h i s i s done i n the second chapter of the t h e s i s . Attention i s also given i n Chapter 2 to the quanti-t a t i v e methods that were considered and p r a c t i c a l concerns of the nature of vegetable farming and of the qua n t i t a t i v e approach used ( l i n e a r programming) as they a f f e c t the theory of the firm. The s p e c i f i c a t i o n of the empirical model was such an involved task that i t was separated i n t o two chapters. In the t h i r d chapter other crop budgeting models, p a r t i c u l a r l y the Purdue Models, are summarized and the machine scheduling system developed f o r the model i s discussed i n d e t a i l . This i s done at t h i s point because the machine scheduling block i s r e a l l y the core of the model and the r e s t of the model i s very straightforward when t h i s section of i t i s known. The structure of the en t i r e model i s introduced, i n t h i s chapter, with aid of a flow diagram i l l u s t r a t i n g source of resources, use of resources and information required by the model. In the fourth chapter the themes established i n the t h i r d chapter are expanded. The sources of farm data are s p e c i f i e d . A picture of the e n t i r e matrix i s given and d e t a i l e d schemata are given of other types of a c t i v i t i e s not explained i n Chapter 3. The t h i r d sub-objective was to v e r i f y the model against i t s a p p l i c a t i o n to a s p e c i f i c case farm. The d e t a i l s of the s e l e c t i o n of the case farm, the p i c t u r e of the applied model and r e s u l t s of using the model to simulate the case farm's 1974 farm plan as recorded i n the CANFARM records are a l l given i n the f i r s t part of Chapter 5. The model was used to produce s i x d i f f e r e n t optimal farm plans based upon a l t e r n a t i v e c o n s t r a i n t s and y i e l d s which are compared i n Chapter 5. One of the plans was used to produce d e t a i l e d projections of income, costs and resource u t i l i z a t i o n which are given i n Appendix G. This material i s presented to s a t i s f y the fourth sub-objective. F i n a l l y the thesis i s summarized and conclusions drawn i n Chapter 6. Suggestions f o r further research are a l s o given i n Chapter 6. CHAPTER 2 THEORETICAL MODEL OF THE FIRM In the previous chapter i t was stated that the objective of the thesis was to b u i l d a farm planning model ap p l i c a b l e to vegetable farms and that l i n e a r programming would be the modeling technique employed. In t h i s chapter an attempt i s made to i n d i c a t e the t h e o r e t i c a l considerations that underlie the approach taken. The farm planning model w i l l maximize income subject to s p e c i f i c resource, technological and al t e r n a t i v e goal c o n s t r a i n t s . The theory of the fi r m i s summarized i n Section 2.1 to point out the r e l a t i o n s h i p s that must hold between resources, between resources and products, and between products at the point of maximum p r o f i t . The nature of the production process implied by the existence of a maximum p r o f i t solution i s also i n d i c a t e d . In Section 2.2, the main p o t e n t i a l a l t e r n a t i v e quantita-t i v e modeling techniques are b r i e f l y i n d i c a t e d . Modeling methods are d i v i d e d i n t o the three categories: l i n e a r pro-gramming, non-linear programming, and simulation. Some major advantages and disadvantages of each are given i n table form and the reasons given why l i n e a r programming was used f o r t h i s study. In the f i n a l section, Section 2.3, the formulation of the l i n e a r programming problem i s explained. An attempt i s made to r e l a t e the l i n e a r programming formulation to the theory of the firm as i t i s thought to apply to vegetable farms by the 19 author. It i s shown that the l i n e a r programming model allows an approximation of the necessary conditions for a s o l u t i o n to the maximizing problem, that i t implies a production process not unlike that suggested by the theory of the firm as i t applies to vegetable farms and that the constraints on the production process for the vegetable farm can be e a s i l y handled. Formulation and t h e o r e t i c a l j u s t i f i c a t i o n of the dual l i n e a r programming problem i s i n d i c a t e d as well as i t s r e l a t i o n s h i p to the constraints imposed on the production process. 20 2.1 THE THEORY OF THE FIRM The f i r m i s the basic uni t of production i n n e o - c l a s s i c a l economics. For each fi r m a r e l a t i o n s h i p i s assumed to e x i s t between the resources or inputs that the fir m uses and the products which the firm s e l l s . The r e l a t i o n s h i p i s c a l l e d the production function and i s expressed i n exact terms i n equation 2.1. 2.1 q = f (x 1 ,x 2 j . . - , ^ ) where q = maximum possible production, and x\ = i - t h input with i = l , 2 , . . . , n . The production function i s usually described as being continuous, twice d i f f e r e n t i a t e , and concave. This d e s c r i p t i o n follows from further assumptions that are made about the rela-. tionships between resources and between resources and output. Both inputs and output are assumed continously d i v i s a b l e . There are diminishing returns to the increased use of one input with other inputs held constant. D i s p o s a b i l i t y of resources may or may not be assumed. The market p o s i t i o n of the firm i s also assumed to approximate perfect competition i n which case four a d d i t i o n a l assumptions have to be made. The f i r m produces a homogeneous product. Both firms and consumers are numerous and small r e l a t i v e to the s i z e of the markets i n which they p a r t i c i p a t e . Both firms and consumers possess p e r f e c t know-ledge about p r i c e and product r e l a t i o n s h i p s and both are maximizers. More s p e c i f i c a l l y , the f i r m i s considered to be a p r o f i t maximizer. Entry and e x i t from the market i s also assumed free i n the long run. 21 With t h i s d e s c r i p t i o n of the firm the conditions under which a firm can achieve i t s objective of p r o f i t maximization can be s p e c i f i e d . The f i r m w i l l obtain the greatest p r o f i t s at the point where the marginal value products of a l l inputs are equal (input-input r e l a t i o n s h i p ) and where the marginal value product equals the p r i c e of output (input-output r e l a t i o n s h i p ) rather than at the maximum output. For the s o l u t i o n to e x i s t the production function has to have constant or decreasing returns to s c a l e . I f the f i r m produces several products then the p r i c e r a t i o of any two products must equal the r a t i o of marginal products of the two products with a l l inputs. However, as pointed out by Heady (1971, p 9): " A l l farms have several l i m i t e d p h y s i c a l resources .... In addi t i o n a l l farms have i n s t i t u t i o n a l or subjective r e s t r a i n t s . " This may be considered to be the short or medium run p o s i t i o n of the firm as with a planning horizon of one year with a f i x e d c a p i t a l stock which i s the s i t u a t i o n being addressed by t h i s study. The p r o f i t function f o r a sing l e product firm i n t h i s s i t u a t i o n may be represented as i n equation 2.2 with a constraint imposed on one input. * The d e s c r i p t i o n of the f i r m i n long run competitive equi-librium can be found i n any standard text, e.g. Henderson and Quandt (1958), Fergu wson (1972), e t c . 22 2.2 //= pq - W3X1-W2X2-W3X3- b subject to x 3£- c or x 3 + s = c where Jl = p r o f i t , P the p r i c e of the f i n a l product, q the production function 2.1 where n = 3, w i = the p r i c e of the i - t h input, x i = the amount of the i - t h input, b = f i x e d costs, c an upper bound on the amount of x av a i -l a b l e and s _ a slack v a r i a b l e . The constrained optimization problem i n equation 2.2 can be solved by forming the Lagrangian equation 2.3 and taking the p a r t i a l d e r i v a t i v e s . 2.3 L=pq - w^x^ - w 2x 2 - w 3x 3 - b + A(c - X3 - s) The p a r t i a l d e r i v a t i v e s f o r x^ and x 2 give the same input-input and input-output r e l a t i o n s h i p s as the unconstrained case but f o r the t h i r d input the p a r t i a l d e r i v a t i v e i s : 2 . 4 L 3=P f 3 - w 3 - A • The marginal value product f o r the t h i r d input i s equal to the sum of i t s wage and the Lagrangian m u l t i p l i e r f o r the co n s t r a i n t . The term w^  + X m a Y D e c a l l e d the shadow p r i c e f o r the input X3 f o r the s o l u t i o n i s as though the pr i c e of the input were w^  + A » Another feature of t h i s model i s that i t does not require an assumption about the returns to scale of the production f u n c t i o n . 23 2.2 QUANTITATIVE MODELING METHODS An e s s e n t i a l feature of a l l three economic models of the fir m i s the maximizing behaviour presumed. C r i t i c i s m s of t h i s assumption u s u a l l y propose another obj e c t i v e or combination of objectives to be maximized or minimized. Boulding (1960) points out that the f i r s t order marginal conditions follow as mathematical tautologies from the f a c t that optimizing behaviour that i s assumed. The objective of developing a mathematical model of the vegetable farm should be r e s t r i c t e d to models that are capable of u t i l i z i n g an optimizing routine to simulate t h i s behaviourial assumption. There i s a trade o f f however between the f l e x i b i l i t y and realism that can be incorporated i n t o the model and the a v a i l a b i l i t y and r e l i a b i -l i t y of the optimizing routines for the model. In Table 2.1, modeling methods that may be considered f o r the fi r m are divided i n t o three main categories and some of the major advantages and disadvantages given f o r each. I t was decided very e a r l y i n the undertaking of the thes i s to use the technique of l i n e a r programming. Simulation was not s e r i o u s l y considered because of the lack of an optimizing procedure. Non-linear programming was considered as a technique necessary f o r taking account of r i s k . I t was f e l t however that r i s k could be accommodated i n a l i n e a r programming framework and that there are other complex problems i n the modeling of the vegetable farm that should be solved f i r s t . There are also a large number of v a r i a t i o n s on the 24 TABLE 2.1 MODELING METHODS COMPARED Linear Programming Non - l i n e a r Programming Simulation Optimizing Method Revised Simplex Method r e a d i l y a v a i l a b l e i n various computer packages Several methods. Not normally a v a i -l a b l e i n packages. Algorithms longer and more expensive Various search techniques employed but there i s no Algorithm which leads to a c e r t a i n optimum Advantages Simplest model as Equations may be a l l equations l i n e a r or non-l i n e a r . Optimizing l i n e a r Method best known because of long h i s t o r y Most r e a l i s t i c i n that there are no r e s t r i c t i o n s i n the formulation of the model Lack of realism due to r e s t r i c t i o n to l i n e a r i t y . Impossible to have even l i n e a r approx-imations of i n c r e a -sing functions Disadvantages Optimizing Method l i m i t s number of non-linear equa-t i o n s . Cost Lack of guarantee that the s o l u t i o n i s optimal 25 technique of l i n e a r programming such as i n t e g e r programming, parametric programming, m u l t i p l e goals programming, and s t o c h a s t i c programming. None of these techniques are used i n the model. There i s c o n s i d e r a b l e room f o r making the model more r e a l i s t i c by i n c o r p o r a t i n g some of these techniques but the b a s i c problem of crop s e l e c t i o n i n a framework t h a t a c c u r a t e l y computes v a r i a b l e c o s t s and f i e l d time c o n s t r a i n t s i s i t s e l f a complex l i n e a r programming problem t h a t does not r e q u i r e any of these e x t e n s i o n s . 26 2.3 PRACTICAL CONSIDERATIONS THAT MODIFY THE THEORETICAL MODEL 2.3 .1 R e l a t i o n s h i p between the Theory o f the F i r m and Ve g e t a b l e Farms Although i t i s i m p o s s i b l e t o say a p r i o r i whether t h e r e i s d i m i n i s h i n g r e t u r n s t o any s p e c i f i c r e s o u r c e on a v e g e t a b l e farm o r whether the p r o d u c t i o n f u n c t i o n f o r v e g e t a b l e farms i s con t i n u o u s and twice d i f f e r e n t i a b l e some of the o t h e r assump-t i o n s may be e v a l u a t e d i n t u i t i v e l y . D i v i s i b i l i t y o f i n p u t s and o u t p u t s i s i n most c a s e s a r e a s o n a b l e a p p r o x i m a t i o n o f r e a l i t y but t h e r e may be some v a r i a b l e s f o r which i n t e g e r v a l u e s o n l y may be r e l e v a n t . Perhaps l a b o u r has to be h i r e d f o r a f u l l day or a grower may o n l y be a b l e t o g e t a s p e c i f i c s i z e o f marketing c o n t r a c t from p r o c e s s o r s * . A l t h o u g h r e t u r n s t o s c a l e are d i f f i c u l t t o e v a l u a t e a l l farms have both p h y s i c a l and s u b j e c t i v e r e s t r a i n t s on s e v e r a l r e s o u r c e s and the t h e o r y o f the f i r m i m p l i e s t h a t a unique s o l u t i o n t o the problem o f p r o f i t m a x i m i z a t i o n can e x i s t i n t h i s c a s e r e g a r d l e s s o f the r e t u r n s t o s c a l e . A non-unique optimum w i t h c o n s t a n t r e t u r n s t o s c a l e may be assumed w i t h o u t c o n t r a d i c t i n g the t h e o r y . S u b s t i t u t a b i l i t y between r e s o u r c e s seems i n t u i t i v e l y p r o b a b l e as does the d i s p o s a b i l i t y o f r e s o u r c e s . The v e g e t a b l e f i r m f o r the most p a r t conforms t o the d e s c r i p t i o n o f the f i r m i n the s h o r t r u n w i t h a m u l t i p l e product o u t p u t . * T h i s type o f i n t e g e r problem i s assumed t o be unimportant. I f i t were an important c o n s i d e r a t i o n then an i n t e g e r p r o -gramming t e c h n i q u e would be n e c e s s a r y . The assumption that the firm i s i n a p e r f e c t l y competitive p o s i t i o n seems less v a l i d . The assumption of perfect competi-t i o n implies that the f i r m has p r o f i t maximization as i t s s i n g l e goal. The s i n g l e goal of p r o f i t maximization ignores the f a c t that the owner-operator of a vegetable f i r m i s also a consumer and as a consumer must be making a preference d e c i s i o n between work and l e i s u r e . The i m p l i c a t i o n of perfe c t knowledge i s also not s a t i s f i e d . Because of the time lag between the formulation of the farm plan and the completion of that plan there i s bound to be a degree of r i s k and uncertainty i n the pri c e s of inputs and product. Because of the c l i m a t i c and b i o l o g i c a l f a c t o r s involved i n crop production there i s bound to be a degree of uncertainty concerning y i e l d s . Future income has at l e a s t two dimensions that should be evaluated: l e v e l and v a r i a b i l i t y . The knowledge c r i t e r i a i s not met i n another completely d i f f e r e n t sense. As pointed out i n the f i r s t chapter a large number of input-output r e l a t i o n s h i p s are unknown. For some resources the grower may be able to point out d i f f e r e n t expected y i e l d s f o r d i f f e r e n t l e v e l s of inputs. This i s the case f o r example f o r inputs l i k e d i f f e r e n t q u a l i t i e s of land. For a great many other a l t e r n a t i v e s the marginal r e l a t i o n s h i p s w i l l remain undefined. I t i s only that part of the production function that i s perceived that can be b u i l t i n t o the model. It w i l l have to be assumed that the grower's usual p r a c t i s e s a t i s f i e s the marginal conditions f o r an optimum f o r a l l other inputs. 28 2.3.2 The S t r u c t u r e o f the L i n e a r Programming Problem and i t s I m p l i c a t i o n s f o r the Theory o f the F i r m Theory s p e c i f i e s a number of r e l a t i o n s h i p s t h a t a re supposed t o h o l d f o r the v e g e t a b l e f i r m and deduces from these the c o n d i t i o n s n e c e s s a r y f o r the f u l f i l m e n t o f the ma x i m i z a t i o n assumption. The q u a n t i t a t i v e model o f the f i r m d e v e l o p e d t o s a t i s f y t he o b j e c t i v e s o f the t h e s i s s h o u l d s i m u l a t e t h i s d e s c r i p t i o n o f the f i r m . The l i n e a r programming problem may be r e p r e s e n t e d as i n e q u a t i o n 2.4: 2.4 Maximize c f cx s u b j e c t t o Ax ^  b and x ^ 0 where c t i s a 1 x n v e c t o r o f p r i c e s , x i s a n x 1 v e c t o r o f a c t i v i t i e s , b i s a m x 1 v e c t o r o f r e s o u r c e c o n s t r a i n t s , and A i s a m x n m a t r i x . T h i s system o f eq u a t i o n s i s s i m i l a r t o the system i n 2.2 The o b j e c t i v e f u n c t i o n c f cx may be a type o f p r o f i t f u n c t i o n w i t h the c o n s t r a i n t m a t r i x g i v i n g the t e c h n i c a l r e l a t i o n s h i p s o f the p r o d u c t i o n f u n c t i o n . The elements o f the v e c t o r x are the v a r i a b l e s ( o r a c t i v i t i e s o r columns) o f the l i n e a r p r o -gramming problem. Some o f these v a r i a b l e s may be i n p u t s w i t h n e g a t i v e c o e f f i c i e n t s i n the o b j e c t i v e f u n c t i o n which r e p r e s e n t l e v e l s o f purchases o f s p e c i f i c r e s o u r c e s . Some v a r i a b l e s may r e p r e s e n t f i n a l p r oducts and have p o s i t i v e c o e f f i c i e n t s i n the o b j e c t i v e f u n c t i o n . Other v a r i a b l e s may have z e r o s f o r c o -e f f i c i e n t s and are c a l l e d t r a n s f e r a c t i v i t i e s . The f u n c t i o n of t r a n s f e r a c t i v i t i e s i s t o t r a n s f o r m one r e s o u r c e i n t o 29 another or change i t i n t o a f i n a l product*. Transfer a c t i v i t i e s are a convenient method of making the t e c h n i c a l r e l a t i o n s h i p s of the production function e x p l i c i t . A main advantage of l i n e a r programming i s i t s ease of use. In a sense each d i f f e r e n t a c t i v i t y i s defined by the resources and t h e i r r e l a t i v e proportions that the a c t i v i t y requires and produces. The s o l u t i o n of the l i n e a r programming problem contains the optimal l e v e l of each a c t i v i t y and thus simultaneously answers the questions of what to produce and how to produce i t . Each resource can be b u i l t i n t o the model as a row and subdivided i n t o as many categories as i s thought necessary. In t h i s way the timeliness of the use of each resource can be b u i l t i n t o the model i n a meaningful way. D i v i s i b i l i t y and d i s p o s a b i l i t y of resources are automatically assumed. Sp e c i a l r e s t r i c t i o n s may be placed on s p e c i f i c resources and f i n a l products to take i n t o consideration sub-j e c t i v e estimates of r i s k and the personal preferences of the grower. A f i n a l advantage of the l i n e a r programming model i s that each l i n e a r programming problem has an associated dual problem. Equation 2.7 i s the dual formulation of equation 2.6. * This i s not necessarily the only approach that can be taken. Variables could be f i n a l products and t h e i r p r i c e s could be the d i f f e r e n c e between revenue and v a r i a b l e costs per unit, e t c . 30 2.7 Minimize b f cy subject to A f c y ^ c and y 2 0 where bt i s a 1 x m vector of resource c o n s t r a i n t s , c i s a n x 1 vector of p r i c e s , At i a a n x m matrix, and y i s a m x 1 vector of dual v a r i a b l e s . The dual v a r i a b l e s i n t h i s case represent the shadow pri c e s of resources. A f i n i t e s o l u t i o n to the primal problem, equation 2.6, implies a unique s o l u t i o n to the dual problem and conversely. The shadow pri c e s are the same ones encounte-red i n the s o l u t i o n to the constrained optimizing problem, equation 2.4. In the case of resources which are not constrained, t h e i r shadow p r i c e s are the same as t h e i r purchase or r e n t a l p r i c e . For constrained resources the value of the shadow pr i c e takes i n t o account the change i n production that would be p o s s i b l e with one more unit of the resource, They are, as i n d i c a t e d i n Section 2.1, what the prices of the resources should be i f the resource were not constrained but the s o l u t i o n was optimal. Shadow pric e s can be valuable i n two ways. Very improbable shadow prices i n d i c a t e possible errors i n co-e f f i c i e n t s which i s useful i n v a l i d a t i n g the model. Believable but high shadow prices i n d i c a t e d i r e c t i o n s i n which the farm operation may be p r o f i t a b l y changed i n a longer time horizon than the model encompasses. As pointed out already the r e s t r i c t i o n to l i n e a r r e l a t i o n s a f f e c t s the r e a l i s m of the model. This can most e a s i l y be seen i n comparing how l i n e a r programming a l t e r s the 31 f i r s t order conditions f o r an optimum. Diminishing returns to a s p e c i f i c resource, f o r example, has to be approximated i n d i s c r e t e terms with separate a c t i v i t i e s f o r production with each d i f f e r e n t r a t i o of resources. Restraints have to be placed on each a c t i v i t y with more e f f i c i e n t resource product r a t i o s . The s e r i e s of these constrained a c t i v i t i e s approximate the t h e o r e t i c a l marginal product curve with a d i s c r e t e step function (see Figure 1.2). S i m i l a r l y separate a c t i v i t i e s are required to represent input s u b s t i t u t i o n and product s u b s t i t u t i o n . To portray the t h e o r e t i c a l isoquant or product s u b s t i t u t i o n curve would require an i n f i n i t e number of a c t i v i t i e s although both may be approximated by a f i n i t e number of points with a l i n e a r seg-ment j o i n i n g the points. Exact tangency between the p r i c e r a t i o and any point i s impossible. There i s no f i r s t d e r i v a t i v e at a point. Tangency between the price r a t i o and the l i n e segment j o i n i n g the points may be possible i n which case the tangency covers a whole range of s o l u t i o n s . A f i n a l consideration i s that a l i n e a r programming model must, because of i t s l i n e a r i t y , imply a production function with constant returns to s c a l e . Without t h i s assumption one must admit that there i s a systematic bias i n the c o e f f i c i e n t s used i n the model depending on whether the optimal s o l u t i o n contains an a c t i v i t y at a l e v e l greater or smaller than at the l e v e l from which the c o e f f i c i e n t s were estimated and whether the production function a c t u a l l y has increasing or decreasing returns i n t h i s area. 32 x^ (input i ) FIGURE 1.2 A COMPARISON OF THE THEORETICAL INPUT-OUTPUT RELATION AND THE LINEAR PROGRAMMING APPROXIMATION 33 To summarize, the underlying economic theory on which the farm planning model r e s t s has been given i n t h i s chapter. The structure of the q u a n t i t a t i v e method employed and i t s r e l a t i o n s h i p to economic theory have also been given. In the next two chapters, the s p e c i f i c s of how the method was used, and the exact formulation of the empirical model are d e t a i l e d . CHAPTER 3 THE DEVELOPMENT OF THE EMPIRICAL MODEL The purpose of t h i s chapter i s to present the method adopted for programming the machinery and handling the var i a b l e time constraints and to introduce the structure of the e n t i r e model i l l u s t r a t i n g the flow of resources and the types of a c t i v i t i e s implied by the machinery s e c t i o n . In the f i r s t section of the chapter a b r i e f review i s given of other empirical models. The structure of the Purdue Crop Budgeting Models are explained i n d e t a i l with s p e c i a l reference to the method used to handle time c o n s t r a i n t s . In Section 3.2 three a l t e r n a t i v e methods of programming the machinery are explained and i l l u s t r a t e d with the a i d of schemata of the structure of a l i n e a r programming tableau. Each of the methods involved the construction of machine operating a c t i v i t i e s and i n one case a number of t r a c t o r t r a n s f e r s . This section explains the r e l a t i o n s h i p s between resources and machinery i n the t h e o r e t i c a l model and how the va r i a b l e machine time constraints on crop production are r e a l i z e d . In the t h i r d section of the chapter the sp e c i a l advantages of the method eventually selected are indicated and r e l a t e d to the problems encountered i n programming the machinery. The method used allows greater f l e x i b i l i t y than the Purdue models but w i l l i n the end require a s u b s t a n t i a l l y larger model. 35 In the f i n a l s e c t i o n of the chapte r the e n t i r e farm p l a n n i n g model i n c l u d i n g the machine o p e r a t i n g a c t i v i t i e s and t r a c t o r t r a n s f e r s i s i l l u s t r a t e d w i t h a f l o w diagram analogous to F i g u r e 1.1. In t h i s d iagram the major c l a s s i f i c a t i o n s of r e s o u r c e s used i n the t h e o r e t i c a l model and the number of t ime p e r i o d s used f o r each are g i v e n . The o r i g i n and use r e s o u r c e s by the major c l a s s i f i c a t i o n s of a c t i v i t i e s are i n d i c a t e d t o g e t h e r w i t h u n i t s tha t are used f o r each r e s o u r c e and a c t i v i t y . 36 3.1 CROP BUDGETING: THE PURDUE MODELS Most farm p l a n n i n g models n e c e s s a r i l y have t o d e a l w i t h c r o p a c t i v i t i e s a t l e a s t i n p a r t . In a model o f a beet farm (Graham and Lopez, 1975; IBM, 1965) f o r example, i t may be t h a t c r o p a c t i v i t i e s a re loo k e d on as an a l t e r n a t i v e demand f o r la b o u r and c r o p s may be s e l e c t e d i n the model on the b a s i s o f gr o s s o r net margins. A l t e r n a t i v e l y , the v a r i o u s p o s s i b l e machinery and time c o n s t r a i n t s may be brought i n t o the model ( K i z e r , 1974; McHardy, 1966; Donaldson, 1970; Barlow, 1974) i f the cr o p a c t i v i t i e s a re thought t o be more important t o the whole e n t e r p r i s e . In a commercial v e g e t a b l e farm the o n l y important p r o d u c t i v e a c t i v i t i e s are the cro p s and the t r e a t -ment of f i e l d o p e r a t i o n s becomes of major importance i n the model. Models have been developed i n the p a s t on farms where the crop d e c i s i o n s are c r i t i c a l t o the s u c c e s s f u l management of the farm. The Purdue Corn E n t e r p r i s e Budget Model A (Purdue A g r i c u l t u r a l Research S t a t i o n , 1969) was a model desig n e d to s e l e c t o p t i m a l p l a n t i n g and h a r v e s t i n g times f o r mid-West American corn farms. F o u r t e e n s e p a r a t e time p e r i o d s were used i n the Purdue model. Four a b s t r a c t types o f f i e l d o p e r a t i o n s a re e v i d e n t : those o p e r a t i o n s which may o c c u r a t any time b e f o r e a c e r t a i n time p e r i o d , those o p e r a t i o n s t h a t can o n l y be done a t ; a s p e c i f i c time, those o p e r a t i o n s which may be done i n a range o f p o s s i b l e i n t e r m e d i a t e time p e r i o d s , and those o p e r a t i o n s which may be done a t any time a f t e r a c e r t a i n d a t e . Each of these types o f o p e r a t i o n s i s programmed d i f f e r e n t l y . 37 Land may be prepared i n any one of the f i r s t 8 periods. Land preparation requires labour and machinery time and one acre of land to produce one acre of prepared land. The pre-pared land i s used by various permutations of a l l of the succeeding operations to produce corn. This process i s i l l u -s trated i n Figure 3.1 The plant-harvest a c t i v i t i e s require land from the land preparation a c t i v i t i e s that occur i n the preceding time periods. The vectors of ones and minus ones co n t r o l t h i s trans-f e r of land. Land can be planted i n s i x of the spring periods and harvested i n three d i f f e r e n t periods i n the f a l l . The f i r s t three a c t i v i t i e s i n the plant-harvest block c o n s i s t of planting i n the f i r s t p lanting period and harvesting i n the three d i f f e r e n t harvest periods. There are 18 of these plant-harvest a c t i v i t i e s needed to program a l l the a l t e r n a t i v e s i n planting and harvesting dates that are f e a s i b l e , each with the appropriate y i e l d . The 18 plant-harvest a c t i v i t i e s i l l u -s t r a t e the necessity, of b u i l d i n g a separate a c t i v i t y f o r each a l t e r n a t i v e that may be done i n an intermediate time range. An operation that has to be done i n a s p e c i f i c time frame i s programmed int o each plant harvest a c t i v i t y i n that time period and does not require any s p e c i a l c o n t r o l rows or extra a c t i v i t i e s . Using equality constraints the model forces i n land preparation i n any of the periods following the harvest with a system of land accounting rows s i m i l a r to those i n the co n t r o l section i n Figure 3.1 F e r t i l i z e r and a v a i l a b l e costs associated with machine operation were added as necessary to each of the plant-harvest a c t i v i t i e s . . Resource Prepare Land i n Period Plant-Harvest Combinations (period; (1) (2) (3) ... (8) (l ) (2) (3) (4) (5) (6) ... (18) Objective Land 1.0 1.0 1.0 1.0 Labour: (1) (2) (3) • (14) .98 .98 .98 .98 Machine: (1) (2) (3) • • (14) .30 .30 .30 .98 -Plant-Harvest Prepare Control: (1) (2) (3) (4) (5) (6) -1.0-1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 ... -1.0 -1.0 -1.0 ... -1.0 -1.0-1.0 ... -1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 ... 1.0 1.0 1.0 1.0 1.0 1.0 ... 1.0 1.0 1.0 1.0 1.0 1.0 ... 1.0 1.0 1.0 1.0 1.0 1.0 ... 1.0 FIGURE 3.1 LAND PREPARATION IN THE PURDUE MODELS 39 The main function of the Purdue Model i s to s e l e c t between d i f f e r e n t planting and harvesting dates based on y i e l d response and subject to machinery and labour time c o n s t r a i n t s . There are four well defined jobs each of which may con s i s t of more than one f i e l d operation with d i f f e r e n t t r a c t o r s and imple-ments. This sequence of operations i s the same f o r a l l a l t e r -natives since only one crop i s considered. The model i s thus oriented to very large farms that are growing a s i n g l e crop,* about which d e t a i l e d y i e l d response data to various planting and harvesting dates i s known. It should be kept i n mind when evaluating themodel f o r a vegetable farm that there are a large number of d i f f e r e n t vegetables each with d i f f e r e n t sequences of machine operations any combination of which may be grown on an i n d i v i d u a l vegetable farm. There i s also very l i m i t e d information a v a i l a b l e on the y i e l d response of even the important vegetables to planting and harvest dates. For t h i s reason a system s i m i l a r to the Purdue approach i s unsuitable f o r our purposes. * The Model has been extended to other s i m i l a r crops (Bruck e t . a l . , forthcoming p u b l i c a t i o n ) . 40 3.2 ALTERNATIVE MACHINE SCHEDULING MODELS The most simple method proposed f o r machine scheduling involves programming each machine operation with each t r a c t o r and the rate at which i t can be performed as a c t i v i t i e s . Each hour of machine operation requires one hour of machine time, one hour of t r a c t o r time and supplies machine capacity i n acres per hour. The sum of the r e p a i r and maintenance costs for t r a c t o r and implement and the cost of f u e l are the c o e f f i c i e n t s f o r the objective function and cash rows. Figure 3.2 i l l u s t r a t e s t h i s method i n the case where two implements and two t r a c t o r s are considered as possibly l i m i t i n g production and e i t h e r t r a c t o r can be used with either implement. Presence of p o s i t i v e s i n the constraint rows indicate the use of resources and negatives represent the re c e i p t of resources. In the objective function negatives represent costs and p o s i t i v e s and r e c e i p t of income. In the r i g h t hand side p o s i t i v e s stand for l i m i t e d owned resources or resource endowments. Blank spaces are ne c e s s a r i l y zero while a l l other c o e f f i c i e n t s may be zero i n p a r t i c u l a r instances. Using Method One as i n Figure 3.2 the same machine operating a c t i v i t i e s can be used by any number of d i f f e r e n t crops. This i s because the a l t e r n a t i v e methods of doing the same job feed into the same accounting row which connects the machine operating a c t i v i t i e s with the crop growing a c t i v i t i e s . The machine c o e f f i c i e n t s f o r the crop growing a c t i v i t i e s are integers f o r the number of times an operation i s done i n the same time period. 4 1 X T co rt) U o o CQ 10 ro U "D C CU CO -P a c H T3 T> C ro 4-> C OJ a: <u CO m x: u 3 CU Time P e r i o d I r l N d N U 3 o X) rd .J C U U •ri •x u cu <4H c ro i-i E-t CU LO c ro U E H S-I (1) a) co co c rd U E H C ro U E H < < CQ CQ c •ri V ro 2 c •H x: u rO CU c •ri sz u rO CU c •H x: O ro Time P e r i o d I I in O £2 ro J CU •H <L> C •H JC u ro 2 CQ CU c •ri XT u rO a a o o u u u u o u O cu CO Maximum O b j e c t i v e - + Cash Land P u r c h a s i n g Inputs + -+ •= + & + & 0 Labour T r a c t o r A cu -a £ ° T r a c t o r B H [u Machine A a, Machine B + + + + + + + + + + + + — + H Labour H cu ^  T r a c t o r A B o £ -H T r a c t o r B •' ^  Machine A + + + + + + 6 + Machine A Acc, Machine B Acc, Y i e l d s + + - + *0 *0 FIGURE 3.2 METHOD ONE OF PROGRAMMING THE MACHINERY 42 The most powerful feature of t h i s approach r e l i e s on a f l e x i b l e d e f i n i t i o n of the accounting rows. The time con-s t r a i n t f or the job i s defined by the combination of the time constraints on each operation a c t i v i t y that i s connected to the same accounting row. The job defined by "Machine A Acc." in Figure 3.2, for example, shows that the operation may be performed i n ei t h e r time period I and time period I I . The job defined by "Machine B Acc." i n Figure 3.2, on the other hand, may be performed only i n time period I. This most important feature i s maintained i n the other two models that are pro-posed. The other models are proposed as possible methods of improving upon the manner tr a c t o r s are handled. It i s possible to eliminate one of the causes of the u p l i c a t i o n of machine operating a c t i v i t i e s by converting the resource t r a c t o r into the resource horsepower hours. In -sit u a t i o n s where the nature of the implement or the job being performed l i m i t s the capacity of the t r a c t o r implement combina-t i o n , larger t r a c t o r s can substitute f o r smaller t r a c t o r s without any change in any of the time c o e f f i c i e n t s . . The assumption may be made that the t r a c t o r s which could be used depends only on tra c t o r horsepower. By converting t r a c t o r hours into horsepower hours, the number of tr a c t o r s a v a i l a b l e to do a job can be r e f l e c t e d i n the r i g h t hand s i d e . Figure 3.3 i l l u s t r a t e s t h i s method of bu i l d i n g the machine t r a n s f e r s . Analogously to the plant-harvest a c t i v i t i e s i n the Purdue Model (Figure 3.1) i t i s necessary i n t h i s approach to have an entry i n the maximum horsepower that the implement uses and a l l lower l e v e l s of horsepower. Borrow Cash Lend Cash Rent Land Hire Labour Purchase Inputs Machine A Operation Machine B Operation Grow Crop Maximum Objective Cash Land Labour Purchased Inputs 0 Horsepower 40 Horsepower 60 Horsepower Machine A Machine B Machine A Acc. Machine B Acc. Yie l d s + + + + + + + + -- + - + + + + + + + + + + + - + - + - + <£+ ^0 * o ^0 FIGURE 3.3 METHOD TWO OF BUILDING MACHINE TRANSFERS 44 A disadvantage of t h i s method i s that repair and mainten-ance costs and f u e l costs have to be an average of what they would be with each t r a c t o r implement combination. Another disadvantage i s that the method may not be applicable f o r some implements such as those l i m i t e d to a s p e c i f i c t r a c t o r by h i t c h , wheel base or some other feature of the t r a c t o r . Imple-ments that may be operated at more than one capacity and are i n f a c t l i m i t e d by the power of the t r a c t o r would s t i l l have to be duplicated. It was thought that i t might be possible to further d i s -aggregate machine operating a c t i v i t i e s so that t r a c t o r f u e l and repair and maintenance costs are separated and s t i l l have the capacity to include the advantages of both the f i r s t and second method by b u i l d i n g a t r a c t o r s e l e c t i o n block. In Figure 3.4 an hour of tractor time i s transferred into an hour of tractor time at a c e r t a i n horsepower which i s used i n the machine tran s f e r s as i n Figure 3.3. Tractor time f o r r e p a i r and maintenance cost c a l c u l a t i o n and f u e l consumption are also b u i l t into the tractor t r a n s f e r s . Implements which require s p e c i f i c t r a c t o r s can have machine tr a n s f e r s as i n Figure 3.2. This i s i n fact the procedure used i n the farm planning model that was b u i l t . A l l machine operations for a l l crops were handled as i n Figure 3.2 or Figure 3.4. The crop growing a c t i v i t i e s c o n s i s t of c o e f f i c i e n t s for land, manual labour, purchased inputs and integers for the frequency of each machine operation performed on an acre of the crop. 45 x: 10 m U o L| u o CQ 10 CO U -o c cu (0 a. CU Cu Cu Cu -P X X X X X 3 a o o o O o Li c CO <\J <tf 0 rH < < < CQ ca < CQ U a a c Xl co o 0 ro rO CO u Li u Li Li CU CU Li Li ra o o o O O c c c U U 4J •P •P 4-) -P •H •H -p CU u 0 u o U u c x: x: rH c u Ll rO ro ro (0 rO u o u 0 rH <u •<H 3 U Li U Li Li rO ro rO Li CO Di X a. H H EH EH 2 2 2 O 10 Maximum Objective Cash Land Labour Purchased Inputs Fuel Tractor Repair Tractor A Tractor . B 20 Horsepower 40 Horsepower 60 Horsepower Machine A Machine B Machine C Machine A Acc. Machine 3 Acc. Machine C Acc. Yields * ± + + + + + + + + + + + + + + + + + + -+ + + + + + - + *0 ^0 ^-^0 ^0 *0 *0 *0 '0 "0 FIGURE 3.4 METHOD THREE OF PROGRAMMING THE MACHINERY 46 3.3 SPECIAL FEATURES OF MACHINE SCHEDULING BLOCK SELECTED The technique of programming each machine operation using e i t h e r method one or method three was i n i t i a l l y attempted to reduce the confusion of aggregation and to s i m p l i f y the scheduling of the crops. There are three aspects of the technique that contribute to t h i s d e s i r a b l e r e s u l t : 1. E x p l i c i t use of the basic parameters of machine use, i . e . Capacity, Horsepower, Fuel Consumption and Repair and Maintenance Costs per Hour. 2. Each crop i s a sequence of crop operations denoted by integers which r e f l e c t the number of times each operation i s done i n each time period. 3. The problem of the v a r i a t i o n i n the length of f e a s i b l e time periods by operation can be e a s i l y handled f o r a large number of d i f f e r e n t crops by the appropriate d e f i n i t i o n of the machine operation accounting rows. The f i r s t of these points i s concerned with the problem of aggregation. The f a c t that a l l the machine parameters are e x p l i c i t , f a c i l i t a t e s changing them when applying the model in a wide range of farms. The schedule of a p a r t i c u l a r crop on the case farm can be used and e a s i l y adapted to another farm with a d i f f e r e n t l i n e of machinery i n a framework that a c t u a l l y r e f l e c t s the c h a r a c t e r i s t i c s and costs of that d i f f e r e n t l i n e of machinery. S i m i l a r l y , changes i n the machinery a v a i l a b l e on a s i n g l e farm can be evaluated i n a r e a l i s t i c manner. The e x p l i c i t use of the parameters f o r 47 machinery performance may a l s o have some p o t e n t i a l e d u c a t i o n a l v a l u e . The second p o i n t c o n c e r n s the s i m p l i f i c a t i o n i n s c h e d u l i n g . The c r o p a c t i v i t i e s are f a i r l y easy to program because they now c o n s i s t o f a sequence o f i n t e g e r s which r e p r e s e n t the frequency of performing the machine o p e r a t i o n s . To a g r e a t e x t e n t the d i f f i c u l t a s p e c t s of programming the c r o p a c t i v i t i e s have been t r a n s f e r r e d t o the t r a c t o r s e l e c t i o n b l o c k and the machine o p e r a t i n g a c t i v i t i e s . Once e s t a b l i s h e d though, the t r a c t o r s e l e c t i o n b l ock and the machine a c t i v i t i e s may be used i n o t h e r c r o p s . F i n a l l y t h e r e i s the problem of the v a r i a b l e l e n g t h of f e a s i b l e time p e r i o d s between o p e r a t i o n s . The Purdue Corn Budget model developed a method of d e a l i n g w i t h t h i s problem d i r e c t l y f o r a s p e c i f i c c r o p . By p r o p e r l y d e f i n i n g the a c c o u n t i n g rows f o r each machine o p e r a t i o n , the problem can be e f f e c t i v e l y handled by the technique h e r e i n d e v e l o p e d . The s m a l l e s t u n i t i n which work done can be c o n s t r a i n e d i s i n one o f the b a s i c work p e r i o d s i n the model. L a r g e r u n i t s c o n s i s t i n g of combinations of one or more of the b a s i c work p e r i o d s can be assembled by f e e d i n g the machine o p e r a t i n g a c t i v i t i e s i n t o a s i n g l e a c c o u n t i n g row f o r the l o n g e r p e r i o d . F o r i n s t a n c e , an o p e r a t i o n l i k e plowing t h a t may be done i n the f i r s t f o u r of the work p e r i o d s perhaps, would have the f i r s t f o u r machine o p e r a t i o n s f o r t h i s implement s u p p l y i n s i n g l e a c c o u n t i n g row. S i m i l a r l y an o p e r a t i o n t h a t may be done i n two i n t e r m e d i a t e time p e r i o d s would connect the two 48 machine o p e r a t i n g a c t i v i t i e s i n t o a s i n g l e a c c o u n t i n g row. . In the Purdue model the d i f f e r e n t p l a n t i n g h a r v e s t combina-t i o n s are a l s o d i s t i n g u i s h e d by d i f f e r e n t y i e l d s . The model t h a t has been developed does not p r e s e n t l y have the c a p a c i t y t o accommodate d i f f e r e n t y i e l d s except by s e p a r a t e c r o p a c t i v i t i e s . However, c r o p s c i e n t i s t s and e n g i n e e r s have not q u a n t i f i e d the e f f e c t o f the t i m e l i n e s s of the machine o p e r a t i o n s on any of the v e g e t a b l e c r o p s . The t e c h n i q u e i s , as f a r as known by the author, a c o m p l e t e l y new method f o r h a n d l i n g c r o p programming. The t h r e e a s p e c t s h i g h l i g h t e d above show t h a t t h e r e are s e v e r a l advantages t o the t e c h n i q u e . The main di s a d v a n t a g e i s the t h e o r e t i c a l l y huge s i z e o f the m a t r i x and the s u b s t a n t i a l s i z e of the m a t r i x i n p r a c t i s e . 49 3.4 SUMMARY OF THE COMPLETE FARM PLANNING MODEL INCORPORATING THE MACHINE SELECTION BLOCK The model i s summarized i n Figure 3.5. The diagram i s a further refinement of Figure 1.1 i n which the technological r e l a t i o n s h i p s and the resources used i n crop production are more c l e a r l y i d e n t i f i e d . The f i r s t two columns of the diagram represent resource a c q u i s i t i o n . It can be seen that there are f i v e categories of 'owned resources' and f i v e categories of 'hired resources'. Although t r a c t o r s and implements are not acquired d i r e c t l y , custom operations can be included as purchased inputs. It i s assumed that stocks i n inventory of purchased inputs and f u e l are zero. This may not be true s t r i c t l y speaking, i n which case the rows fo r f u e l and f o r purchased inputs can be looked upon as a valuation of the change i n inventory as a r e s u l t of the crop production a c t i v i t i e s . The time period i n which each resource may conceivably be considered constraining i s also given here i n parenthesis. The decision on the number of time periods and t h e i r breakdown i s somewhat a r b i t r a r y . Land may be broken into as many time periods as consecutive crops that may be produced. The maximum for B.C. farms would, therefore, be f i v e although only one may be needed for most vegetable farms. Only one time period i s needed for each purchased input. Fuel i s divided i n t o 12 time periods so that i t s use i n each month can be predicted. A d i s t i n c t i o n i s made between f u e l and the other purchased inputs because f u e l i s an input used by a l l crops i n a l l times Owned Resources Hired Tractor Resources Transfers (variable u n i t s ) (hours) Land (5) Labour (33) Tractors (33)  impie-bents (33)1 Cash (13) J Land (5? Machine Operating (hours) Ac/Harvested Ac. Crop Production (acres) Crop Sales ~TTT j {Purchased — * Inputs n ft? Units/Ac, Labour (33) Hours/Ac. Fuel ft Gal./Hr. Hour ^Horsepowej Hour Prices/Unit W J,Men/Hr HP/Hr.v_ . Ac./Hr^ —?Operation:; Fre- " Cash T (13) £31 Repair Costs/Hr. quency Family J ^— with- Family 8= drawals Group transfers taxes Legend: Cash Flow" Resource & Product Flow FIGURE 3.5 RESOURCE FLOW IN THE THEORETICAL MODEL 51 of the year whereas other inputs may only be purchased once or twice during the year. Thirteen p'eriods are needed f o r cash. Twelve periods are needed f o r the cash flow predictions throughout the year and a 'thirteenth month' i s required to account f o r cash that w i l l be held at the end of the year. Labour i s a r b i t r a r i l y divided into 33 periods. 5 periods are used to represent labour i n the months January, February, March, November and December. The r e s t of the months are divided in t o 4 roughly equal periods chosen so as to make the number of work days i n each period as equal as p o s s i b l e . More s p e c i f i c work periods could be defined f o r a more narrow range of crops but i t i s f e l t that time may be c r i t i c a l i n any of these weeks for some vegetable farms. Tractor and implement time i s divided i n t o the same number of periods. The production a c t i v i t i e s are separated into three types i n the diagram: t r a c t o r t r a n s f e r s , machine operating a c t i v i t i e s , and crop production a c t i v i t i e s . The i n t e r a c t i o n between the a c t i v i t i e s and inputs have already been i l l u -s trated i n Figure 3.4. The arrows i n Figure 3.5 i n d i c a t i n g f a c t o r and product flow are another way of i l l u s t r a t i n g t h i s i n t e r a c t i o n . The units of each input that each a c t i v i t y requires are also given i n Figure 3.5. In addition, p r i c e s for a l l products and hired inputs and possible c o n s t r a i n t s on resource purchases and crop production and sales have to be s p e c i f i e d . 52 In the next c h a p t e r the sources of the data and the r e l a t i o n s h i p s between d i f f e r e n t s e c t i o n s of the model a r e g i v e n i n d e t a i l . A p i c t u r e of the complete farm p l a n n i n g model i n m a t r i x i s g i v e n i n F i g u r e 4.1. F i g u r e 4.2 p r o v i d e s a key i l l u s t r a t i n g where the machine o p e r a t i n g a c t i v i t i e s o f F i g u r e 3.4 or 3.2 f i t i n t o the s t r u c t u r e of the e n t i r e m a t r i x . A f t e r the p r e s e n t a t i o n of the e n t i r e m a t r i x schemata are g i v e n to i l l u s t r a t e the p u r c h a s i n g a c t i v i t i e s and o t h e r s u b - s e c t i o n s of the e n t i r e model. CHAPTER 4 DETAILED PRESENTATION OF THE MODEL The method of scheduling machine a c t i v i t i e s and the structure of the en t i r e model has been explained i n Chapter 3. In Chapter 4, these two themes w i l l be enlarged upon i n d e t a i l considering the p r a c t i c a l problems of data sources and the manner i n which a l l the elements of the model can be brought together i n a s i n g l e matrix. The data required by the model has already been indicated i n Figure 3.5. Almost a l l of t h i s data may be obtained d i r e c t l y from the farmer or his CANFARM records. The data required by the model i s summarized i n tables presented i n Section 4.1. The use of engineering formulae to provide a data base f o r some machine operating parameters that may not be known by the farmer i s discussed i n the Appendices. A picture of the e n t i r e model i n matrix form i s given i n Figure 4.1 followed by an explanation of the objective function and the resources and c o n s t r a i n t s i n the model. The most important a c t i v i t i e s i n the model (the t r a c t o r t r a n s f e r s , the machine operating a c t i v i t i e s , and crop production and s e l l i n g a c t i v i t i e s ) have already been discussed i n Chapter 3 and are i l l u s t r a t e d i n Figure 3.4. The labour h i r i n g a c t i v i t i e s and labour t r a n s f e r s , the resource purchasing a c t i v i t i e s and the f i x e d cost a c t i v i t i e s are explained i n d e t a i l i n Section 3.3 Perhaps the most important part of the chapter i s the tying together of the disparate parts of the matrix i n Figure 3.2 which shows how the a c t i v i t i e s shown i n d e t a i l i n Figures 3.4 and 4.3 - 4.9 are a l l brought together to make the complete matrix of the farm planning model i n Figure 3.1. 55 4.1 SOURCES OF DATA The information required by the model can be c l a s s i f i e d into three general categories: cost information, i n t e r n a l and external c o n s t r a i n t s , and physical input-output parameters. By cost information i s meant the prices that a farmer faces as well as the overhead and f i x e d costs of his business. Some cost information may be obtained from CANFARM or other accounting records. The type of information most r e l i a b l y a v a i l a b l e from t h i s source would be overhead costs. For vari a b l e costs i t i s necessary to know the unit p r i c e s of inputs and outputs which may not be a v a i l a b l e at a l l from CANFARM records. It i s necessary therefore to have a l l input prices evaluated by farmer. Internal constraints are d i r e c t l y r e l a t e d to the farmer's goals so i t i s only he who can specify these c o n s t r a i n t s . The farmer himself w i l l also be the best source of information for external c o n s t r a i n t s . Thus a l l resource and a c t i v i t y con-s t r a i n t s must be s p e c i f i e d d i r e c t l y by the farmer. For information about input-output c o e f f i c i e n t s such as machine capacity, y i e l d s , f e r t i l i z e r use and so on the farmer himself i s s t i l l the most important source. The CANFARM records may provide some help but i t w i l l be the ph y s i c a l record system that w i l l be most valuable here. In some instances the parameters may be too te c h n i c a l to be known by the farmer, or they may be concerned with a c t i v i t i e s with which he does not have any experience. This might apply i n si t u a t i o n s where information such as'horsepower required to operate his seeder 1 i s required or when the farmer i s considering growing a new crop. In t h i s case standard package data w i l l have to be supplied. It should be noted that i n a l l s i t u a t i o n s the farmer himself should evaluate the c o e f f i c i e n t s and as many of the c o e f f i c i e n t s as possible should be s p e c i f i c to the farm. The data required according to type i s summarized i n Table 4.1. In Table 4.2 i t can be seen that a l l the parameters i n the resource r e n t i n g , cropping and crop s e l l i n g a c t i v i t i e s are farm s p e c i f i c . Some of the parameters i n the t r a c t o r trans-f e r s and i n the machine operating a c t i v i t i e s may require the use of various formulae i n one of the following c a l c u l a t i o n s : 1. Repair and maintenance costs f o r tr a c t o r s and implements. 2. Fuel required to operate the t r a c t o r s . 3. Horsepower required to operate the implements. The use of these formulae and the information they require i s dealt with i n d e t a i l s i n Appendices B, C and D. TABLE 4.1 SUMMARY OF DATA REQUIRED BY TYPE AND SOURCE Data Required Farmer CANFARM Records Physical Records Package Data Cost Information a. Variable Costs, Prices b. Fixed Costs X X X X Constraints a. Internal b. External X X Physical Parameters X X X X 5 7 TABLE 4.2 SUMMARY OF DATA REQUIRED AND SOURCES BY SECTION OF THE MODEL Section of Model Date Required Units Source Own Resources (Land, Labour, Tractors, Implements, and Cash) Maximum Amount Available by Time Period units Farm S p e c i f i c Rented, Re-sources (Land, Labour, Fuel, Limits on Renting A c t i v i t i e s units Farm S p e c i f i c Cash and Pur-chased Inputs) Prices $/unit Farm S p e c i f i c Horsepower Transfers Fuel Required gaL/hour Hunt's Fuel Formulae Repair Costs $/hour ASAE Repair Formulae Machine Operating A c t i v i t i e s Fuel Required gaL/hour Farm S p e c i f i c Repair Costs $/hour Implement Standards Horsepower Req'd HP/hour Huntte Power Formulae Implements Req'd Farm S p e c i f i c Labour Required men/hour Farm S p e c i f i c Capacity acres/hr ASAE Capacity Formula Cropping A c t i v i t i e s Limits on Crop-ping A c t i v i t i e s acres Farm S p e c i f i c Land acres Farm S p e c i f i c \ Purchased Inputs units/acre Farm S p e c i f i c Labour hr/acre Farm S p e c i f i c Machine.Operations Frequency Farm S p e c i f i c Y i e l d tons/acre Farm S p e c i f i c Crop S e l l i n g A c t i v i t i e s Limits on S e l l i n g A c t i v i t i e s tons/acre Farm S p e c i f i c Prices $/ton Farm S p e c i f i c 58 4.2 PRESENTATION OF THE MODEL The complete model i n matrix form i s i l l u s t r a t e d i n Figure 4.1. Figure 4.2 i s a key showing how s p e c i f i c sub-matrices shown i n Figure 4.1 and i n Figures 4.3, 4.4, 4.5, 4.6, 4.7, 4.8 and 4.9 f i t i n t o the e n t i r e p i c t u r e . A l l a c t i v i t i e s are discussed i n the context of these sub-matrices. The objective function and resources and c o n s t r a i n t s i n the model are discussed i n d e t a i l below. 4.2.1 The Objective Function The o b j e c t i v e function consists s o l e l y of the d i f f e r e n c e between the value of purchases and the value of s a l e s . C a p i t a l purchases or sales are not included i n the model. Beginning inventories and accounts due or receivable at the beginning of the planning period are e i t h e r assumed to be zero or can be expressed i n monetary value and used to increase the o r i g i n a l endowment of cash i n January. Ending inventories and accounts due and accounts receivable are used to increase the cash received i n the 'thirteenth' month. The ob j e c t i v e function i s s i m i l a r to 2.2: 4.1 n m Objective =T = ? _ 1 P i q i - j ? l w j x j where TT = p r o f i t (income above v a r i a b l e and f i x e d expenses) p^ = price Of product i , Q J L = amount of produce i s o l d , w j = price of input j , and w. = amount ofinput j purchased. 59 w Cu nd La T J . — . 4 J <o —i—-CU fO . C c—-a c*— Cf. c Pur< FIGURE 4.1 PICTURE OF THE EMPIRICAL MATRIX R e p a i r T r a n s f e r R e p a i r R e p a i r T r a c t o r - T r a c t o r T r a n s f e r T r a n s f e r T r a n s f e r T r a n s f e r One Two Three 0-10HP 10-20HP (12) (12) (12) (33) (33) " 6 , 1 4 " 6 , 1 5 A l l , l l A l l , 1 2 A l l , 1 3 " A 1 2 , U " A 1 2 , 1 2 " A 1 2 , 1 3 A 1 2 , 1 4 A 1 2 , 1 5 A 1 3 , H A 1 3 , 1 2 A 1 3 , 1 3 A 1 4 , 1 4 A 1 4 , 1 5 " A 1 5 . 1 4 " A 1 5 , 1 5 T r a c t o r T r a n s f e r 130-140HP (33) Machine Operat ing (33) Labour -Machine Supply Grow Crop S e l l Crop RIGHT HAND SIDE " A l , 2 8 A l , 3 1 | A 2 , 2 8 " A 2 , 3 1 .*» i 1 3 1 A 4 , 3 0 i % i I A 5 , 3 0 A 6 , 2 7 A 6 , 2 8 A 7 , 3 0 A 8 , 2 8 " A 8 . 2 9 A 8 , 3 0 A 9 , 2 8 A 9 , 3 T A 1 0 , 2 8 A 1 0 , 3 0 A 1 2 , 2 7 4 b 1 3 A 1 4 , 2 7 " A 1 4 , 2 9 " A 1 5 , 2 7 A 1 5 , 2 8 A 1 6 , 2 8 " A 1 6 , 2 9 A 1 7 , 2 9 " A 1 8 , 2 8 A 1 8 . 3 0 A 1 9 . 3 1 A 1 9 , 3 1 A 1 9 , 3 1 A 2 0 . 3 1 T l r ^ H-I Q • C ro fD fD ro ro ro ro ro Cash (13) r'K«; Ccsts Control ten;* t Lend Fuel Totil Repair Percent Sepair Hcurs Cor.trc' ?.;?a1r Hours (12) Porseprver •33) plere-t Hears. 3orrcw Cash (12) tA2.1 Lent! Cash (12) IttO'jr.&cfciw Control Operjtlans Account Fixed Costs (1) Rent Land (1) Fuel (12) Buy Inout • (1) Hire Labour (33) -S.7 Hired Labour Transfer (33) Own Labour Trans fer 03) Tractor Recalr Costs (12) Sepal r Transfer One (12) Repair Transfer Two (12) Repair Transfer Three (12) Tractor Transfer O-IOHP (33) "9.8 *8.9 Tractor Transfer 10-2CHP (33) Vu Vis '12.14 "12,15 *U,14 *14.15 •*15.14 ''lS.lS Tractor Transfer . 1K-140HP (33) *4Ch1ne Operating. (33) laSeur-Machine Supply Grow Crop Sell Crop SHE •*1.2S A1.31 • 1 1 *2.28 -'2.31 1 "3 | *4.33 •*» *5.r. A6,27 *f.2S *7.B A8.28 •A8.29 *S.30 *9,28 V* *10.2B A10,30 A12,27 *14.27 •*14.29 "*15.27 *15,28 *16.28 "*15.29 *17.29 '*18.28 A18.33 A19.31 A».JI *19,J1 "lO.Sl FIGURE 4.2 KEY TO FIGURES ILLUSTRATING SECTIONS OF THE COMPLETE MATRIX The variables i n the obj e c t i v e function are the products sold and inputs purchased. The pr i c e s are the c o e f f i c i e n t s which appear i n the objective f u n c t i o n . The major items purchased or sold can be r e a d i l y i d e n t i -f i e d from Figure 3.1. The items sold c o n s i s t s of crop sales and i n t e r e s t on unused cash. As the model i s set up to maximize these w i l l have p o s i t i v e c o e f f i c i e n t s . The items purchased are i n t e r e s t on borrowed cash land r e n t a l , f u e l and other 'purchased inputs', hired labour, tractor, r e p a i r and maintenance costs, and implement rep a i r and maintenance costs. The items purchased a l l have negative c o e f f i c i e n t s i n the objective f u n c t i o n . 4.2.2 Resources and Constraints The major resources i n the model are cash, f u e l , pur-chased inputs, labour, t r a c t o r s and implements. Cash may be constrained with upper bounds and there i s an i n t e r e s t charge f o r cash and an o r i g i n a l endowment of cash i n the cash period for January. Fuel, purchased-inputs and hired labour are s i m i l a r to cash i n that they are unconstrained but may only be acquired through purchasing a c t i v i t i e s . Labour i s divided i n t o three c l a s s i f i c a t i o n s : own labour which i s the labour supplied by the farm operator and his family without charge but with an upper l i m i t , the unconstrained hired labour and a t h i r d c l a s s i f i c a t i o n which i s e i t h e r own labour or hired labour. There may be any number of t r a c t o r s or implements i n the model each of which constitutes a separate resource measured i n machine time per work period. Each piece of machinery i s constrained and although the farmer may define s u b s t i t u t e s f o r a s p e c i f i c machine by assigning i t s use i n an adjacent time period, by defining another crop production a c t i v i t y that does not use the machine but uses more labour or custom work obtained as a purchased input as a s u b s t i t u t e . The l e v e l of any a c t i v i t y which supplies resources may be e a s i l y constrained introducing bounds on these a c t i v i t i e s although t h i s i s not i l l u s t r a t e d i n Figure 3.1 and was not done on the applied model that i s discussed i n the s i x t h chapter. A l l other rows i n the model are e i t h e r accounting rows or are rows introduced to c o n t r o l the l e v e l of s p e c i f i c a c t i v i t i e s or groups of a c t i v i t i e s . The most important accounting rows are used f o r horsepower, machine jobs, and y i e l d s . Control rows are introduced to f i x the l e v e l of f i x e d costs, and of the hours av a i l a b l e per day f o r labour, t r a c t o r s and implements. Special c o n t r o l rows may be used on crops or groups of crops and crop sales to take account of s p e c i f i c marketing, r i s k , and/or r o t a t i o n c o n s t r a i n t s . 64 4.3 MAJOR ACTIVITIES IN THE MODEL The most important a c t i v i t i e s i n the model have been explained and i l l u s t r a t e d i n Chapter 3. Other a c t i v i t i e s are c l a s s i f i e d i n t o major types and are i l l u s t r a t e d i n t h i s s e c t i o n . These include the labour h i r i n g a c t i v i t i e s and labour t r a n s f e r s and resource purchasing a c t i v i t i e s and the fi x e d costs a c t i v i t y . With t h i s section the picture of the en t i r e empirical model i s complete. 4.3.1 Labour H i r i n g and Labour Transfers There are two aspects of the labour block which require comment. The f i r s t aspect i s the manner i n which the own labour c o n s t r a i n t s i n the d i f f e r e n t time periods are made (see Figure 4.3). A vector of work days per period i s i n t r o -duced. This vector i s bounded by a con s t r a i n t f o r the number of hours per day that the farm family i s able to provide. The advantage of using t h i s approach i s that only one c o e f f i c i e n t i n the r i g h t hand side has to be a l t e r e d to change the amount of time a v a i l a b l e i n a l l t h i r t y three time periods. The same method i s used to constrain a l l implement and tractor time c o n s t r a i n t s . The second notable feature i s the three c l a s s i f i c a t i o n s of labour included i n the model: own labour, hired labour, and a t h i r d c l a s s i f i c a t i o n f o r eit h e r owned labour or hired labour. To accomplish t h i s , transfer columns which transfer own and hired labour into 'either' labour are u t i l i z e d . A l l three c l a s s i f i c a t i o n s are f e l t to be needed. Certain supervisory jobs can only be performed by the farm H X P] r > o G PO to m n t-3 H O z o -d H o D CD r H o c ?o to n tn X X X o o o o H- H- H" H- s: K s: rf r f r f fi f l 3 3 3 3 3" 3" sr CD CD CD CD CD CD • • . a a a • • • r r r r fj fj CU CU Cu r r r tr tr cr tr r r r o cu Cu 0 o o 0 CJ tr tr cr c c c c cr tr cr 0 0 o .fj fj fj 0 0 o c c c c • C c fs f$ n TJ TJ TJ f$ fj o CD CD CD TJ TJ TJ 3 f$ h f l TJ TJ CD CD CD r f H* H* n> CD CD f( f( 1^ o o O f l H* H* H" 0 a a a H - 0 O o H- 1 o 0 O a a a o o o a a a o o o to ro o o o to ro H i to ro H i + i i + + + + + + + + + n cu to zr + + + IK it ir o o o » ^ o o o IN. fr * IK + o o o + o tr CD n r f < CD Own L a b o u r S u p p l y Own L a b o u r T r a n s f e r 01 Own L a b o u r T r a n s f e r 02 Own L a b o u r T r a n s f e r 03 i H i r e ' L a b o u r 01 i H i r e L a b o u r 02 i H i r e L a b o u r 03 H i r e * L a b o u r T r a n s f e r 01 H i r e L a b o u r T r a n s f e r 02 H i r e L a b o u r T r a n s f e r 03 M a c h i n e O p e r a t i n g A c t i v i t y 2 cu X 3 <X> C tn 3 66 operator. The farm operator may also want to r e s t r i c t him-s e l f to family labour f o r c e r t a i n jobs and time periods i n the year. For other jobs, i n harvesting f o r example, i t may be necessary to hire labour. In most cases the c l a s s i f i c a t i o n of e i t h e r labour may be most useful so that labour i s not a con s t r a i n t . The labour h i r i n g a c t i v i t i e s simulate the h i r i n g of hourly labour. The cost per hour f o r the labour i s entered i n the objective function and i n the cash section i n the appropriate month. Each a c t i v i t y supplies one hour of labour i n a s p e c i f i c work period i n the hired labour rows. A labour h i r i n g a c t i v i t y i s b u i l t f o r each of the t h i r t y three work periods. 4.3.2 Resource Purchasing and Hiring A c t i v i t i e s There are s i x c l a s s i f i c a t i o n s of resources i n the model that may be purchased or h i r e d : f u e l , land, purchased inputs, cash, r e p a i r and maintenance, and labour. Labour h i r i n g i s explained i n Section 4.3.1. The other f i v e types are explained here. Each f u e l purchasing a c t i v i t y supplies a p a r t i c u l a r type of f u e l i n a s p e c i f i c month that may be used by the t r a c t o r s i n the t r a c t o r s e l e c t i o n block or by the machine t r a c t o r combinations i n the machinery a c t i v i t i e s . The f u e l buying a c t i v i t i e s are i l l u s t r a t e d i n Figure 4.4. The e n t r i e s i n the objective function and cash rows are the cost per gallon f o r the f u e l . The entries i n the f u e l rows would normally be ones but these e n t r i e s are adjusted to allow f o r the d i f f e r e n c e of 15% between t h e o r e t i c a l f u e l use and actual W cn u c • • • cu •H c £} U C in 4J ro <U m fO w fO *-> EL, s >-> c SH ro CU < < < CQ a > H O -P rH rH rH rH •H CU CU CU <U SH CD > D Cr-3 Ct. • 3 • • • fjLi • • 0 • H-> C - r l •rH 4J Maximum u SI u >i >i >i fd u < 3 3 in (0 CQ CQ CQ CQ IH Objective - - - -Cash + + + + Fuel A January - + + £0 Fuel A February - + + 6 0 Fuel A March • — + + 6 0 • Fuel B January + + * 0 FIGURE 4 .4 THE FUEL PURCHASING ACTIVITIES OF THE MODEL < Land Crop c o Maximum CU ct; u o Objective -Cash + Land A Period I - + Land A Period II - + * 0 Land A Period III - + Land A Control + FIGURE 4.5 THE LAND RENTAL ACTIVITIES OF THE MODEL 63 f u e l use. The e n t r i e s are therefore - 0 . 8 6 . Rented land requires a payment i n one or two months which are to be s p e c i f i e d by the farmer and supply land i n each of the land periods that are defined f o r use (see Figure 4.5). The c o e f f i c i e n t s f o r the rented land i s a vector of ones except f o r the e n t r i e s i n the objec t i v e and cash rows. A constraint i s provided to l i m i t the amount of land that may be rented. Except f o r labour and cash a l l other purchased inputs are treated the same i n the purchased input section of the model. Purchased inputs include such things as f e r t i l i z e r , sprays, s o i l t e s t s , custom work, twine and so on. Each of these inputs are included by the construction of a purchasing a c t i v i t y r e q u i r i n g cash i n one or more months s i m i l a r to the land r e n t a l a c t i v i t i e s and supply the input i n a s i n g l e row (see Figure 4.6). The e n t r i e s i n the cash rows are propor-t i o n a l to the amount of the input that i s purchased i n that month. The sum of the cash e n t r i e s i s the purchase p r i c e per unit of the input and appears i n the objec t i v e f u n c t i o n . The en t r i e s i n the input rows are ei t h e r negative ones or are a conversion f a c t o r to convert the input from the u n i t s i t i s normally purchased into those that i t i s used. The cash row f o r January has an o r i g i n a l endowment of cash i n the r i g h t hand s i d e . More cash may be acquired e i t h e r through the cash borrowing a c t i v i t i e s or through the sale of crops. The model has to generate enough cash i n the next month to repay any cash borrowed i n the previous month plus i n t e r e s t charges. Any cash not used i s c o l l e c t e d i n the transfer cash columns which add to the objective function the i n t e r e s t that would be earned by the money i n a savings account.- The money i n the transfers are the cash endowments for the succeeding months and at the end of the year (see Figure 4.7). For t r a c t o r s the model ca l c u l a t e s r e p a i r and maintenance costs as folbws. The model s e l e c t s a r e p a i r and maintenance cost c o e f f i c i e n t f o r each t r a c t o r based upon the t r a c t o r ' s age i n accumulated hours of use. Three c o e f f i c i e n t s from Table B.4 i n Appendix B are used f o r three 1,000 hour i n t e r v a l s of t r a c t o r use f o r each t r a c t o r . These c o e f f i c i e n t s are used i n the row "Tractor Repair %* i n Figure 4.8. The product of these co-e f f i c i e n t s times the accumulated hours of use i s m u l t i p l i e d with the l i s t p r i c e of the t r a c t o r which appears i n the objective function to come up with the r e p a i r and maintenance costs for a p a r t i c u l a r t r a c t o r i n a p a r t i c u l a r month. This cost accounting system was thought to be too large to use f o r each of the implements so i t was decided to use si n g l e c o e f f i c i e n t s for each implement. These c o e f f i c i e n t s are the hourly r e p a i r and maintenance costs i n d o l l a r s per hour which can be determined by multiplying the appropriate c o e f f i c i e n t from Table B.3 i n Appendix B against the l i s t price for any p a r t i c u l a r implement. These c o e f f i c i e n t s are used i n the machine operating a c t i v i t i e s as e n t r i e s i n the objective function and the relevant cash row. Buy Input 01 Buy Input 02 Buy Input 03 • • Maximum Objective _ _ -Cash Input 01 Input 02 Input 03 + + + - + - + - + *0 60 6 0 FIGURE 4.6 THE PURCHASED INPUT BUYING ACTIVITIES u u rd to 3 Li 3 Li Li rd c £! rd 3 rO CU 3 Li •"3 C Xi rd CU x: x: CL, w n rd rd x: x: U u w to rd rd U U ro O • Li • • X I XJ Maximum Li LI c c o o cu CU CQ CQ •J •J Objective - - + + Cash January - + +^ Cash February + - - + 60 Cash March + - 60 FIGURE 4.7 THE CASH BLOCK OF THE MODEL CO CO CO 0 Li c •C o EH EH Li LI LI Li L, CO CO CO Li CO CO in in 4H CO 4H 4H to to to to in CO CO c C C to C C ro ro rO CO C rrj rO Li Li Li o (0 Li Li EH EH EH U Li EH EH H LI L I LI Li a. a. X 0u • • X ro •H ro •rH ro •H ro Maximum X a a a a o o CO CO CO co o cc: Cd ! O b j e c t i v e -Cash F u e l + + + i O Repair Hours + + + - - - *0 C o n t r o l One + ^+ C o n t r o l Two + *+ C o n t r o l Three + T o t a l R epair % + + + -T r a c t o r Hours + + + 0 Horsepower - £ 0 10 Horsepower - £ 0 20 Horsepower - iSO FIGURE 4.8 THE TRACTER TRANSFER BLOCK TOGETHER WITH ROWS AND COLUMNS FOR REPAIR AND MAINTENANCE COST CALCULATIONS 72 4.3.3 Fixed Costs . Fixed Costs have to be forced i n t o the model so that cash flow p r e d i c t i o n i s accurate and l i m i t a t i o n s on a v a i l a b l e cash are recognized r e a l i s t i c a l l y . Fixed costs are aggregated by month and a vector of monthly fi x e d costs are forced i n t o the model with an equality c o n s t r a i n t , as i n Figure 4.9. The entry i n the objective function i s the sum of the fix e d costs of the twelve months. The entry f o r each month i s the sum of f i x e d costs incurred from a l l sources f o r that month. The f i x e d costs control row i s an equ a l i t y with ones i n the f i x e d cost column and i n the r i g h t hand side. Costs Fixed Maximum Objective -Cash January + s£ + Cash February + *0 Cash March + *0 • • • • • Fixed Costs Control 1.0 = 1.0 • FIGURE 4.9 SCHEMATA OF THE METHOD USED FOR FIXED COSTS 73 4 . 4 SUMMARY In t h i s chapter the p r a c t i c a l considerations of the empirical model put f o r t h i n the previous chapter have been explained i n d e t a i l . The empirical model documented i n t h i s chapter i s proposed as a model which s a t i s f i e s the requirements of the second sub-objective of the t h e s i s . The model may be examined i n l i g h t of the c h a r a c t e r i s t i c s that were deemed des i r a b l e i n the statement of o b j e c t i v e s . The data required by the model can nearly a l l be determined d i r e c t l y from a farm manager so that the model should be able to r e f l e c t the s p e c i f i c technological r e l a t i o n -ships and constraints of that farm. The model i s completely general with respect to input-output c o e f f i c i e n t s and time periods. This means that the model i s able to incorporate f l e x i b l e time constraints and thus overcome the c r i t i c a l pro-blem of the timeliness of the use of c a p i t a l inputs. Neglec-tin g the problem of converting data supplied by a farmer into a format usable by a l i n e a r programming solver, the model i s , therefore, adaptable to a wide range of farms. Furthermore, the model functions to s e l e c t a crop plan and production techniques that can be defined by varying the schedule of crop inputs i n the crop production a c t i v i t i e s . L o g i c a l l y the model i s sound. This i s shown i n Appendix F i n which the production, sales, resource use, and costs shown in the s o l u t i o n of a p a r t i c u l a r farm plan f o r a s p e c i f i c farm are compared with the production, sales, resource use, and costs c a l c u l a t e d a r i t h m e t i c a l l y from the crop plan selected by the model and u s i n g the i n t e r r e l a t i o n s h i p s proposed i n Chapter 3 and Chapter; 4. The r e a l e v a l u a t i o n of the model comes i n the a p p l i c a t i o n o f the model t o a r e a l farm ( t h i r d o b j e c t i v e ) which i s the s u b j e c t of the next c h a p t e r . f CHAPTER 5 APPLICATIONS OF THE EMPIRICAL MODEL TO A CASE FARM The subject matter of t h i s chapter i s presented to s a t i s f y the t h i r d o b j e c t i v e of the thesis which was to v e r i f y the model through i t s a p p l i c a t i o n to a s p e c i f i c farm. The v e r i f i c a t i o n of the model should provide answers to at l e a s t the following three questions: Can the model accurately simulate the production of vegetables on a r e a l farm, Can the model be used to produce an optimal farm plan that i s useful to the decision-maker on the farm? What sort of records can be projected with the model? Before addressing these questions the sp e c i a l c h a r a c t e r i -s t i c s of the case farm are discussed i n the context of how t y p i c a l of vegetable farms i s the case farm. This i s necessary as the s p e c i a l circumstances of the case farm may provide d i f f e r e n t answers to the three questions than would normally be obtained so an e f f o r t i s made to r e l a t e the types of s i t u a t i o n s that may be found and which i t would be d i f f i c u l t to cope with using the model as i t i s applied to the case farm. In the second section of the chapter the model as i t was b u i l t f or the case farm i s described. In the t h i r d section an attempt i s made to provide an answer to the f i r s t question. The procedure used to simulate the 1974 farm plan i s given. The r e s u l t s of comparing the 1974 CANFARM records with s i m i l a r records produced from the sol u t i o n of the farm planning model used i n simulation mode i s provided although an evaluation of the comparison i s ne c e s s a r i l y subjective. 76 In the f i n a l section of the chapter the results of using the model to produce five optimal farm plans for varying market conditions and yields are summarized and compared with the plan selected without using the model. This i s an attempt to show how the model may be used and the value of the infor-mation available from the model. An appropriate form for the farm report and the type of records that should be given is discussed with a complete set of records for one of the farm plans in Appendix G . , 77 5.1 SELECTION OF THE CASE FARM The case farm was selected soon a f t e r work on the thesis was i n i t i a t e d . The p a r t i c u l a r problems and structure of the case farm has been kept i n mind throughout the processes of problem i d e n t i f i c a t i o n and the development of the empirical model. Knowledge of the problems of vegetable farms was acquired through meetings with other farmers and persons d i r e c t l y involved with vegetable production at seminars and f i e l d t r i p s . The problems of other farms have modified the approach taken to the case farm but the case farm has been c r i t i c a l to the perception of many parts of the empirical model. To a large extent t h i s can be j u s t i f i e d by the s p e c i a l c h a r a c t e r i s t i c s of the case farm. At the same time, an under-standing of the s p e c i a l features of the case farm i s necessary to appreciate d i f f i c u l t i e s that may be encountered i n an attempt to apply the model to a second farm. The following i s a d i s -cussion of the c r i t i c a l features of the case farm and how they have influenced the empirical model. A d e t a i l e d account of the actual resources a v a i l a b l e , the a c t i v i t i e s considered and the tech n i c a l c o e f f i c i e n t s used i n the empirical model i s given i n a paper produced separately. The s p e c i a l c h a r a c t e r i s t i c s * o£: the case farm that have influenced the model i n a p o s i t i v e manner are associated with the s i z e and complexity of the case farm, the large number of crops of several types that are considered, the wide range of machinery used, the d e t a i l e d CANFARM records that have been maintained over the years, and the experience and influence of * These are documented separately i n "An Optimal Farm Plan f o r a Vegetable Farm." 78 of the farm operator within the vegetable industry as well as on his own farm. The complexity of the case farm i s mainly due to the large number of d i f f e r e n t crops grown. At present, the farm i s producing both early and l a t e potatoes, the processing crops of beans and e a r l y and l a t e peas, the b i e n n i a l seed crops, cabbage, turnips and sugar beets, barley and two annual berry crops. The large range of crops involve the model i n the most important vegetable, potatoes, i n annuals, b i e n n i a l and perennials, i n marketing contracts, quotas and u n r e s t r i c t e d sales, i n crops req u i r i n g v a s t l y d i f f e r e n t r e l a t i v e l e v e l s of such important inputs as labour, machinery, and purchased i n -puts and i n various degrees of complexity i n the manner i n which each input i s u t i l i z e d . The usual vegetable farm c h a r a c t e r i s t i c a l l y produces only two or three d i f f e r e n t vege-ta b l e s . There are some elements of other farms missing of course. Only one planting date i s considered f o r each crop. The farm i s completely made up of a mineral s o i l so c u l t u r a l p ractices necessitated by muck s o i l s are not attempted. The perennial crops are s t i l l at the experimental stage so they are treated as annuals i n many respects. F i n a l l y , despite the large number of crops produced, many important vegetables are not produced on the case farm such as l e t t u c e , onions, carrots and tomatoes. The s i z e of the case farm and the number of crops that are produced make i t necessary f o r the operator to maintain and operate a large and varie d complement of machinery. Seven 79 t r a c t o r s are operated which range i n s i z e from 30 HP to 140 HP and i n age from 2 8 years to 1 year. The farm operates several trucks, two combines one of which i s f o r potatoes the other f o r seed crops, several c u l t i v a t o r s and various other types of t i l l a g e implements, sprayers, f e r t i l i z e r spreaders, seeders and so on. Two of the implements are s e l f powered and a l l vary greatly i n the demands they make on power, labour and with respect to f i e l d e f f i c i e n c y , capacity and other machine c h a r a c t e r i s t i c s . A shortcoming of the case farm i n t h i s area i s the dearth of phy s i c a l records maintained. The extensive use of the CANFARM records perhaps has induced the operator to not worry about a physical record system. In the CANFARM records much of the information i s given i n the form of cost so prices and units used are concealed making i t d i f f i c u l t to make even inter-year comparisons based s o l e l y on the records a v a i l a b l e . The case farm does not have a cash constraint although i t would be easy to introduce such a c o n s t r a i n t by bounding the cash borrowing a c t i v i t i e s . The case farmer does not do custom operations so t h i s type of a l t e r n a t i v e a c t i v i t y has not been b u i l t . The farm family i s the source of most of the labour required. Although temporary labour i s a fa c t o r , permanent hired labour i s not, so a h i r i n g a c t i v i t y f o r labour on a weekly or monthly basis i s not included. To some extent the three classes of labour included i n the t h e o r e t i c a l model are not r e a l l y needed on the case farm and the i n c l u s i o n of the three classes i s a concession to the needs of other farms. The case farm also does not have an animal production enter-p r i s e competing f o r the resources used on the crops so t h i s type of operation has not been b u i l t . Some vegetable producers produce only one vegetable and the s p e c i a l trade-offs they encounter has not been evaluated. 81 5.2 PICTURE OF THE EMPIRICAL MODEL In t h i s section of the thesis an attempt i s made to summarize the s a l i e n t parts of the input data and show how i t was used to make the empirical model. Family and hired labour i s a v a i l a b l e i n a l l periods with a d d i t i o n a l family labour being a v a i l a b l e i n c e r t a i n periods of the year. Labour h i r i n g a c t i v i t i e s were included f o r a l l work periods. Labour u t i l i z e d by the machine operating a c t i v i t i e s and by the crop a c t i v i t i e s i s the labour type 'either labour' i n every case. This was done to ensure that labour would not be a c o n s t r a i n t . Three types of land i n two time periods f o r each were included i n the model. This was to keep track of the crops planted on two separate f i e l d s and a section of rented land, although d i f f e r e n t y i e l d s are recognized only on the rented land. Two time periods are needed to accommodate the p o s s i b i l i t y of double cropping. There are a t o t a l of 22 purchased inputs a l l of which were paid f o r i n one period only. Interest rates f o r the opportunity cost of operating cash are approximately 10% and 8.75%. annually f o r borrowed cash and transferred cash respec-t i v e l y . I t was presumed that borrowed cash would be withdrawn from term deposits i n banks and transferred cash would be put into a savings account. Fixed costs f o r the model are calcula t e d d i r e c t l y from the 1974 CANFARM records. One of the most important sections of the model i s the tr a c t o r s e l e c t i o n block. There are seven t r a c t o r s on the farm. 82 The two largest t r a c t o r s are too heavy to do a l o t of the operations done by the smaller tractors so t r a c t o r t r a n s f e r s for these t r a c t o r s are not b u i l t f or the lower leve l s of horsepower output. A t o t a l of 294 separate machine operating a c t i v i t i e s were b u i l t f o r the operation of 29 pieces "of machinery. Many of these a c t i v i t i e s are b u i l t f or more than one job time con-s t r a i n t and each job may require several columns. For three operations s p e c i f i c t r a c t o r s are required so method one i n Figure 3.2 was used. This was necessitated by considerations of wheel width and the s p e c i a l operating circumstances of the potato combine and the rotovator. For a l l the other imple-ments the t r a c t o r s e l e c t i o n block (method three i n Figure 3.4) was used. , Separate a c t i v i t i e s were made for the growing of each crop on each land c l a s s i f i c a t i o n except for seed crops and the berry crops which were produced on only one land c l a s s i f i c a t i o n . Separate s e l l i n g a c t i v i t i e s were b u i l t f o r the sales of each crop on each market. Constraints are imposed, on s e l l i n g a c t i v i t i e s to represent market c o n s t r a i n t s . A l l the c o e f f i c i e n t s of the model were ei t h e r supplied d i r e c t l y by the farm operator from memory with the aid of his CANFARM records and b i l l s of sale or they were reviewed by him. The parameters.for machine costs and power requirements which he disagreed with were al t e r e d to accord with his experience. Parameters for f u e l consumption and t r a c t o r r e p a i r 83 costs were not a l t e r e d . The t r a c t o r s e l e c t i o n part of the model occupies 320 rows and 351 columns. 162 rows and 287 columns are used to c a l c u -l a t e t r a c t o r r e p a i r and maintenance c o s t s . The e n t i r e s i z e of the matrix i s 963 rows by 1,150 columns. The matrix was solved using IBM's l i n e a r programming package MPSX using the 'macro' command 'primal'. Solving the problem required 678 pages of temporary f i l e s and 98 seconds of computer time. The matrix was modified to run i n simulation mode so that the farm's 1974 farm records could be used to v e r i f y the model. Solution to the revised problem required e s s e n t i a l l y the same computer parameters. Figure 5.1 gives a r e v i s e d version of Figure 3.5. The case farm i s depicted as a flow diagram with numbers i n brackets to indicate the number of rows and columns r e s p e c t i v e l y required to simulate each section of the farm. Owned Resources Land Labour (34.33) Tractors (360.287) jlmpLementsj (199,0) Cash (12,12) Renting Resource A c t i v i t i e s -. v » Land 7*-> ( 3 - D Li Purchasedl —> Inputs f l (22 T22) I 1 Labour 3fS,fiFi), Fuel (24,24) Horsepower Transfers {iorsepoweq (122,351) t Machine Operating A c t i v i t i e s Operation (120,294) Cash T (o7i2) Cropping A c t i v i t i e s ^Cropping A c t i v i -t i e s (0,23) Legend: Cash Flow' Resource and Product Flow FIGURE 5.1 Crop S e l l i n g A c t i v i t i e s Crop S e l -ing (14,15) co FLOW DIAGRAM SHOWING THE CLASSIFICATION OF RESOURCES AND TIME PERIODS FOR EACH RESOURCE AND USE OF RESOURCES ON THE CASE FARM 85 5.3 EMPIRICAL RESULTS OF MODEL VERIFICATION 5.3.1 Procedure for Simulation 1974 Farm Plan To v e r i f y the c o e f f i c i e n t s and r e l i a b i l i t y of the model i t was necessary to attempt to simulate the actual farm operations and r e s u l t s obtained i n 1974 which are summarized i n Table 5.1 To do t h i s several major modifications of the model were made. Actual p r i c e s and y i e l d s achieved i n 1974 were ca l c u l a t e d from the 1974 income statement. The y i e l d s obtained were alt e r e d f o r each crop grown. Crops not produced were dropped as was the resource 'rented land'. Where market and r i s k c onstraints were v i o l a t e d i n 1974 due to the d i f f e r e n t s i t u a t i o n and markets, the constraints were dropped. A single s e l l i n g a c t i v i t y was constructed for each product at the average p r i c e per unit of the crop that was received i n that year. The p r i c e of the products were proportioned i n t o the months i n which the cash f o r the sales of those crops were a c t u a l l y received with crops i n inventory increasing the value of the cash row f o r the 'thirteenth' month. Constraints were introduced to bound each crop production a c t i v i t y to the l e v e l of acres that were produced i n 1974 with equality c o n s t r a i n t s . In t h i s way crop production, crop sales and inventory changes should be almost exactly simulated. The di f f e r e n c e between actual r e s u l t s and the CANFARM records should be due e n t i r e l y to the opportunity cost of cash that the model c a l c u l a t e s and rounding e r r o r s i n the computer. The f i r s t of these sources of d i f f e r e n c e was eliminated by reducing the i n t e r e s t rate to zero for borrowed cash and eliminating the t r a n s f e r cash columns altogether. 86 TABLE 5.1 INCOME STATEMENT ACTUAL 1974 FARM PLAN Crop Sales Barley F i e l d Beans F i e l d Peas Potatoes Strawberries Sugar Beet Seed L e a f / F r u i t Vegetable Seed (Turnip) Cabbage Seed Pea Vines Total Cash $ 7,769 28,238 13,287 16,496 500 6,755 405 3,529 2,370 79,348 Accrual $ 7,643 28,238 13,287 58,800 500 6,815 3,522 6,434 2,370 127,735 Expenses Seed Grain Corn 41 41 F i e l d Beans 105 105 Roots & Tubers 28 28 Potatoes 6,612 6,612 F r u i t Bushes 900 Herbicides 4,170 4,170 Chemical F e r t i l i z e r 13,907 13,907 Lime 388 388 Gen.Crop S & S 221 221 Seed Treating 106 106 Baler Twine 1,044 1,044 Binder Twine 2 2 Purple Gasoline 980 980 •Car Gas 1,058 1,058 Diesel Fuel 382 382 •Oxygen 90 90 Tractor R & M 662 662 •Truck R & M 504 504 •Automobile R & M 1,364 1,364 Harvest Equip. R & M 7 7 Gen. Farm Equip. R & M 2,438 2,438 •Building R & M 4,528 4,528 •Yard R & M 114 114 •Structures R & M 367 367 •Tools 1 1 Part Time Labour 3,346 3,346 •Custom Work 63 63 •General Expenses 99 99 •Handling Charge 120 120 87 TABLE 5.1 continued Cash Accrual $ $ Expenses continued •Freight & Trucking 288 288 •Interest 111 111 •Insurance 857 857 •Equip. & Machine Insurance 22 22 •Car Insurance 406 406 •Truck Insurance 691 691 •Telephone 118 118 •H y d r o / E l e c t r i c i t y 692 692 •Property Tax 6,119 6,119 •Administration Costs 45 45 •Fees & Subscriptions 45 45 •Legal Service 55 55 •Other Prof. Services 105 105 •Office Supplies 18 18 •Miscellaneous Expense 78 78 Total 53,295 52,395 •Considered a Fixed Expense, i.e . independent of the l e v e l of crop production for each crop. Source: 1974 version 1 CANFARM records. 88 5.3.2 R e s u l t s f o r V e r i f i c a t i o n The model run i n s i m u l a t i o n mode was f e a s i b l e ; machinery and t r a c t o r time was i n s l a c k i n a l l time p e r i o d s . Labour was o n l y f u l l y u t i l i z e d i n the f o u r t h p e r i o d i n May and i n the l a s t t h r e e p e r i o d s i n September i n which h i r e d l a b o u r was r e q u i r e d . The f e a s i b i l i t y of the farm p l a n does not imply t h a t the time c o e f f i c i e n t s and c o n s t r a i n t s are c o r r e c t but i t does imply t h a t m a t r i x time c o e f f i c i e n t s a r e not e x c e p t i o n a l l y l a r g e r i n the model than i n f a c t and t h a t time c o n s t r a i n t s are not e x c e p t i o n -a l l y s m a l l e r . The income statement f o r the s i m u l a t e d 1974 farm p l a n i s g i v e n i n T a b l e 5.2 T o t a l v a r i a b l e c o s t s were und e r e s t i m a t e d by 4.84% (see T a b l e 5.3). T h i s number i s due i n p a r t t o a g r e a t many d i f f e r e n c e s between a c t u a l 1974 c o s t s and p r e d i c t e d c o s t s by the model c a n c e l l i n g each o t h e r o u t . The e x t e n t t o which the u n d e r e s t i m a t i o n i s a c c e p t a b l e must be judged comparing how the v a l u e f o r t o t a l v a r i a b l e c o s t s o r i g i n a t e s both i n the model and i n the CANFARM r e c o r d s . Purchased i n p u t s c o s t s were o v e r e s t i m a t e d by 6.34%. There a r e s e v e r a l s o u r c e s o f the d i f f e r e n c e . The model spends almost $2,000 more on f e r t i l i z e r , $900 l e s s on h e r b i c i d e , $2,000 more on o t h e r c h e m i c a l s . Other c h e m i c a l s i s one of s e v e r a l items f o r which i t i s d i f f i c u l t t o match the CANFARM names w i t h those used i n the model. The CANFARM r e c o r d system uses a l a r g e number of package names. In e n t e r i n g a purchased i n p u t i n the r e c o r d system the user has to i d e n t i f y the items by the CANFARM names. I t may be more c o n v e n i e n t to e n t e r most p e s t i c i d e s under 89 TABLE 5.2 Crops Sales Barley INCOME STATEMENT 1974 SIMULATED FARM PLAN Cash Accrual 7,769 7,643 F i e l d Beans 28,238 28,238 F i e l d Peas 13,287 13,287 Potatoes 16,496 58,800 Strawberries 500 500 Sugar Beet Seed 6,755 6,815 Le a f / F r u i t Vegetable Seed (Turnip) - 3,522 Cabbage Seed ~ " Pea Vines w/ J w* t_ £_ 3,529 6,434 2,370 2,370 Total 78,944 127,609 Expenses Purchased Inputs 87 Twine 87 Premerge 1,021 1,021 Pea F e r t i l i z e r 675 675 Potash 1,741 1,741 Eptam 2,216 2,216 F e r t i l i z e r 0-0-22 489 489 F e r t i l i z e r 11-55-0 3,315 3,315 Benlate 461 461 Beet F e r t i l i z e r 2,000 2,000 Turnip F e r t i l i z e r 459 459 Bees 230 230 Cabbage F e r t i l i z e r 726 726 Raspberry F e r t i l i z e r - — Strawberry F e r t i l i z e r 297 297 Barley Seed 266 266 Barley F e r t i l i z e r 570 570 Early Potato Seed - — Potato F e r t i l i z e r 5,610 5,610 Late Potato Seed 6,500 6,500 Bl i g h t 42 42 Sprout I n h i b i t o r 1,050 1,050 Monitor I n s e c t i c i d e 556 556 Total Purchased Inputs 28,312 28,312 Purple Gasoline 504 504 Diesel Fuel 525 525 Tractor R & M 441 441 Gen.. Farm Equip. R & M 1,185 1,185 Part Time Labour 2,057 2,057 Interest on Operating C a p i t a l - — Total Variable Inputs 33,023 33,023 90 TABLE 5.2 c o n t i n u e d Cash A c c r u a l F i x e d Expenses Car Gas 1,058 1,058 Oxygen 90 90 Truck R & M 504 504 Automobile R & M> 1,364 1,364 B u i l d i n g R & M . 4,528 4,528 Yard R & M 114 114 S t r u c t u r e s R & M 367 367 T o o l s 1 1 Custom Work 63 63 General Expenses 99 99 H a n d l i n g Charge ,' 120 120 F r e i g h t & T r u c k i n g 288 288 I n t e r e s t 111 111 Insurance 857 857 Equi p . & Machine Insurance 22 22 Car I n surance , 406 406 Truck Insurance 691 691 Telephone 118 118 H y d r o / E l e c t r i c i t y 695 695 P r o p e r t y Tax 6,119 6,119 A d m i n i s t r a t i o n C o s t s 45 45 Fees & S u b s c r i p t i o n s 45 45 L e g a l S e r v i c e s 55 55 Other P r o f . S e r v i c e s 105 105 O f f i c e S u p p l i e s 18 18 M i s c e l l a n e o u s Expense 78 78 T o t a l F i x e d Expenses 17,961 17,961 T o t a l Expenses 50,984 50,984 Income l e s s Expenses 27,960 76,625 Source: S o l u t i o n to farm p l a n n i n g model i n s i m u l a t i o n mode and CANFARM r e c o r d s . TABLE 5.3 A COMPARISON OF ACTUAL 1974 COSTS WITH MAJOR ITEMS OF VARIABLE COSTS IN THE SIMULATED FARM PLAN Item Difference as % CANFARM D i f f e r - of CANFARM Model Records ence Records —T~ $ $ % T o t a l Variable Costs 33,023 34,439 1,415 - 4.10 Purchased Inputs 28,312 26,624 1,688 6.34 Chemical F e r t i l i z e r •-- 15,883 13,907 .1,976 14.21 Herbicide 3,237 4,170 - 933 - 22.37 •Other P e s t i c i d e 2,109 - 2,109 Seed 6,766 6,786 - 20 - 0.29 230 - 230 •Bees Baler Twine 87 1,046 - 959 - 91.68 •*Lime 388 - 388 221 - 221 106 - 106 ••Gen. Crop S & S ••Seed Treating Fuel 1,029 1,362 - 333 - 24.38 Purple Gasoline 504 980 Diesel Fuel 525 382 Repair & Maintenance Costs Tractors 441 662 - 221 - 33.38 Gen. Equip. R & M • . 1,185 2,445 -1,250 - 51.49 Part Time Labour Potato Harvest 2,057 2,027 - 30 1.48 Other - 1,319 -1,319 -100.00 •Items which are i n the model but do not obviously correspond to items i n CANFARM records. ••Items which are i n the CANFARM records but do not obviously correspond to elements i n the model Source: CANFARM records (Appendix G) and farm records created from solution to the matrix (Appendix I ) . 92 the name • h e r b i c i d e 1 f o r example. Some of the names used are a l s o simply d i f f e r e n t from those t h a t the farmer would n o r m a l l y use to d i s c u s s the i n p u t . F o r example, i t appears t o p r o b a b l y be the case t h a t bees are e n t e r e d under the heading 'Gen. Crop S & S'. I n v e n t o r i e s a l s o account f o r some o f the d i f f e r e n c e as the CANFARM r e c o r d s are r e c o r d e d on a c a s h b a s i s . The farm o p e r a t o r r e p o r t e d t h a t he d i d i n f a c t c a r r y an i n v e n -t o r y of f e r t i l i z e r and c h e m i c a l s over from 1973 worth around $2,000 but d i d not c a r r y any i n v e n t o r y i n t o 1975. Lime, on the o t h e r hand, i s a purchased i n p u t t h a t was l e f t out through an o v e r s i g h t . In g e n e r a l then although t h e r e are s e v e r a l d i f f e r e n c e s the most major d i f f e r e n c e s can be accounted f o r and i t i s f e l t t h a t the models i n p u t purchases are p r o b a b l y more a c c u r a t e on an a c c r u a l b a s i s than those r e f l e c t e d i n the farm r e c o r d s . F u e l consumption was u n d e r e s t i m a t e d by 24%. There are s e v e r a l r e a s o n s to expect t h a t the model may u n d e r e s t i m a t e the t o t a l f u e l b i l l . The t r a c t o r s e l e c t i o n b l o c k of the model was working so t h a t the t r a c t o r s are s c h e d u l e d to minimize f u e l and r e p a i r and maintenance c o s t s g i v e n the l e v e l o f c r o p s s e l e c t e d . The model was a b l e to perform almost a l l o p e r a t i o n s w i t h o n l y t h r e e of the seven t r a c t o r s . The farm p l a n r e p r e -s e n t s the u s u a l u t i l i z a t i o n o f machinery p r o v i d i n g e v e n t s f o l l o w t h e i r normal c o u r s e . I t i s to be expected however t h a t over the c o u r s e of the y e a r something i s bound to happen to cause a d e v i a t i o n from the normal c o u r s e o f events i n some p a r t of the farm o p e r a t i o n . I t seems l i k e l y t h a t such a s i t u a t i o n 93 would l i k e l y cause more f u e l to be used rather than l e s s . Fuel consumed during transporting implements to the f i e l d and in the trucks on farm business i s also not accounted f o r . The r e s u l t s f o r t r a c t o r r e p a i r and maintenance costs are quite s i m i l a r . The model underestimates t r a c t o r r e p a i r and maintenance costs by 33%. Part of the reason f o r the d i f f e r -ence must l i e i n the f a c t that the t r a c t o r s e l e c t i o n part of the model was operating and part of the answer must be that i t i s not possible to follow the farm plan at least part of the year. The lumpiness of r e p a i r and maintenance costs must also be kept i n mind. 1974 was i n f a c t an exceptionally high year f o r repair and maintenance c o s t s . Tractors and implements together i n 1974 required $3,000 to r e p a i r and maintain but only $1,428 i n the preceding year. In 1974 implement r e p a i r and maintenance costs were $2,445 but they only amounted to $1,853 i n 1975. The estimate made i s therefore probably an underestimate over the long term for implements and t r a c t o r s but not of the magnitude 33%. The estimate for implements i s probably more of an underestimate than the estimate f o r t r a c t o r s because the age of the operator's equipment has not been taken int o account. The comparison with the CANFARM r e s u l t s probably overstates the d i f f e r e n c e i n the long term between the actual r e p a i r and maintenance costs and predicted costs. The f i n a l v a r i a b le cost i s part time labour and r e s u l t s f o r part time labour are the most i n t e r e s t i n g . In the actual farm plan part time labour was used i n the potato, peas, beans, berry and barley crops as well as i n general farm 94 maintenance. In the model on the other hand hired labour was only required f o r the potato harvest. The d i f f e r e n c e between the predicted and the actual amount f o r the potato harvest. The d i f f e r e n c e between the predicted and the actual amount f o r the potato enterprise i s l e s s than 1%%. This r e s u l t suggests very strongly that not only i s the labour h i r i n g a c t i v i t i e s accurate but the time c o e f f i c i e n t s f o r labour and machinery and the co n s t r a i n t s on these resources are very accurate at lea s t i n the month of September. The f a c t that part time labour was also required on several other crops i s also i n t e r e s t i n g . When asked about t h i s labour the farm operator stated that i t was necessary to hire part time labour f o r harvest operations on these crops i n 1974 although t h i s would not normally be the case. Part of the reason the f u e l and re p a i r and maintenance b i l l was underestimated might be due to the unusual harvest circumstances. By the nature of the v a l i d a t i o n the r e s u l t s could not i n any circumstances be described as f i n a l but they are very p o s i t i v e on the whole. Several anomolies appeared i n the purchased inputs which could, f o r the most part, be explained i n terms of inventories and the problem of i d e n t i f y i n g items recorded i n the CANFARM records with those used by the farm operator. Labour costs were predicted within 1J#» i n the month of September which together with the f e a s i b i l i t y of the farm plan suggests that time c o e f f i c i e n t s are reasonably accurate. Fuel and r e p a i r and maintenance costs were underestimated by up to 50% but there are several reasons f o r thinking the model 9 5 would underestimate these c o s t s . I t i s probably the case that these c o s t estimates are s y s t e m a t i c a l l y lower than should be but not by an amount s u f f i c i e n t l y l a r g e to i n f l u e n c e crop s e l e c t i o n . Based on the r e s u l t s i t i s f e l t t hat the model i s s u f f i c i e n t l y accurate to use i t to suggest an o p t i m a l farm pl a n which i s the subject of the next s e c t i o n of t h i s chapter. 96 5.4 RESULTS OF USING THE MODEL TO SERVE THE OPTIMAL FARM PLAN Because of the changing market conditions some crop plans that were f e a s i b l e i n 1974 are no longer p o s s i b l e . The farm operator f e e l s that he may wish to reduce the amount of land i n potatoes and peas because of the p o s s i b i l i t y of lower p r i c e s for those crops. In e f f e c t he f e e l s the demand and/or supply curves f o r these crops may have s h i f t e d . At the same time he f e e l s that he may be able to obtain higher y i e l d s f o r beans, barley and sugar beets. The farm operator i s also considering the renting of 100 acres f o r the production of barley. I t was thought i n i t i a l l y that three d i f f e r e n t optimal plans might be prepared with increasing y i e l d s for beans, sugar beet seed and barley. This course of action was changed a f t e r seeing the f i r s t optimal farm plan (see Table 5.4 and Appendix G). In the optimal plan 86 acres of land was rented. A l l crops with exception of barley came i n at the upper l i m i t of t h e i r respective market, r i s k or r o t a t i o n c o n s t r a i n t . Barley, the only crop without an upper l i m i t because of the market r i s k or r o t a t i o n c o n s t raint, was selected at a l e v e l of 108 acres where a machine c o n s t r a i n t came i n t o e f f e c t . For a l l other implements machine time was not an important c o n s t r a i n t . Several implements were f u l l y u t i l i z e d i n some time periods but p o s s i b i l i t i e s existed to substitute implement time i n an adjacent time period so the model was not forced to a l t e r the farm plan. The implements which were f u l l y u t i l i z e d 97 TABLE 5.4 INCOME STATEMENT 1976 OPTIMAL 'PLAN A * Crop Sales Straw Barley F i e l d Beans F i e l d Peas Potatoes Strawberries Sugar Beet Seed L e a f / F r u i t Vegetable Seed (Turnip) Cabbage Seed Pea Vines Raspberries Total Accrual $ 10,800 23,760 16,200 25,920 110,380 6,000 18,240 4,500 34,000 2,925 2,800 255,525 Expenses Rent Purchased Inputs Twine Premerge Pea F e r t i l i z e r Potash Eptam F e r t i l i z e r 0-0-22 F e r t i l i z e r 11-55-0 Benlate Beet F e r t i l i z e r Turnip F e r t i l i z e r Bees Cabbage F e r t i l i z e r Raspberry F e r t i l i z e r Strawberry F e r t i l i z e r Barley Seed Barley F e r t i l i z e r E a r l y Potato Seed Potato F e r t i l i z e r Late Potato Seed B l i g h t Sprout I n h i b i t o r Monitor I n s e c t i c i d e 7,740 87 747 675 2,348 2,274 463 1,912 266 2,000 573 400 1,453 124 297 756 1,620 2,240 9,312 8,190 53 1,323 700 To t a l Purchased Inputs 37,814 98 TABLE 5.4 continued Accrual * Expenses continued Purple Gasoline 977 Diesel Fuel 934 T r a c t o r R & M 678 Gen. Farm Equip. R & M 1,906 Part Time Labour 4,478 Interest on Operating C a p i t a l - 662 T o t a l Variable Inputs 53,864 Fixed Expenses Car Gas 1,058 Oxygen 90 Truck R & M 504 Automobile R & M 1,364 B u i l d i n g R & M 4,528 Yard R & M 114 Structures R :& M 367 Tools 1 Custom Work 63 General Expenses 99 Handling Charge 120 Freight & Trucking 288 Interest 111 Insurance 857 Equip. & Machine Insurance 22 Car Insurance 406 Truck Insurance 691 Telephone 118 H y d r o . E l e c t r i c i t y 695 Property Tax 6,119 Administration Costs 45 Fees & Subscription 45 Legal Services 55 Other Prof. Services 105 O f f i c e Supplies 18 Miscellaneous Expense 78 T o t a l Fixed Expenses 17,761 Total Expenses 71,825 Income le s s Expenses 183,700 Source: Solution' to farm planning model i n optimization mode and CANFARM records. 99 i n some time periods were the pulvi-mulcher throughout A p r i l , the power mulcher i n March, the plow i n the t h i r d week of A p r i l , the potato combine i n two weeks i n September, and the d i s c i n two weeks i n A p r i l . Tractor time was not a l i m i t i n g f a c t o r at any power l e v e l because of the p o s s i b i l i t i e s f o r s u b s t i t u t i o n . Tractor time was f u l l y u t i l i z e d f o r the 1370 Case throughout A p r i l and f o r the smaller t r a c t o r s at odd periods i n the year. The shadow p r i c e on these resources remained very low. Labour was not c r i t i c a l i n any time period because of the p o s s i b i l i t y of s u b s t i t u t i n g hired labour. Hired labour was required i n May, the f i r s t week i n August, and with potato harvest i n September. Consideration was next given to which crops i t would be most p r o f i t a b l e to expand above the r i s k and/or market con-s t r a i n t . This was r e a l l y an attempt to deal with the question brought up by the farmer about which crops i t would be most p r o f i t a b l e to substitute f o r peas and potatoes f o r which market conditions were becoming more uncertain. The market and/or r i s k c o n straint f o r beans and sugar beets was eased so the e f f e c t of incorporating more of these crops could be evaluated. The r e s u l t s are summarized i n Table 5.7 i n Plans B, C and D. Plan A, or the 'base plan', i s the f i r s t optimal plan prepared without easing r i s k and/or market c o n s t r a i n t s The e f f e c t of the easing of the r i s k and/or marketing constraint was to substitute these crops f o r barley. There was no e f f e c t on the acreages of peas and potatoes. An upper 100 bound on the l e v e l of the sugar beet crop also appears as t h i s crop competes f o r land with potatoes. I t i s i n t e r e s t i n g to note that with reduction of the l e v e l of barley production none of the resources f o r t r a c t o r or implement time i s c r i t i c a l ; machinery i s not a c o n s t r a i n t . The f i v e acres of turnips are dropped from the farm plan however. To f i n a l l y get at the question of whether increased y i e l d s might lead to a s u b s t i t u t i o n f o r potatoes or peas, two more plans were prepared with the y i e l d s increased by 12.5% and 25% f o r barley, beans and sugar beet seed. Risk and market constraints were set at the l e v e l of those i n Plan C to give the computer considerable space to bring i n more barley and possibly sugar beets at the expense of pease and/or potatoes. The r e s u l t s of these changes are Plan E and Plan F i n Table 5.5. It can be seen that even i n t h i s case no s u b s t i t u t i o n i s made for potatoes or peas. The conclusion i s , therefore, that i n the circumstances considered no substituion should take place i n v o l v i n g e i t h e r barley, beans or sugar beet seed for e i t h e r potatoes or peas. There i s some c o n f l i c t between the seed crops and l a t e potatoes when both of these are at t h e i r upper l i m i t s imposed by the marketing, r i s k and r o t a t i o n constraints on 'Land A' but t h i s i s resolved i n favour of potatoes even at 25% higher y i e l d s f o r sugar beet seed or any equivalent change i n pr i c e s and y i e l d s f o r sugar beets and potatoes. If i t i s possible to increase the acreage of any of the crops above the l e v e l s i n Plan A i n Table 5.5 then c o n f l i c t s TABLE 5.5 A COMPARISON OF ALTERNATIVE •OPTIMAL•PLANS Simulation of Plan Selected Base Relaxed Risk and Increased (Withou Crop Plan Market Constraints Yields Model) A B C D E F G acres acres acres acres acres acres acres Bean Constraint 30 45 60 75 60 60 N.A. Sugar Beet Constraint 20 30 40 50 40 40 N.A. Y i e l d Index 100% 100% 100% 100% 112.5% 125% 100% Late Potatoes 63 63 63 63 63 63 50 Earl y Potatoes 20 20 20 20 20 20 15 Late Peas 15 15 15 15 15 15 30 Earl y Peas 30 30 30 30 30 30 Beans 30 45 60 75 60 60 30 Barley 108 97 78 63 78 78 40 Sugar Beets 20 30 39 39 39 39 30 Turnip 5 5 0 0 0 0 4 Cabbage 20 20 20 20 20 20 20 Raspberries 2 2 2 2 2 2 2 Strawberries 5 5 5 5 5 5 5 To t a l Harvested 318 332 332 332 332 332 226 Net Income $ 183,700 189,184 192,025 193,072 203,058 214,524 157,788 Net Income as % 104.5% 105.1% 86% of Base Plan 100% 103% N.A. N.A. Source: Solutions to the farm planning model i n optimal mode. O 102 should be resolved i n the d i r e c t i o n of a decrease i n the pro-duction of bar l e y . Some conclusions can also be made i n comparing the optimal farm plans with the plan that the operator selected f o r 1976 without the use of the model (Plan G i n Table 5.5). The l e v e l of income i n Plan G i s 86% the l e v e l of income i n Plan A. Some d i s c r e t i o n i s required i n comparing these two plans as both involve the use of the farm planning model. The question a r i s e s whether the dif f e r e n c e between the optimal 1976 farm plan and the 1976 farm plan selected without the model are s i g n i f i c a n t enough to j u s t i f y the construction and use of a l i n e a r programming model. Providing the r e l i a b i l i t y of the model i s acceptable I bel i e v e the answer i s yes. The d i f f e r -ence i n net income between Plan A and Plan G i s $25,712. Furthermore, the model d e f i n i t e l y shows a course of action on two a l t e r n a t i v e s the farm operator i s considering: i t would be p r o f i t a b l e to rent the land a v a i l a b l e and produce barley but i t would not be p r o f i t a b l e to reduce his production of potatoes or peas. CHAPTER 6 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY 6 . 1 SUMMARY OF THE THESIS The o v e r a l l objective of the thesis was to construct a farm planning model that would be of value to vegetable pro-ducers i n making planning d e c i s i o n s . More s p e c i f i c a l l y , the objective was to b u i l d a model that would in d i c a t e the most appropriate s e l e c t i o n of crops and production methods. This objective was subdivided i n t o four s e c t i o n s : i d e n t i f y the sp e c i a l problems of vegetable producers that have to be inco r -porated i n t o the model, construct the model, v a l i d a t e the model through i t s a p p l i c a t i o n to a case farm, and use the model to produce an optimal farm plan. It was pointed out that the vegetable industry i s extremely d i v e r s e . The large v a r i e t y of vegetables produced, methods of production and regions i n Canada meant that the model had to be a very general crop budgeting model. The d i v e r s i t y of the industry also i s probably responsible f o r the lack of basic ' t e s t i n g ' to demonstrate the a f f e c t of changes i n the use of various inputs on y i e l d s . A further r e s u l t of the d i v e r s i t y of the industry i s that a great many vegetable producers become s p e c i a l i s t s part of whose income derives from t h e i r very s p e c i f i c experience, a b i l i t y and resource base. These aspects of the industry have influenced the model. I t was f e l t that i t would be impossible to develop general 104 p r i n c i p l e s f o r varying y i e l d s with inputs but that i t i s necessary to have the c a p a b i l i t y to e a s i l y include various a l t e r n a t i v e s i n the use of v a r i a b l e inputs and t h e i r e f f e c t on y i e l d s i n so f a r as they can be q u a n t i f i e d by the i n d i v i d u a l farmer. To s e l e c t crops on a p a r t i c u l a r farm the s p e c i f i c resource base and production r e l a t i o n s of that farm have to be included i n the model so that v a r i a b l e costs and resource constraints accurately r e f l e c t the r e a l marginal r e l a t i o n s h i p s i n the farms production f u n c t i o n . The v a r i a b l e inputs, purchased inputs such as f e r t i l i z e r and other chemicals were seen as f a i r l y straightforward given the degree of 'testing* that has been done; to achieve an expected y i e l d a prescribed amount of each chemical has to be purchased. In a l l cases there would not be constraints on the amount that can be acquired at a constant p r i c e and f o r most cases the a f f e c t of marginal changes i n the amount used would not be known. The scheduling of machine operations on the other hand was seen as the main d i f f i c u l t y . Each machine operation uses labour, t r a c t o r and implement time. The con-s t r a i n t s on the amount of time a v a i l a b l e of each of these resources i n the section of the t o t a l year i n which a job has to be completed and the amount of time required to complete the job was seen as a very complicated and possibly very c r i t i c a l consideration i f the farm plan that i s recommended i s to be t r u l y f e a s i b l e . Consequently, the c h a r a c t e r i s t i c s of machine operation were studied i n d e t a i l f o r the dual purpose of developing a 105 method of machine scheduling and of p r e d i c t i n g costs of use s p e c i f i c to the farm. Although the s p e c i f i c farm was envisaged as the f i n a l source of a l l data engineering p r i n c i p l e s were used as a source of 'standard' data f o r r e p a i r and maintenance cost r a t i o s and f u e l consumption. ASAE r e p a i r and maintenance formulae and Donnell Hunt's f u e l formulae are used f o r data that may not be known by the farmer. These include ASAE f i e l d capacity formulae and Hunt's power formula. Engineering p r i n c i p l e s were incorporated i n t o the structure of the matrix to specify the i n t e r r e l a t i o n s h i p s between resources. The core of the t h e o r e t i c a l model developed involved the construction of machine operating a c t i v i t i e s for each job that has to be performed on each crop. The advantage of t h i s method was that the time constraints for each job could be s p e c i f i e d i n a f l e x i b l e manner and the p a r t i c u l a r parameters of each job could be used e x p l i c i t l y i n the model. A t r a c t o r s e l e c t i o n block was b u i l t to e x p l i c i t l y incorporate the t r a c t o r s a c t u a l l y a v a i l a b l e f o r a p a r t i c u l a r operation i n terms of power. The schedule of machine a c t i v i t i e s for each crop becomes a column of integers i n the crop a c t i v i t i e s . The complete t h e o r e t i c a l model also included various resource purchasing a c t i v i t i e s . A s l i g h t l y d i f f e r e n t method was used to include each c l a s s of resources: land, labour, f u e l , purchased inputs, borrowed cash, t r a c t o r r e p a i r and maintenance, and implement r e p a i r and maintenance. A vector of fixed costs was forced i n t o the model to accurately r e f l e c t the farm's cash flow p o s i t i o n . Rotation and marketing con-106 s t r a i n t s were to be added as required to crop and crop s e l l i n g a c t i v i t i e s . The model was applied to a large commercial vegetable farm i n B r i t i s h Columbia. Eleven crops were evaluated on three d i f f e r e n t classes of land. The p r i c e s , y i e l d s and acre-ages of each crop were f i x e d at l e v e l s a c t u a l l y obtained i n 1974. The l o g i c of the model was validat e d by c a l c u l a t i n g by hand the resources and costs required by the s o l u t i o n and comparing these with those obtained by solv i n g the model on the computer. The r e s u l t s were exactly the same i n a l l cases except f o r d i f f e r e n c e r e a d i l y a t t r i b u t a b l e to rounding e r r o r s . The cost predictions of the computer so l u t i o n were also compared with CANFARM records f o r 1974 to evaluate the para-meters of the empirical model and the methods proposed to pre-d i c t v a r i a ble costs i n the t h e o r e t i c a l model. Although these r e s u l t s were more ambiguous they were f o r the most part very p o s i t i v e . Several s i g n i f i c a n t d i f f e r e n c e s did appear between actual costs and predicted costs but they could be a t t r i b u t e d to p e c u l i a r i t i e s of the farm operation i n 1974 and to the optimization routine i n the t r a c t o r s e l e c t i o n block of the model. 107 6.2 CONCLUSIONS The hypothesis implied by the objectives of the t h e s i s was that i t was possible to b u i l d a farm planning model that would be useful to vegetable producers i n making planning d e c i s i o n s . The t e s t i n g of t h i s hypothesis i s n e c e s s a r i l y a subjective valuation of the usefulness of the model. The model b u i l t i s e s s e n t i a l l y a crop budgeting model whose main function i s to s e l e c t crops based on gross margins and c o n s t r a i n t s on labour, machinery, land, operating cash, and considerations f o r r i s k and r o t a t i o n s . The usefulness of such a model that can s u c c e s s f u l l y make an e f f i c i e n t s e l e c t i o n i s obvious. By making a modification i n his farm plan based on the r e s u l t s of the model the grower should be able to receive a higher farm income than he would otherwise using a very s i m i l a r combination of resources. The model also provides information on which t r a c t o r s are the most economical to operate although t h i s i n f o -mation i s a v a i l a b l e through arithmetic c a l c u l a t i o n s outside the framework of the model. This l a s t point i s i l l u s t r a t i v e of the educational value of the model. By working out the input data that the model requires f o r a s o l u t i o n the farm operator i s made aware of the great deal of information that he has to deal with i n making e f f i c i e n t d e c i s i o n s . The shadow pri c e s of the resources of the model also i n d i c a t e d i r e c t i o n s i n which the farm business may be a l t e r e d i n the future to improve the p r o f i t a b i l i t y of the operation. The model also gives the farmer a valuation of the cost to him i n following a s l i g h t l y d i f f e r e n t plan. 108 Whether the model s u c c e s s f u l l y performs a l l these functions depends upon i t s r e l i a b i l i t y . The l o g i c of the model has proven to be sound. Given that the l o g i c i s sound, the r e l i a b i l i t y depends upon the v a l i d i t y and completeness of the input data. For the case farm i t has been possible to very c l o s e l y simulate 1974 costs using the model. Although some reservations about the r e l i a b i l i t y of the p r e d i c t i o n s f o r some parts of the model must be held, most e s p e c i a l l y concerning the estimate of imple-ment re p a i r and maintenance costs, the pred i c t i o n s are f o r the most part quite accurate. The conclusion i s that f o r the case farm at le a s t the model does achieve i t s o b j e c t i v e s . It i s also apparent that the model i s r e a d i l y a p p l icable to any s i m i l a r vegetable farm, i . e . large commercial vegetable farms that produce a range of crops. Indeed the model would be useful i n making crop selections on any type of farm although the large number of time periods i s more d i r e c t l y r e l a t e d to the vegetable industry. I t i s not obvious how the model would be used on farms which are organized i n a very d i f f e r e n t manner. One s i t u a t i o n i n which i t would be most d i f f i c u l t to adapt the model i s the case where there i s only one crop considered unless a great deal more information can be supplied about a l t e r n a t i v e production methods than was a v a i l a b l e on the case farm. The reason why the model i s of l i t t l e value i n t h i s s i t u a t i o n i s that with one crop and one production method the farm plan i s pretty well predetermined. The other case i s where there i s i . . . , . . an a l t e r n a t i v e animal enterprise f o r which the model has not r e a l l y means to evaluate. Other than these two s i t u a t i o n s i t 109 would not be d i f f i c u l t to adapt the model t o any farm where c r o p s e l e c t i o n i s an:important problem. Whether the model can be r e l i a b l y used on these o t h e r farms i s s t i l l an open q u e s t i o n . The r e l i a b i l i t y o f the model can o n l y r e a l l y be e v a l u a t e d through e x t e n s i v e t e s t i n g o f the model on a l a r g e number of farms. 110 6.3 SUGGESTIONS FOR FURTHER STUDY As with any study the f i n a l r e s u l t i s to i n d i c a t e the wide range of extensions and associated problems that may be p r o f i t a b l y i n v e s t i g a t e d . To f a c i l i t a t e the presentation of topics for fur t h e r research the topics have been divided into three c l a s s i f i c a t i o n s : f u r t h e r developments of the present model, te c h n i c a l subjects, and extensions of the present model to include more complex farm planning problems. 6.3.1 Further Developments of the Present Model The o r i g i n a l plan as conceived by CANFARM c a l l e d f o r the development of software packages to a i d i n the a p p l i c a t i o n of the model. I t i s reasonable to ask at t h i s stage whether the model should be applied to several more farms or whether the software packages should be b u i l t now. I f e e l the software packages should wait u n t i l further evaluation of the model has been made. Questions should f i r s t be asked about the s u i t a b i -l i t y of the time periods and the r e l i a b i l i t y of the cost pre-d i c t i o n s that are i n the model. Work should be done to develop an adequate and complete set of input and output forms. The usefulness of these forms i n extension should be a major con-s i d e r a t i o n . The farm plans (see Appendix G) f o r the case farm with the model i n optimization mode are an attempt to provide the output forms. The experience with the Purdue crop budgeting models would be extremely use f u l as a reference here. F i n a l l y , i t may be useful to make minor adjustments i n the l i n e a r pro-gramming problem to provide the software packages with useful information and v i c e versa. To summarize, the software I l l packages should be constructed i n conjunction with a thorough review of the l i n e a r programming model and with a great deal of thought going into the input and output forms. Concurrent with the development of the software package a decision has to be made on the manner i n which CANFARM i s to service the large number of vegetable farms i n the country. The d i r e c t i o n of development can take the form of using a large number of very s p e c i f i c models f o r s p e c i f i c producers i n s p e c i f i c regions or a s i n g l e more complex and general model. The problems of other vegetable farms that have not been inc o r -porated into the model may have to be dealt with i n t h i s context. For example, should the p o s s i b i l i t y of custom h i r i n g i n and out of the farm operation be b u i l t into the t h e o r e t i c a l model or should there be two models one of which includes custom h i r i n g and one which does not? The model may have to be adapted one way or the other to farms which produce only one crop and farms with an animal enterprise making demands on resources. When these type p o l i c y decisions have been made i t w i l l be possible to go on to the next stage of model development. 6.3.2 Technological Studies Needed The type of technical information that i t would be worth-while to in v e s t i g a t e more thoroughly f a l l s into several c l a s s i -f i c a t i o n s . There i s a great deal of work that can be done on machinery r e p a i r and maintenance costs. The c o e f f i c i e n t s used f o r the t r a c t o r s i n the model could be re-estimated at smaller i n t e r v a l s . Four or f i v e hundred hour i n t e r v a l s might be more accurate than the present thousand hour i n t e r v a l s . The re p a i r and maintenance c o e f f i c i e n t s used f o r the other implements 112 c o u l d be r e v i s e d to take account of age of the implement. T h i s may be done by u s i n g the o t h e r ASAE formulae f o r r e p a i r and maintenance c o s t s and d e v e l o p i n g t a b l e s of c o e f f i c i e n t s f o r each c l a s s o f machinery. A s i n g l e c o e f f i c i e n t s h o u l d s t i l l be used f o r each implement however. I t may be t h a t the formulae s h o u l d be r e v i s e d upwards a l t o g e t h e r to take account of Canadian c o n d i t i o n s and i n f l a t i o n . T h i s can o n l y r e a l l y be determined by the f u r t h e r a p p l i c a t i o n of the model to s e v e r a l farms. Hunt's f u e l formulae may a l s o be r e v i s e d . I t would not be d i f f i c u l t t o r e - e s t i m a t e the formulae based on the Nebraska t e s t s u s i n g e i t h e r the same or a d i f f e r e n t f u n c t i o n a l form from t h a t developed by Hunt. A f o r m u l a t h a t used one of the summary s t a t i s t i c s of the Nebraska T e s t s might be e s p e c i a l l y v a l u a b l e i n p r o v i d i n g a t r a c t o r s p e c i f i c e s t i m a t i o n of f u e l consumption a t v a r i o u s l o a d s . Some e v a l u a t i o n o f the f o r m u l a may a l s o be made i n a c t u a l farm use. I f t h i s c o u r s e were taken then i t might be p o s s i b l e to i n c l u d e the use of f u e l f o r r e a s o n s o t h e r than d i r e c t l y i n f i e l d o p e r a t i o n s so t h a t the e s t i m a t e may be r a t i o n a l l y r e v i s e d upwards. Perhaps the most important t e c h n i c a l i n f o r m a t i o n t h a t i s r e q u i r e d i s some method to r e l a t e y i e l d s and p r o d u c t i o n methods i n a s y s t e m a t i c f a s h i o n w i t h formulae s i m i l a r t o the e n g i n e e r i n g f o r m u l a e . I t i s a l r e a d y p o i n t e d out i n s e v e r a l p l a c e s t h a t i t i s l e f t to the grower to d e f i n e a s e t o f b e s t p r o d u c t i o n p r a c t i s e s . However, i t i s n e c e s s a r y to be a b l e to d e a l w i t h the e f f e c t of a d e v i a t i o n from these b e s t p r a c t i s e s i n a q u a n t i -113 t a t i v e manner. An example of the type of information needed can be seen i n the Purdue Crop Budgeting Model B-9. In the model corn y i e l d s are reduced by l/Bu./day f o r a l t e r n a t i v e planting periods between May 10 and May 23 and by 2/Bu./day fo r planting periods between May 24 and June 10. Data ex-pressed i n t h i s manner or perhaps i n percentage y i e l d reduc-tions are needed for the timeliness of operations w.r.t. planting dates, harvesting dates and on weed c o n t r o l . Similar data i s also needed for such fac t o r s as f e r t i l i z e r use, p e s t i c i d e s and water. I d e a l l y the information would be based on actual farm r e s u l t s rather than crop t e s t s but whatever the source systematic r e l a t i o n s h i p s are needed f o r each vegetable or c l a s s of vegetable. A f i n a l area f o r t e c h n i c a l i n v e s t i g a t i o n i s i n the e f f e c t of weather. Weather i s a subject area which r e a l l y cuts across a l l three c l a s s i f i c a t i o n s of areas f o r further study. The e f f e c t of weather on machine time i s i m p l i c i t l y incorporated i n t o the data as i t i s c o l l e c t e d on machine constraints and on i crop production a c t i v i t i e s i n the schedule of machine a c t i v i t i e s f o r each crop. I t may be that i t would be useful to make the e f f e c t of weather e x p l i c i t . This would necessitate the i n v e s t i -gation of how weather v a r i a b l e can be used e x p l i c i t l y i n the model. Weather may provide f o r a systematic method f o r dealing with a l t e r n a t i v e planing and harvesting dates f o r example. 6.3.3 Expanding the Model to More Complex Farm Planning Problems The t h i r d c l a s s i f i c a t i o n of areas f o r further research i n 114 e x t e n d i n g the c o m p l e x i t y of the p r e s e n t model. At p r e s e n t the model i s a s i n g l e year l i n e a r programming model assuming a f i x e d c a p i t a l s t o c k and c e r t a i n t y . The assumptions of f i x e d c a p i t a l stock and c e r t a i n t y i s a s t r i c t d e s c r i p t i o n of the model and i s not to say t h a t r i s k i s i g n o r e d c o m p l e t e l y and the model has n o t h i n g t o say about c a p i t a l p u r c h a s e s . Both of t h e s e t o p i c s are handled i n d i r e c t l y . R i s k i s e v a l u a t e d sub-j e c t i v e l y by the farmer when he s p e c i f i e s upper and lower bounds he w i l l c o n s i d e r on the c r o p s i n h i s farm p l a n . S i m i l a r l y a l t h o u g h c a p i t a l b u d g e t i n g i s not handled e x p l i c i t l y , the shadow p r i c e s on r e s o u r c e s i n the f i n a l farm p l a n g i v e an i n d i c a t i o n of the machinery t h a t may be p r o f i t a b l y r e p l a c e d . The s u b j e c t s of r i s k and c a p i t a l b u d g e t i n g are both v e r y important t o p i c s of farm management and a r e f o r m u l a t i o n of the c r o p budgeting problem from the p o i n t of view of the economist s h o u l d p r o b a b l y be i n t h i s d i r e c t i o n . CANFARM a l r e a d y has a few s m a l l farm p l a n n i n g packages used t o make c a p i t a l b u d g e t i n g d e c i s i o n s . These packages work o u t s i d e the c o n t e x t o f the whole farm p l a n i n a manner analogous t o a p a r t i a l budget and thus do not r e a l l y take i n t o c o n s i d e r a -t i o n the e f f e c t o f machine purchases on c o n s t r a i n t s and the r e s u l t a n t change i n c r o p p l a n t h a t may become f e a s i b l e . Programs are a l s o being developed to e x p l i c i t l y i n c o r p o r a t e r i s k i n t o farm p l a n n i n g models i n o t h e r s e c t o r s of a g r i c u l t u r e . The q u e s t i o n a r i s e s , however, i n the c o n t e x t of the p r e s e n t model as to which o f these s u b j e c t s i t would be the most p r o f i t a b l e t o i n v e s t i g a t e next. The q u e s t i o n may be 115 divided into three aspects: the r e l a t i v e importance of r i s k and c a p i t a l budgeting to the farmer, the improvement over the present c a p a b i l i t y of the model, and the ease with which the model can be r e v i s e d . The importance to the farmer of having more information about r i s k or more information for his c a p i t a l purchases i s r e a l l y impossible to evaluate. For each farmer the r e l a t i v e importance of the two types of information may change from time to time. The s o l u t i o n to the optimization problem i n Chapter 5.5 i l l u s t r a t e s how the model may be used to take account of r i s k and uncertainty. The farmer s p e c i f i e d r i s k c o nstraints on his crop plan and f i v e d i f f e r e n t plans were prepared based on d i f f e r e n t possible outcomes based on y i e l d . The farmer i s l e f t to s e l e c t a farm plan f o r himself based on the a d d i t i o n a l information provided by the model. The r e a l value of incorporating r i s k i n a more e x p l i c i t fashion must e i t h e r be i n the a b i l i t y of the model to include more informa-t i o n i n the evaluation of r i s k or to be able to express the farmer's valuation of r i s k i n more precise mathematical terms so that the exact trade-off between r i s k and other f a c t o r s may be more exactly c a l c u l a t e d . I doubt i f more information can be incorporated. If the farm management s p e c i a l i s t had s p e c i a l information on future p r i c e s and y i e l d s he would not have to work for a l i v i n g . Most r i s k models r e l y heavily on past prices and y i e l d s . There are such a great many dimensions to r i s k , however, that i t i s d i f f i c u l t to incorporate a l l of them i n a simple p r e d i c t i o n model. Growers may sometimes have f a i r l y 116 strong reasons to suspect the prices of a crop w i l l be good or bad based on a complex perception of changes i n supply or demand which i t i s r e a l l y impossible to incorporate i n a pre-d i c t i o n model. This being the case, i t i s r e a l l y questionable whether there i s a great deal to be gained i n t r y i n g to b u i l d i n r i s k . I f e e l on the other hand that i n c l u d i n g c a p i t a l budgeting would dramatically increase the scope of the problem. The shadow prices of machinery i s only an i n d i c a t i o n of where machinery might be a problem. The i n c l u s i o n of c a p i t a l budgeting would enable the model to a i d i n these type of decisions i n a much more r e a l i s t i c fashion. New pieces of machinery are acquired nearly every year on the case farm. C a p i t a l budgeting would be a u s e f u l guide as to which machines should be replaced. McHardy's model demonstrates r e l a t i o n s h i p s that may be used i n a machine budgeting section of the model that not only give a yes or no d e c i s i o n on machine purchases but can be used to s e l e c t appropriate s i z e of machinery. The i n c l u s i o n of c a p i t a l budgeting would also allow the expansion of the plan to include several years and the growth rate of the f i r m . F i n a l l y , consideration must be given to the formulation of the objective function. The farm planning model maximizes income above v a r i a b l e costs but i t ignores inventories and the e f f e c t of taxes. Some consideration should be given to these v a r i a b l e s so that i t i s r e a l l y net farm income a f t e r taxes that i s maximized. V LIST OF REFERENCES 118 LIST OF REFERENCES 1. A l l e n , R.G.C. Mathematical Analysis f o r Economists. London: Macmillan & Co. Ltd., 1956. " 2. American Society of A g r i c u l t u r a l Engineers. 1974 A g r i -c u l t u r a l Engineers' Yearbook. 3. Arrow, Kenneth J . , Hurwicz, Leonid, and Uzawa, Hirofumi. Studies i n Linear and Non-Linear Programming. Stanford: Stanford University Press, 1958. 4. Bain, Joe S. "Economies of Scale, Concentration, and the Condition of Entry." In Theory of the Firm. Edited by G.C. Archibald. Middlesex, England: Penguin Books, 1972. 5. Barlow, C r a i g Douglas. "A Farm Management Analysis of a Vegetable Farm." B.Sc. Thesis. Department of A g r i c u l t u r a l Economics, U n i v e r s i t y of B r i t i s h Columbia, 1974. 6. Batterham, R.L., Brown, D.M., and Van Die, P. "Agronomic, Engineering, and Meteorological Data Required i n an Economic Model of Farm Machinery S e l e c t i o n . " Cana- dian A g r i c u l t u r a l Engineering, 15 (dec. 1973). 7. Beneke, Raymond R., and Winterboer, Ronald. Linear Programming Applications to A g r i c u l t u r e . Ames, Iowa: Iowa State University Press, 1973. 8. Boulding, Kenneth E., and Spivey, W. A l l e n . Linear Pro-gramming and the Theory of the Firm. New York: The Macmillan Co., 1960. 9. Braff, A l l a n J . Microeconomic A n a l y s i s . New York: John Wiley & Sons Inc., 1969. — 10. Brink, Lars, McCarl, Bruce A., and Haster, D. Howards. "Methods and Procedures i n the Purdue Crop Budget (Model B-9): An Administrators' Guide." Forthcoming Purdue A g r i c u l t u r a l Experiment Station B u l l e t i n . 11. B r i t i s h Columbia Department of A g r i c u l t u r e . "A Summary Report of the Seminar on the Vegetable Industry of B r i t i s h Columbia." Richmond, B.C.: Oct. 1974. 12. . 1975 Vegetable Production Guide. 13. Bauer, L. "Uses of Farm Records." Guelph: CANFARM, 1971. 119 Candler, Wilfred, Boehlje, Michael, and Scathoff, Robert. "Computer Software f o r Farm Management Extension." In American Journal of A g r i c u l t u r a l Economics 52 ( , 1971), p.71. Canfarm. "Machine Planning Buy vs Custom." Paper presented to persons using Canfarm computer programs, 1975. Canfarm. "Machine Planning Replacement." Paper presented to persons using Canfarm computer programs, 1975. Chiang, Alpha C. Fundamental Methods of Mathematical  Economics. New York: McGraw-Hill, Inc., 196 7. Dantzig, George B. Linear Programming and Extensions. Princeton, New Jersey: Princeton University Press, 1963. Donaldson, Graham F. Farm Machinery Capacity. Royal Commission on Farm Machinery, Study No. 8. Ottawa: Queens P r i n t e r , 1970. . Farm Machinery Testing. Royal Commission on Farm Machinery Study No. 10. Ottawa: Queen's P r i n t e r , 1970. Federal Task Force on A g r i c u l t u r e . " F r u i t s & Vegetables." A paper prepared f o r the Canadian A g r i c u l t u r a l Congress. Ottawa: 1969. Fergueson, C.E. Microeconomic Theory. 3rd E d i t i o n . Homewood, I l l i n o i s : Richard C. Irwin Inc., 1972. Friedman, E. Milton. "Theory and Measurement of Long-Run Costs." In Theory of the Firm. Edited by G.C. A r i c h i b a l d . Middlesex, England: Penguin Books, 1972. Galbraith, John Kenneth. Economics and the Public  Purpose. Boston: Houghton M i f f l i n Co., 1973. Heady, E a r l 0., ed. Economic Models and Quantitative Methods for Decisions and Planning i n A g r i c u l t u r e  Proceedings of an East-West Seminar. Ames, Iowa: The Iowa State U n i v e r s i t y Press, 1971. Henderson, James M, and Quandt, Richard E. Microecono- mic Theory A Mathematical Approach. New York: McGraw-Hill Inc., 1971. Hunt, Donnell. " E f f i c i e n t F i e l d Machine S e l e c t i o n . " A g r i c u l t u r a l Engineering 44 (Feb. 1963), p. 78. 1 2 0 . Farm Power and Machinery Management. 6th ed. Ames, Iowa: The Iowa State Uni v e r s i t y Press, 1973. . A Fortran Program for Selecting Farm Equipment. St. Joseph, Mich.: American Society of A g r i c u l t u r a l Engineers No. 66-154, 1966. International Business Machines. "Mathematical Program-ming System Extended (MPSX) Control Users* Manual." White Pl a i n s , New York: International Business Machines, SH20-0932, 1971. . "Mathematical Programming System Extended (MPSX) and Generalized Upper Bounding (GUB) Program Descrip-t i o n . " White P l a i n s , New York: International Business Machines, SH20-0981, 1972. I n t r i l i g a t o r , Michael D. Mathematical Optimization and Economic Theory. Englewood C l i f f s , N.J.: P r e n t i c e - H a l l , Inc., 1971. Jones, Fred R. Farm Gas Engines and Tractors. 4th ed. New York: McGraw-Hill, Inc., 1963. Kepner, R.A., Bauer, Roy, and Barger, E.L. P r i n c i p l e s of  Farm Machinery. 2nd ed. Westport, Conn.: Avi P u b l i -shing Company, Inc., 1972. Kizer, Lennie G. "Farm Simulation with Emphasis on Machinery Management." St. Joseph, Mich.: American Society of A g r i c u l t u r a l Engineers No. 74-5042, 1974. Lancaster, Kelvin. Mathematical Economics. Toronto: The Macmillan Company C o l l i e r Macmillan Canada, Ltd., 1969. McCarl, Bruce A., Candler, Wilfred, Doster, D. Howard, and Robbins, Paul R. "Purdue Top Farmers Automatic Crop Budget: Design A p p l i c a t i o n and Experience." Forthcoming Purdue A g r i c u l t u r a l Research Station B u l l e t i n . McHardy, F.V. "A Method f o r Sizi n g Farm Machines f o r Weather Dependent Operations." In Canadian A g r i c u l t u r a l  Engineering 8 (Feb. 1966), p. _. "Programming Minimum-Cost Machine Combinations." In Canadian A g r i c u l t u r a l Engineering 8 (Feb. 1966), p. . 121 Peart, Robert McDermanet. "Optimizing Materials Handling Systems by Mathematical Programming." Ph.D. Disser-t a t i o n , Purdue U n i v e r s i t y , 1960. Russell, D.G., and McHardy, F.V. "Optimum Combining Time f o r Minimum Cost." In Canadian A g r i c u l t u r a l  Engineering 12 (May 1970), p. Schmeidler, Neal F., Clark, S.J., Grosh, L.E., and Schrock, M.D. Optimization of Farm Equipment Selec- t i o n . St. Joseph, Mich.: American Society of A g r i c u l t u r a l Engineers No. 73-1531, 1973. S t a t i s t i c s Canada. Census of A g r i c u l t u r e B r i t i s h Columbia. Ottawa: Queen's P r i n t e r , 1971. S t a t i s t i c s Canada. Census of A g r i c u l t u r e Canada. Ottawa: Queen's P r i n t e r , 1971, 1966, 1961. S t a t i s t i c s Canada. Quarterly B u l l e t i n of A g r i c u l t u r a l  S t a t i s t i c s . Ottawa: Queen's P r i n t e r , 1970-74. United Grain Grower. "How to Pin Down Your Machinery Operating Costs." United Grain Grower, 1970. . "How to Predict Tractor F i e l d Performance." United Grain Grower, 1973. . "What the Nebraska Tractor Tests T e l l You." United Grain Grower, 1973. United States Department of A g r i c u l t u r e . A g r i c u l t u r e S t a t i s t i c s 1974. Washington, D.C: U.S. Government P r i n t i n g O f f i c e , 1974. Wentz, Walter B. Marketing Research: Management and  Methods. New York: Harper & Row, 1972. '. ~ Winter, G.R. "Future Developments Export P o s s i b i l i t i e s f o r the Future." Paper presented at the Seminar on the Vegetable Industry of B.C. Richmond, B.C.: Oct. 1974. APPENDICES APPENDIX A THE IMPORTANCE AND PERFORMANCE OF THE VEGETABLE INDUSTRY IN BRITISH COLUMBIA AND CANADA 124 TABLE A . l IMPORTANCE OF THE VEGETABLE INDUSTRY IN CANADA AND BRITISH COLUMBIA: AREA 1970-74 Area under Vegetables Vegetable Acres as Per of T o t a l 1971 Cropped . B.C. (acres) Can. (acres) B.C. % Can. > 1970 22,900 554,610 2.10 0.81 1971 22,610 470,580 2.07 0.68 1972 22,740 467,360 2.45 0.68 1973 27,550 511,790 2.52 0.74 1974 25,270 536,810 2.31 0.78 Source: "Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s " , S t a t i s t i c s Canada, 21-003, A g r i c u l t u r a l D i v i s i o n , Ottawa, July-September, 1975, 1973, 1971. "1971 Census of A g r i c u l t u r e Canada", S t a t i s t i c s Canada, 96-701, V o l . 4, Part 1, Census Branch, Ottawa, July, 1973. TABLE A.2 1970 1971 1972 1973 1974 IMPORTANCE OF THE VEGETABLE INDUSTRY IN CANADA AND BRITISH COLUMBIA: FARM VALUE OF PRODUCTION 1970-74 Farm Value of Vegetable Production Per Cent of Total Value of Production B.C, $000's 14,481 13,412 17,468 29,977 n.a. Can. $000's 144,021 168,779 243,480 355,282 n.a. B.C. % 6.48 5.98 7.03 8.99 n.a. Can. % 4.63 3.71 4.48 5.20 n.a. Source: "Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s " , S t a t i s t i c s Canada, 21-003, A g r i c u l t u r a l D i v i s i o n , Ottawa, July-September, 1975, 1973, 1971. "1971 Census of Ag r i c u l t u r e Canada", S t a t i s t i c s Canada, 96-701, Table 1, V o l . 4, Part 1, Census Branch, Ottawa, July, 1973. 125 TABLE A.3 IMPORTANCE OF THE VEGETABLE INDUSTRY IN CANADA AND BRITISH COLUMBIA: THE NUMBER OF FARMS REPORTING VEGETABLE PRODUCTION 1961, 1966 AND 1971 The Number of Farms Reporting Vegetable Production (Potatoes i n Parenthesis) Per Cent of Number of Farms To t a l B.C. Can. B.C. Can. No. No. % % 1961 1,191 22,874 5.97 4.76 1966 1,146 17,420 6.00 4.04 1971 1,144 16,120 6.22 4.40 ( 707) (23,311) Source: "1971 Census of Canada A g r i c u l t u r e Canada", S t a t i s t i c s Canada, 21-701, Census Branch, V o l . 4, Part 1, Ottawa, Jul y , 1971, 1966, 1961. TABLE A.4 RELATIVE IMPORTANCE OF SELECTED VEGETABLES IN THE BRITISH COLUMBIA AGRICULTURE INDUSTRY: AVERAGE 1970-74 Vegetable Per cent of farm T o t a l vegetable Income o ^ ^ „ T ^ ^ ^ m « Farm Income Acres Harvested Per cent of Total Vegetable Acres Harvested $000's % acres % Potatoes 10,736* 54.5 11,920 47.3 Cucumbers 324 2.0 356 1.5 Lettuce 1,165 6.1 614 2.5 Onions 1,036 5.5 644 2.6 Tomatoes** 439 3.0 240 1.0 Cabbage 818 4.2 802 3.2 Carrots 695 3.6 460 1.8 Processed Peas 1,281 6.0 4,648 18.5 Processed Beans 562 2.8 1,660 6.9 Residual 1,779 12.3 3,730 14.7 Total 18,835 100.0 25,074 100.0 * Average f o r the years 1970-73 only. •* Average f o r the years 1971-72 only. Source: "Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s . " S t a t i s t i c s Canada, 21-003 , A g r i c u l t u r a l D i v i s i o n , Ottawa: Sept.-Dec, 1972, 1973, 1974, 1975. 126 Vegetable TABLE A.5 YIELD PER ACRE COMPARED FOR SELECTED CROPS IN BRITISH COLUMBIA, CANADA, UNITED STATES, AND WASHINGTON STATE: AVERAGES 1970-74 B r i t i s h Columbia Canada Washington tons per acre . . United States Potatoes Carrots Onions 11.18 11.57 12.52 9.1 11.57 11.78 19.10 21.47 18.92 11.65 12.64 14.80 Peas Beans Corn 2.05 3.05 5.60 1.29 2.00 4.01 1.66 3.21 5.80 1.29 2.48 4.78 Lettuce Cabbage Cucumbers 14.45 7.42 6.28 6.39 9.84 6.63 8.57 10.88 n.a. 10.80 10.70 n.a. Source: "Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s . " S t a t i s t i c s Canada, 21-003, A g r i c u l t u r e D i v i s i o n , Ottawa: July-Sept., 1971, 1973, 1975 and 1971, 1973, 1975. " A g r i c u l t u r a l S t a t i s t i c s 1974." United States Depart-ment of A g r i c u l t u r e , Chapter IV, pages 149-203, Washington. 127 TABLE A.6 A COMPARISON* OF FARM SIZE IN CANADA, BRITISH COLUMBIA AND WASHINGTON STATE MEASURED IN ACRES AND VALUE OF PRODUCTS SOLD Average Size (acres) Value of Sales ($/year) Year 1971 1966 1961 1971 .1966 1961 Canada A l l Farms 463 404 359 11,328 7,752 4,880 Vegetable Enterprise 15.8 13.7 9.5 5,749 3,791 2,390 Potato Enterprise 21.7 1.9 1.4 10,090 5,056 3,560 Year 1971 1966 1961 1971 1966 1961 B.C. A l l Farms 316 277 226 11,386 7,326 5,222 Vegetable Enterprise 15.7 13.8 8.3 8,432 5,481 2,951 Potato Enterprise 16.1 2.5 2.6 7,478 4,748 3,481 Year 1959 1964 1969 1959 1964 1969 Washington A l l Farms 516 418 363 22,661 13,979 11,042 Vegetable Enterprise 70. 58 39 18,211 9,887 6,732 Potato Enterprise 779 n.a. n.a. 43,857 n.a. n.a. * Numbers are not r e a l l y comparable as they were c o l l e c t e d from many diverse sources with d i f f e r e n t d e f i n i t i o n s of what i s here c a l l e d 'potato e n t e r p r i s e ' . This i s e s p e c i a l l y evident i f you use the numbers to c a l c u l a t e the revenue per 'acre f o r potato farms i n Canada and B r i t i s h Columbia. The terms 'potato e n t e r p r i s e ' and 'vegetable e n t e r p r i s e ' are used here as there was no way of assuring that a farm not be counted twice. Source: "Census of Canada A g r i c u l t u r e Canada", S t a t i s t i c s Canada, Ottawa, Canada; Queens P r i n t e r , 1971, 1966, 1961. "1969 Census of A g r i c u l t u r e Washington", U.S. Dept. of Commerce, Bureau of Census, V o l . 1, Part 46, Washing-ton, D.C; U.S. Government P r i n t e r , 1972. 128 TABLE A.7 FARM VALUE PER ACRE A COMPARISON OF FIVE YEAR AVERAGES FOR BRITISH COLUMBIA, CANADA, WASHINGTON AND UNITED STATES AVERAGES 1970-74 1 B.C. 1 Can. Wash. U.S. 2 Potatoes 900* 342 665 653 Carrots 1,510* 619 868 1,212 Onions 1,687 1,056 1,926* 1,571 Peas 213* 150 186 144 Beans 271 173 326* 243 Corn 170 141 171* 123 Lettuce 1,889* 837 962 1,300 Cabbage 1,004* 1,706 850 827 Cucumbers 940* 649 n.a. n.a. "Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s " , J u l y -September, 1971, 1973, 1975. "Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s " , J u l y -September, 1971, 1973, 1975, Average 1970-73 only. " A g r i c u l t u r a l S t a t i c s 1974", U.S. Department of A g r i c u l t u r e , Chapter IV, S t a t i s t i c s for Vegetables & MelIons, Average 1970-73 only. APPENDIX B THE CALCULATION OF REPAIR AND MAINTENANCE COSTS 130 B. l REPAIR AND MAINTENANCE COSTS Repair and maintenance costs may be predicted using formulae developed by the ASAE and reproduced annually i n t h e i r yearbook. There are seven basic formulae which a l l have the same str u c t u r e although they d i f f e r i n the value of the para-meters used. The formulae applicable depends upon the type of machine being used. For instance, f o r a two wheel drive t r a c t o r formula number two i n Table B . l should be used. The formulae gives the t o t a l accumulated r e p a i r cost i n per cent of the purchase price as a function of the hours of use of the machine. A graph of. formulae 2 i s shown i n Figure B . l . I t can be seen that r e p a i r and maintenance costs are an increasing function of age. To c a l c u l a t e the average hourly r e p a i r costs i n the next time period the formulae have to be modified as i n B . l . B . l R = TAR% . - TAR% n + 1 n H where R = r e p a i r and maintenance costs per hour, TAR% ss t o t a l accumulated r e p a i r costs at the end of period n, and Hj = t o t a l hours of use i n the time period. CANFARM (1975) use these formulae i n t h e i r various machine packages i n t h i s form as does Hunt (1966). However, CANFARM has divided a l l the A c o e f f i c i e n t s by two. (CANFARM c o e f f i c -ients are also given i n Tab'le B . l ) . Approximations of these formulae have often been suggested. For example, United Grain Growers determine r e p a i r and maintenance costs as a per cent of purchase p r i c e for four 131 TABLE B . l ASAE FORMULAE FOR REPAIR AND MAINTENANCE COSTS C o e f f i c i e n t s Formulae 1. TAR% a(X/Y) ASAE CANFARM a b a b 0.100 1.5 0.0500 1.5 2. TAR% a(X/Y) D 0.120 1.4 0.0600 1.4 3. TAR% a(X/Y) D 0.096 1.4 0.0480 1.4 4. TAR% a(X/Y) D 0.127 1.4 0.0635 1.4 5. TAR% a(X/Y) D 0.159 1.4 0.0795 1.4 6. TAR% a(X/Y) 7. TAR% a(X/Y) ] 0.191 1.4 0.0955 1.4 0.301 1.3 0.1500 1.3 Machinery Applicable 4 wheel drive t r a c t o r s , t r a c t o r crawlers. 2 wheel drive t r a c t o r s , s t a t i n a r y power u n i t s . s.p. combines and forage harvestors, f r o n t end loader, pick-up truck, manure spreader, baler with engine f l o a t s , rotary c u t t e r s . Sprayer, p u l l type harvestor, b a l e r , potato harvestor, truck, corn picker, beet harvestor. PTO combine, s.p. swather, wagon, hay con-d i t i o n e r , rake, seeding equipment, mounted sprayers. F e r t i l i z e r equipment.. Mower, t i l l a g e equip-ment such as plows, planters, c u l t i v a t o r s , harrows, e t c . Source: 1974 A g r i c u l t u r a l Engineers' Yearbook, section 0230.2, page 299 and page 303 Table 2. "Machinery Planning Replacement." CANFARM p u b l i c a t i o n . According to correspondence with CANFARM the 'a' co-e f f i c i e n t s were simply divided by two as engineers working on the CANFARM package thought the formulae gave r e s u l t s that were too high. Note: TAR% i s t o t a l accumulated r e p a i r and maintenance costs to date as a per cent of purchase p r i c e . X i s 100 times accumulated hours of use, and Y i s the wearout l i f e of the machine. See Table B.3 for t y p i c a l values f o r wear-out l i f e . 132 120 4-4J o 100 u ~ CD U V •H - r l (0 S-i a a CL) K 5 <U T3 C 80 1 60 4-40 1 20 i I 1 1 1 2000 4000 6000 8000 10000 12000 Age (hours) FIGURE B . l TOTAL ACCUMULATED REPAIR AND MAINTENANCE COSTS IN PER CENT OF PURCHASE PRICE AS A FUNCTION OF AGE FOR A TWO WHEEL DRIVE TRACTOR 133 broad c l a s s i f i c a t i o n s of machinery regardless of age (see Table B.2). Lubricants are i n t h i s case considered separately at 15% of f u e l costs. Kepner, Bauer and Barger (1972) use a si m i l a r approach but give t h e i r r e s u l t s f o r more s p e c i f i c c l a s s i f i c a t i o n s of machinery (see Table B.3). Such systems are n e c e s s a r i l y an average over the l i f e of the machine and overestimate when the machine i s r e l a t i v e l y new and under-estimate when the machine i s older. This can e a s i l y be seen i n Figure B.2 i n which average hourly r e p a i r costs f o r a two wheel dr i v e t r a c t o r i s determined by using equation B . l with TAR% c a l c u l a t e d with formulae two i n Table B . l . The average rep a i r costs over the l i f e of the t r a c t o r i s .01%/hour as r e -ported i n Kepner, Bauer and Barger (Table B.3) and t h i s f i g u r e i s represented by the hor i z o n t a l l i n e . When comparing the two methods however i t should be kept i n mind that there i s a large s t o c h a s t i c element i n estimating r e p a i r and maintenance costs and they tend to be lumpy so that any estimate may well be quite wide of the mark. TABLE B.2 REPAIR AND MAINTENANCE COSTS PER HOUR AS A PER CENT OF LIST PRICE ACCORDING TO BROAD IMPLEMENT CLASSIFICATION Machine Type Cost/Hour Tractor 0.012 T i l l a g e 0.060 Harvesting 0.030 Planting 0.075 Source: United Grain Growers, " How to Pin Down Your Machin-ery Operating Costs". 134 TABLE B.3 REPAIR AND MAINTENANCE COSTS PER HOUR AS A PER CENT OF LIST PRICE ACCORDING TO MACHINE TYPE •irs per Year Repair Costs, Years Wear- for Wear-out Per cent of New Cost U n t i l out L i f e to Equal Average r o t a l During Obso- L i f e Obsolescence per Wear-out Machine le t e Hours L i f e Hour L i f e Tractors Wheel-type 12* 12,000 1,000 0.010 120 Track-type 12* 12,000 1,000 0.0065 78 T i l l a g e implements C u l t i v a t o r 12 2,500 208 0.060 150 Disk harrow 15 2,500 167 0.048 120** Disk plow 15 2,500 167 0.045 113 Moldboard plow 15 2,500 167 0.080 200** Spike-tooth harrow 15* 2,500 167 0.040 100 Spring-tooth harrow 15* 2,000 133 0.060 120 Seeder Grain d r i l l 15* 1,200 80 0.080 96 Row-crop planter 15 1,200 80 0.070 84 Harvesting equipment 54 Combine, s e l f - p r o p e l l e d 10 2,000 200 0.027 Corn picker 10 2,000 200 0.032## 64 Cotton picker 10* 2,000 200 0.026## 52 Cotton s t r i p p e r 10 2,000 200 0.020## 40 F i e l d chopper, pull-type 10 2,000 200 0.040 80** Hay baler, aux. eng. 10 2,000** 200 0.022 55 Hay baler, PTO 10 2,000 ** 200 0.031 78 Hay conditioner 10 2,500 250 0.040 100 Mower 10* 2,000 200 0.120 240 Rake, side d e l i v e r y 10* 2,500 250 0.070 175 Sugar beet harvester 10 2,500 250 0.025## 63 Windrower, self-propelledlO* 2,500 250 0.040 100 Miscellaneous Forage blower 12 2,000 167 0.025 50 Wagon (rubber t i r e d ) 15 5,000 333 0.018 90 From 1963 A g r i c u l t u r a l Engineers Yearbook, p.232. ASAE, St. Joseph, Mich. * Changed by authors. ••Changed by authors, based on references 4 and 7. # When average annual use exceeds t h i s number of hours, machine w i l l wear out before i t becomes obsolete. ## If machine i s mounted type, add t o t a l of 1% of new cost f o r each time machine i s mounted and dismounted (normally once a year). Source: R.A. Kepner, Roy Bauer, and E.L. Barger i n P r i n c i p l e s of  Farm Machinery, 2nd Ed., 1972. 135 ASAE Formula ,014 u 3 .012 o X u cu au.010 w u •H Li a -4J W o u 3, CU CU o c c ro MH c o CU -P 4J . 008 006 c •H rO O •g £.004 (0 >— Li •H ro a cu OS .002 Lifetime Average JL 2000 4000 6000 8000 10000 12000 Age (hours) FIGURE B.2 REPAIR AND MAINTENANCE COSTS PER HOUR IN PER CENT OF LIST PRICE AS A FUNCTION OF AGE: ASAE FORMULA COMPARED WITH LIFETIME AVERAGE AS AN APPROXIMATION 136 B.2 REPAIR AND MAINTENANCE COST COEFFICIENTS IN THE MODEL Two d i f f e r e n t approaches are used f o r r e p a i r and mainten-ance costs i n the model. For t r a c t o r s , repair and maintenance costs c o e f f i c i e n t s are estimated using l i n e a r approximations of Formula B . l . Average r e p a i r and maintenance costs per hour as a per cent of l i s t p r i c e f o r each 1000 hour period from when a tra c t o r i s new u n t i l i t i s worn out at 12000 hours were c a l c u -l a t e d . Formula 2 i n Table B . l was used to c a l c u l a t e TAR%. The r e s u l t s are given i n Table B.4. The c o e f f i c i e n t s i n Table B.4 are u t i l i z e d i n the model to c a l c u l a t e r e p a i r and maintenance costs for t r a c t o r s . I t can be seen i n Figure B.3 that the co-e f f i c i e n t s overestimate r e p a i r and maintenance costs i n the f i r s t part of the 1000 hour i n t e r v a l and underestimate i n the res t of the i n t e r v a l . However, the c o e f f i c i e n t s do follow the curve much more c l o s e l y than the si n g l e c o e f f i c i e n t method, i l l u s t r a t e d i n Figure B.2 TABLE B.4 AVERAGE REPAIR AND MAINTENANCE COSTS PER HOUR AS A PER CENT OF LIST PRICE FOR TWO WHEEL DRIVE TRACTORS Hours of Use 0-1000 1000-2000 2000-3000 3000-4000 4000-5000 5000-6000 Repair Costs as a per cent of New Pr i c e (thousandths) 2.89 5.28 6.84 8,09 9.18 10.15 Hours of Use 6000-7000 7.000-8000 8000-9000 9000-10000 10000-11000 11000-12000 Repair Costs as a per cent of New Price (thousandths) 11.04 11.86 12.61 13.34 14.03 14.68 137 14 J-l w 3 JC O -P X -o c u a OJ w a 3 o w x: -P 4-> w o c U -H (U OJ u u C >H ro M c a <u -p 3 c cy • H c rO O -D C -P ro C <D U O • H rfl U a <u QJ a 12 10 8 2000 4000 6000 8000 10000 12000 Age (hours) FIGURE B.3 REPAIR AND MAINTENANCE COSTS PER HOUR IN PER CENT OF LIST PRICE AS A FUNCTION OF AGE: ASAE FORMULA FOR TWO WHEEL DRIVE TRACTORS COMPARED WITH APPROXIMATIONS OF THE FORMULA USED IN THE MODEL 138 The model computes the t o t a l hours of use of each t r a c t o r i n each month and then c a l c u l a t e r e p a i r and maintenance costs as the product of the c o e f f i c i e n t s i n Table B.3, accumulated hours of use, and new p r i c e . The data that has to be supplied by the farmer are new p r i c e and the age of the t r a c t o r i n ac-cumulated hours of use at the s t a r t of the planning period. The c o e f f i c i e n t s required f o r the implements w i l l be obtained from Table B.3. The only information required from the farmer f o r re p a i r and maintenance costs for implements w i l l be the l i s t p r i c e of his implements and the implement type so the proper c o e f f i c i e n t can be selected. The matrix parameter w i l l be the product of these two numbers. APPENDIX C FUEL CONSUMPTION COEFFICIENTS 140 Some authors have suggested using average f u e l consumption i n gallons per hour at 75% of maximum load as determined by the Nebraska tests f o r each s p e c i f i c t r a c t o r . This method does take i n t o account the si z e and p e c u l i a r i t i e s of the p a r t i -c ular t r a c t o r being used but completely ignores the amount of horsepower required by the s p e c i f i c job.* Figure C . l i l l u -s trates the v a r i a t i o n i n f u e l consumed according to the v a r i a b l e load f u e l consumption t e s t s f o r two s p e c i f i c t r a c t o r s tested at the Nebraska Tests. Another method proposed has been to use an average f i g u r e f o r horsepower hours per gallon and multiply t h i s by the horse-power required to do the s p e c i f i c job. In t h i s method an average f i g u r e f o r a l l t r a c t o r s i s us u a l l y used i n which case the si z e of the trac t o r being used i s ignored. Tractors are made i n a complete range of sizes measured i n maximum PTO HP within l i m i t s which depend on the type of f u e l the t r a c t o r uses (see Table C . l ) . Even i f a s p e c i f i c f i g u r e f o r horse-power hours per gallon i s used for each s p e c i f i c t r a c t o r , there i s a systematic b i a s ; i n the estimate as the o r i g i n i s implied as a point on the curves i n Figure C . l Hung (1966) developed formulae to predict f u e l consump-ti o n as a function of per cent load on the t r a c t o r and so take into account the siz e of the t r a c t o r and the load. When the * Hunt (1973, p. 41) reports that only 16.8% of time i s spent i n the top range i n actual farm conditions. 141 FIGURE C . l FUEL EFFICIENCY OF A DEUTZ D10006 AND A DEUTZ D5506 TRACTOR FROM NEBRASKA TESTS REPORTS 142 TABLE C . l FREQUENCY DISTRIBUTION OF TRACTOR SIZE IN MAXIMUM PTO HORSEPOWER AT RATED ENGINE SPEED OF TRACTORS TESTED IN THE NEBRASKA TESTS Maximum PTO HP at Rated Engine RPM 1958 - 1968 1964 - 1973 more than not more than gaso-l i n e d i e s e l LP gas gaso-l i n e d i e s e l LP gas 15 20 1 20 25 1 3 1 25 30 2 1 2 30 35 14 15 1 4 4 35 40 16 24 1 12 13 40 45 4 5 3 1 9 45 50 10 12 1 7 5 50 55 9 15 1 11 16 55 60 7 7 5 5 8 1 60 65 7 10 5 7 11 1 65 70 9 11 2 9 11 70 75 4 4 6 5 7 2 75 80 2 6 3 3 4 1 80 85 5 3 3 1 8 85 90 3 1 2 5 6 2 90 95 4 7 3 • 3 9 1 95 100 2 2 1 4 7 1 100 105 8 4 9 105 110 5 10 110 115 3 2 6 2 115 120 3 6 120 125 2 6 125 130 1 7 130 135 2 5 135 140 5 140 145 9 145 150 5 150 155 3 155 160 2 160 165 165 170 2 170 175 1 175 180 3 143 horsepower to operate an implement i s known the f u e l required to power that implement can be c a l c u l a t e d f o r a s p e c i f i c t r a c -tor using one of the formulae developed by Hunt: C . l Y = 0.54A + 0.62 - 0.04 697.OA C.2 Y = 0.52A + 0.768 - 0.04 738.5A + 173.0 C.3 Y = 0.289A + 0.386 - 0.04 213.9A - 25.7 where A = HP required/maximum PTO HP. Y = gal./hr. of f u e l consumption. The formulae are parabolic curves f i t t e d to the r e s u l t s for the v a r i a b l e f u e l e f f i c i e n c y tests of 118 t r a c t o r s i n the Nebraska t e s t s . The formulae are f o r gasoline, d i e s e l and LP gas t r a c t o r s r e s p e c t i v e l y . In p r a c t i c e at lease a 15% increase should be made to allow f o r d i f f e r e n c e s between f i e l d conditions as opposed to the i d e a l conditions during theNebraska tests according to Hunt (1973, p. 37). These formulae have been used to c a l c u l a t e f u e l consump-tio n for fourteen horsepower l e v e l s f o r the t r a c t o r transfer section of the model. Fuel consumption has been c a l c u l a t e d using Hunt's formulae fo r the e n t i r e range of t r a c t o r s i z e for gasoline and d i e s e l f u e l t r a c t o r s with maximum PTO HP i n c r e a -sing i n 5 HP increments. Loads are set at the median l e v e l s for the fourteen i n t e r v a l s 0-10 HP, 10-20 HP, 130-140 HP. Results are given i n Tables C.2 and C.3 f o r gasoline and d i e s e l t r a c t o r s r e s p e c t i v e l y . The c o e f f i c i e n t s i n these tables are used f o r the f u e l e n t r i e s i n the t r a c t o r t r a n s f e r a c t i v i t i e s i n the model (see Figure 3.4). 144 A f o r t r a n program was used to produce the f u e l para-meters i n Table C.2 as given i n Figure C.2. The output from t h i s program i s deposited i n a f i l e named 'FUEL' s t a r t i n g at l i n e 190. A header f o r the table can then be ins e r t e d i n the f i l e just before the output. Table C.3 was created by r e p l a -cing l i n e 0013 the f o r t r a n program with: Z = 0.289*R*0.386-0.04*(213.9*R-25.7)*«0.5 The formula on l i n e 0013 estimates the solut i o n f o r gasoline t r a c t o r s . The other two formulae are f o r l i q u i d propane and d i e s e l t r a c t o r s r e s p e c t i v e l y . The v a r i a b l e s i n the f o r t r a n program are: X = maximum PTO HP, Y = load i n HP,: Z = f u e l consumption i n g a l . per HP per hour, and GAL = f u e l consumption i n gallons per hour. TABLE C.2 FUEL CONSUMPTION FOR GASOLINE TRACTORS ACCORDING TO TRACTOR SIZE AND LOAD Maximum PTO HP 15 25 35 LOAD (PTO Horsepower) 45 55 65 75 85 95 105 115 125 135 25 1.1 1.6 2.2 30 1.2 1.8 2.2 35 1.2 2.0 2.4 3.0 40 1.3 2.2 2.6 3.1 45 1.4 2.4 2.8 3.2 3.9 50 1.4 2.5 3.0 3.3 3.9 55 1.5 2.7 3.2 3.5 4.0 4.8 60 1.5 2.8 3.4 3.7 4.1 4.8 65 1.5 3.0 3.6 4.0 4.3 4.8 5.6 70 1.6 3.1 3.8 4.2 4.5 5.0 5.6 75 1.6 3.2 4.0 4.4 4.7 5.1 5.7 6.5 80 1.6 3.3 4.1 4.6 4.9 5.3 5.8 6.5 85 1.6 3.4 4.3 4.8 5.2 5.5 5.9 6.5 7.4 90 1.7 3.5 4.4 5.0 5.4 5.7 6.1 6.6 7.3 95 1.7 3.6 4.6 5.2 5.6 5.9 6.3 6.7 7.4 8.2 100 1.7 3.6 4.7 5.4 5.8 6.1 6.5 6.9 7.5 8.2 105 1.7 3.7 4.9 5.5 6.0 6.3 6.7 7.1 7.6 8.2 9.1 110 1.7 3.8 5.0 5.7 6.2 6.6 6.9 7.3 7.7 8.3 9.1 115 1.8 3.9 5.1 5.9 6.4 6.8 7.1 7.5 7.9 8.4 9.1 10.0 120 1.8 3.9 5.2 6.0 6.6 7.0 7.3 7.7 8.0 8.5 9.2 9.9 10 . 8 125 1.8 4.0 5.3 6.2 6.8 7.2 7.5 7.9 8.2 8.7 9.2 9.9 130 1.8 4.0 5.4 6.3 7.0 7.4 7.8 8.1 8.4 8.8 9.4 10.0 10.8 135 1.8 4.1 5.5 6.5 7.1 7.6 8.0 8.3 8.6 9.0 9.5 10.1 10.8 140 1.8 4.1 5.6 6.6 7.3 7.8 8.2 8.5 8.8 9.2 9.7 10.2 10.9 11.7 11.7 TABLE C.3 FUEL CONSUMPTION BY DIESEL TRACTORS ACCORDING TO TRACTOR SIZE AND LOAD Maximum PTO HP 15 25 35 LOAD (PTO Horsepower) 45 55 65 75 85 95 105 115 125 135 25 0.6 1.1 1.7 30 0.7 1.2 1.6 35 0.7 1.3 1.7 2.3 40 0.8 1.4 1.8 2.3 45 0.8 1.5 1.9 2.3 3.0 50 0.8 1.6 2.0 2.4 2.9 55 0.8 1.7 2.1 2.5 2.9 3.7 60 0.8 1.8 2.2 2.6 3.0 3.6 65 0.8 1.8 2.3 2.7 3.1 3.6 4.3 70 0.8 1.9 2.5 2.8 3.2 3.6 4.3 75 0.9 1.9 2.5 2.9 3.3 3.7 4.2 5.0 80 0.9 2.0 2.6 3.0 3.4 3.7 4.2 4.9 85 0.9 2.0 2.7 3.2 3.5 3.8 4.3 4.9 5.7 90 0.9 2.1 2.8 3.3 3.6 4.0 4.4 4.9 5.6 95 0.9 2.1 2.9 3.4 3.7 4.1 4.4 4.9 5.5 6.4 100 0.9 2.2 2.9 3.5 3.9 4.2 4.5 5.0 5.5 6.3 105 0.9 2.2 3.0 3.6 4.0 4.3 4.6 5.0 5.5 6.2 7.0 110 0.9 2.2 3.1 3.7 4.1 4.4 4.8 5.1 5.6 6.2 6.9 115 0.9 2.2 3.1 3.7 4.2 4.5 4.9 5.2 5.7 6.2 6.9 7.7 120 0.9 2.3 3.2 3.8 4.3 4.7 5.0 5.3 5.7 6.2 6.8 7.6 125 0.9 2.3 3.2 3.9 4.4 4.8 5.1 5.4 5.8 6.3 6.8 7.5 130. 0.9 2.3 3.3 4.0 4.5 4.9 5.2 5.6 5.9 6.3 6.9 7.5 135 0.9 2.3 3.3 4.1 4.6 5.0 5.3 5.7 6.0 6.4 6.9 7.5 140 0.9 2.4 3.4 4.1 4.7 5.1 5.5 5.8 6.1 6.5 7.0 7.5 8.4 8.3 8.2 8.1 9.0 8.9 H* cn 0001 DIMENSION A(14,25) 0002 X=20.0 0003 DO 2 1=1,25 0004 DO 2 J=l,14 0005 2 A(J,I)=0.0 0006 CALL FTNCMDCSET ZEROSUPPRESS=ON » , 19 ) 0007 DO 21 1=1,25 0008 Y=5.0 0009 DO 22 J=l,14 0010 1F(X.EQ.20.0) GOTO 10 0011 R=Y/X 0012 lF(R.GT.l.O) GOTO 30 0013 Z=0.540*r+0.620-0.04*(697.0*R-00.0)**0. 0014 GAL=Z»Y*231/277.42 0015 GOTO 12 0016 10 GAL=Y 0017 12 A(J,I)=GAL 0018 Y=Y+10.0 0019 22 CONTINUE 0020 30 X=X+5.0 0021 21 CONTINUE 0022 WRITE (6,1)(<A<J,1),J=l,14),1=1,25) 0023 1 FORMAT (8X,14F5.1) 0024 STOP 0025 END Execution terminated $ run - load 6 = f u e l (190) Execution begins Execution terminated FIGURE C.2 FORTRAN PROGRAM USED TO PRODUCE TABLE C.2 AND TABLE C.3 APPENDIX D FIELD CAPACITY AND POWER REQUIREMENTS 149 F i e l d capacity can normally expect to be known by the farmer. In cases where i t i s not known, f i e l d capacity can be estimated using D.l. D.l F i e l d Capacity =Width Speed E f f i c i e n c y 8.25 where F i e l d Capacity = the acres per hour of work done,. Width = the width of the implement's operating edge, Speed = the speed i n miles per hour, and E f f i c i e n c y = the per cent of the t h e o r e t i c a l capacity f o r the s p e c i f i c operating condition. T y p i c a l values f o r speed and e f f i c i e n c y are given i n Table D . l . The p a r t i c u l a r conditions under which an implement i s operated w i l l normally determine capacity through s e t t i n g l i m i t s on speed and e f f i c i e n c y . The amount of f u e l required to operate an implement i s a function of the power required to operate the implement and thus i n d i r e c t l y on f i e l d capacity and the c h a r a c t e r i s t i c s of the implement and f i e l d conditions as well as the f u e l economy of the power source being used. The power required by an implement also determines which t r a c t o r s of those a v a i l a b l e are capable of operating the implement although there are several other fac t o r s that have to be considered. I t could normally be expected that the farmer w i l l be able to estimate the power required i n the f i e l d operations he performs. Where t h i s i s not the case, engineering formulae have been developed by Hunt (1963 and 1966) and r e f i n e d by Schmeidler et a l (1973) 150 TABLE D.l MACHINERY PERFORMANCE DATA Typical Speed T y p i c a l Energy, or Range f o r Machine Power or Perform- F i e l d Require- ance E f f i c i e n c y ment Rate Per Cent T i l l a g e 70-90 Moldboard or disk plow See F i g . 2 3.5-6 mph Ch i s e l plow 200-800 lb per 4-6.5 mph 70-90 f t L i s t e r 400-800 l b per 3-5.5 mph 70-90 bottom One-way disk, 3-5 i n . 180-400 l b per 4-7 mph 70-90 depth f t 70-90 Subsoiler 70-110, 100- 3-5 mph 160 lb per i n . depth* Land plane 300-800 lb per .. ,7 — Powered rotary t i l l e r , f t 3-4 i n . increment of cut 5-10 PTO HP 1-5 mph 70-90 per f t Harrow Single disk 50-100 l b per 3-6 mph 70-90 f t Tandem disk 100-280 lb per 3-6 mph 70-90 f t Offset or heavy tandem 250-400 lb per 3-6 mph 70-90 disk f t Spring tooth 75-310 lb per f £ 3-6 mph 70-90 Spike tooth 20-60 lb per f t 3-6 mph 70-90 Roll e r or packer 20-150 lb per ' 4.5-7. .5 70-90 (cultipacker) f t mph Rotary hoe 30-100 lb per 5-10 mph 70-85 f t Rod weeder 60-120 lb per 4-6 mph 70-90 f t F i e l d c u l t i v a t o r 150-500, 340- 3-8 mph 70-90 650 l b per ft# Row crop c u l t i v a t o r Shallow 40-80 lb per f t 2.5-5 mph 70-90 Deep 20-40 l b per f t 1.5-3 mph 70-90 per i n . depth Bed sled or shaper 15 HP per row 2-4 mph 70-90 Unpowered rotary - 3-7 mph 70-90 c u l t i v a t o r 151 TABLE D.l continued F e r t i l i z e r and Chemical Application F e r t i l i z e r spreader, pull-type Anhydrous ammonia applicator Sprayer Planting Corn, soybeans, or cot-ton, d r i l l i n g seed only Corn, soybeans, or cot-ton, d r i l l i n g , a l l attach. Grain d r i l l Harvesting/ Mower only Mower-conditioner, cutterbar-type Mower-conditioner, f l a i l type S e l f - p r o p e l l e d mower-conditioner-windrower Conditioner only Rake Baler Hay cuber Loose hay sweep Hay stacker, separate bucking operation Bale loader-stacker, loading only Forage harvester, f l y -wheel or c y l i n d e r knife Green forage Wilted forage Day hay or straw Corn s i l a g e 3-5 mph 60-75 420 lb per knife 3-5 3-5 mph mph 60-75 50-80 100-180 lb per 3-6 mph 50-85 row 250-450 lb per 3-6 mph 50-85 row 30-100 lb per f t 2.5-6 mph 65-85 1 DB HP per f t , 0.5 PTO HP per 5-7 mph 75-85 f t 1- 1.5 DB HP per f t , 2-2.5 PTO HP per f t 10-17 PTO HP 2- 2.5 DB HP per f t , 2-2.5 PTO HP per f t 2 PTO HP per f t 1.5-2.5 HP hr per ton 15-20 HP hr per ton 1- 2.5 HP hr per ton 1.5-5 HP hr per ton 2- 5 HP hr per ton 1-2.5 HP hr per ton 4-6 4-6 mph mph 3-6 mph 5-7 mph 4-5 mph 3-10 tons per hr 3-5 tons per hr 7-24 tons per hr 24-38 tons| per hr 9-15 tons per hr Perform-ance rate i s generally a d i r e c t function of the PTO | horsepower a v a i l a b l e | 60-85 60-85 55-85 75-85 60-85 60-85 60-85 152 TABLE D.l concluded Harvesting (contd) Forage harvester, f l y -wheel or c y l i n d e r knife Corn s i l a g e recutter attachment Windrower, small grain Combine Small grain Corn Corn picker 1 row, t r a i l e d 2 row, t r a i l e d 2 row, mounted Cotton picker 1 row, mounted 2 row, s e l f - p r o p e l l e d Cotton s t r i p p e r , 2 row Beet topper Beet harvester Rotary mower, h o r i -zontal blade Open f i e l d Row crop Forage blower Wilted forage Corn or grass s i l a g e 0-100 per cent increase i n above fi g u r e s 1.5-2 HP per f t cut 1 PTO HP per i n . c y l i n d e r width 8-10 HP 12-20 HP 12-18 HP 6-8 HP per row 30-45 HP per row 3-8 HP per f t cut 9-18 HP per f t cut 1-2 HP hr per ton 1-1.5 HP hr per ton from the power source. Usual t r a v e l speeds are 1.5 to 4 mph 5-7 mph 75--85 2-4 mph 65--80 2-4 mph 65--80 2-4 mph 60--80 2-4 mph 60--80 2-4 mph 60--80 0.6--0.8 60--75 acres per hour 0.9--1.2 60--75 acres per hour 1-2 acres 60 -75 per hour 2-3 mph 60 -80 3-5 mph 60 -80 3-8 mph 75 -85 3-6 mph 75 -85 20- 30 tons — per hour 20- 50 tons -per hour * Ranges shown are f o r sandy loam and medium or c l a y loam, r e s p e c t i v e l y . # Second range shown i s f o r heavy cl a y s o i l s . / For t r a i l e d harvesting equipment, add power required to overcome r o l l i n g r e sistance to the l i s t e d s o i l or crop power requirements. § Energy requirements per ton are lowest with high feed rates, low cutterhead speeds, and long c u t s . 153 may be used to predict power requirements. Hunt's c a l c u l a t i o n of the power required to operate an 'implement' i s based on what he terms 'force f a c t o r s ' . A force f a c t o r i s the pounds of force needed to power a foot of width of an implement. T y p i c a l ranges f o r the force f a c t o r s of various implements are given i n Table D . l . When the force f a c t o r i s known or can be estimated from engineering tables, the drawbar horsepower required to operate the implement can be calcu l a t e d as i n 3.4. D.2 Drawbar Horsepower = force f a c t o r x width x speed 375 where width i s i n fe e t , speed i n miles per hour, force, f a c t o r i n l b s . / f e e t , and 1/375 i s a conversion f a c t o r . Schmeidler et a l noted that t r a c t o r horsepower i s normally rated i n PTO horsepower rather than Drawbar horse-power so they provided a method to convert drawbar int o an equivalent PTO HP using formula D.3 D.3 Drawbar Horsepower = Drawbar Horsepower (PTO equivalent) 0.96 x TER Where TER = the " t r a c t i v e e f f i c i e n c y r a t i o " or r a t i o of drawbar horsepower to axle horsepower. and 0.96 = the r a t i o of axle horsepower to PTO horsepower. The r a t i o 0.96 i s taken as a constant. The value of TER i s a function of s o i l type and per cent s l i p of the drive wheels which i n turn depends on rear t r a c t o r weight, method of imple-ment attachment and t i r e c h a r a c t e r i s t i c s . Schmeidler et a l 154 takes the optimum value of TER f o r each s o i l type. A c e r t a i n percentage (optimum) s l i p of the dr i v e wheels give the maximum (or optimum) TER f o r each s o i l type. V a r i a -t i o n from the optimum wheel s l i p does not bring about a great change i n the TER though the value of TER varies considerably from one s o i l type to another (see Table D.2). The main change i n the TER comes when the wheel s l i p declines from the optimum. TABLE D.2 EFFECT OF SOIL TYPE ON TRACTIVE EFFICIENCY RATIO S o i l Type Optimum Non-Optimal Per Cent Wheel S l i p % Wheel S l i p TER Optimal Wheel S l i p Plus 5% Optimal Wheel S l i p Minus 5% % Wheel S l i p TER % Wheel S l i p TER Concrete 6.0 .92 11.0 .90 1.0 .80 Firm S o i l 9.0 . 78 14.0 .75 4.0 .68 T i l l e d S o i l 11.5 .64 16.5 .62 6.5 .60 Soft orSandy 12.5 .53 17.5 .51 7.5 .49 This method i s s u i t a b l e f o r machines whose main demand on the t r a c t o r i s drawbar horsepower. For machines whose main demand i s f o r PTO horsepower ( c a l l e d processing machines), the c a l c u l a t i o n of HP required i s somewhat d i f f e r e n t . Examples of t h i s type of machine are b a l e r s , combines, and other harvesting machines. The HP required to operate these machines i s rated i n HP per ton and t h e i r capacity i s measured i n tons/hour. The HP required to operate t h i s type of machine i s given by D.4. . 155 D.4 PTO HP = P r o c e s s i n g C a p a c i t y x PTO Energy, where PTO Energy = c o e f f i c i e n t i n HP/ton from s t a n -dard t a b l e s , and P r o c e s s i n g C a p a c i t y = F i e l d C a p a c i t y x Y i e l d . APPENDIX E GLOSSARY OF ENGINEERING TERMS 157 Axel Horsepower: The amount of horsepower a t r a c t o r d e l i v e r s at the rear wheel axels. ASAE: The American Society of A g r i c u l t u r a l Engineers. Organization which sets standards f o r a g r i c u l -t u r a l machinery and publishes many engineering research papers. Capacity: The rate of work done f o r f i e l d operations measured i n acres per hour. Capacity i s a function of the width of the implement, f i e l d speed and f i e l d e f f i c i e n c y . Drawbar Horsepower: The amount of horsepower the t r a c t o r makes ava i l a b l e to p u l l an implement at the drawbar. For operations that do not require the power take o f f t h i s i s the t o t a l amount of power which i s being used by the implement. The amount of drawbar horsepower a t r a c t o r can develop depends on the weight on the rear wheels, wheel charac-t e r i s t i c s , the surface and the design of the t r a c t o r . E f f i c i e n c y : E f f i c i e n c y i s a measure of the amount of time l o s t due to the c h a r a c t e r i s t i c s of the implement being used and the shape of the f i e l d i n per cent. 100% i s defined as the capacity of the implement operating on an i d e a l f i e l d the width of the implement (so turning i s unnecessary) and without having to deviate from normal operating speed to adjust the implement, e t c . Typ i c a l values range from 50% to nearly 100%. Force Factor: Term invented by Donnell Hunt to represent the amount of force required to operate one foot of an implement measured i n l b s . per f o o t . Horsepower: Unit used to measure power. Power i s the rate of doing work. Work i s merely the use of energy to accomplish c e r t a i n goals. For t r a c -tors energy i n the form of f u e l i s converted into the physical motion of an implement. Implement: Three terms are used to describe the machinery i n t h i s t h e s i s . Implements are used to des-cr i b e machinery other than t r a c t o r s . Machine i s a general term which includes both imple-ments and t r a c t o r s . Implement i s used i n t e r -changeably with equipment. 158 Job: Two terms are used to describe the use of machinery i n t h i s t h e s i s : job, and operations. Jobs are the task which machinery i s used to accomplish. Plow an acre i n a c e r t a i n time of the year f o r example. An operation on the other hand i s the use of s p e c i f i c implements i n a s p e c i f i e d manner (power, speed, etc.) to perform a job. Machine: See implement. Operation: See job. Power Take Off: Also c a l l e d PTO. Some implements operate through the action of being pulled across the surface of a f i e l d . Others require a source of rotary power from the t r a c t o r , mowers and balers f o r example. This rotary power i s delivered by the PTO. An archaic term i s be l t power. Tractor s i z e i s usually rated i n terms of the maximum PTO power the t r a c t o r can produce. The maximum PTO power of a t r a c t o r i s usually more than the maximum drawbar because less power i s l o s t i n operating the PTO than i n moving the t r a c t o r . Tractor E f f i c i e n c y Ratio: The r a t i o of drawbar horsepower to axel horsepower which would be equal to one i n the i d e a l world. Some power i s loss because of wheel s l i p so t h i s f i g u r e i s less than one i n r e a l l i f e . Tractor Size: Usually measured i n maximum PTO horsepower. See power take o f f . Speed at which an implement or t r a c t o r moves i s measured i n miles per hour r e l a t i v e to the ground when themachine i s operating normally and t r a v e l l i n g i n a st r a i g h t l i n e . The s l i g h t spinning of the drive wheels of a tra c t o r that normally takes place. Wheel s l i p i s measured i n the percentage reduction i n tra v e l speed from what the speed would be were there; no wheel s l i p . A c e r t a i n amount of wheel s l i p i s best (optimal) f o r converting the energy expanded i n the drive wheels into forward motion. Speed: Wheel S l i p 159 The width of an implement i s usually the theo-r e t i c a l width which can be determined by a simple measurement with a ya r d s t i c k . The actual width i n use i s t y p i c a l l y less than the t h e o r e t i c a l width because of the s l i g h t over-lap of the machine's operations'which w i l l be r e f l e c t e d i n the e f f i c i e n c y f i g u r e f o r the implement. APPENDIX F VALIDATION OF THE LOGIC OF THE MODEL 161 The c e n t r a l section of the model i s the machine operating a c t i v i t i e s . Consequently the l e v e l of machine operations was taken as a s t a r t i n g point from which the arithmatic of a s o l u t i o n of the model could be worked through by hand to v a l i d a t e the l o g i c of the model. The l e v e l of machine a c t i v i t y was com-pared with that required by the crop plan i n the s o l u t i o n to see i f exactly the r i g h t amount was a v a i l a b l e (see Table 1.1). The crop plan was used to c a l c u l a t e the land and purchased i n -puts used which i n turn was compared with the amount of these resources selected by the model. The r e s u l t s of t h i s c a l c u l a t i o n are given i n Tables F.2 and F.3. The crop plan and the record of machine operating a c t i v i t y together were used to c a l c u l a t e the labour required by the plan. The r e s u l t s of t h i s c a l c u l a -t i o n are given i n Table F.4. The record of machine operating a c t i v i t y only was used to c a l c u l a t e the amount of t r a c t o r time required at various loads. The ca l c u l a t e d time i s compared with the time selected by the model i n Table F.5. Repair and maintenance costs were c a l c u l a t e d based on tra c t o r time while f u e l costs were calcul a t e d based on hours of t r a c t o r use at each horsepower l e v e l . These r e s u l t s are given i n Tables F.5 and F.3 r e s p e c t i v e l y together with model r e s u l t s f o r comparison. Errors of diffe r e n c e between c a l c u l a t e d r e s u l t s and model r e s u l t s are very small i n a l l cases. Usually d i f f e r e n c e s can be found i n conjunction with a point where i t i s necessary to divide by a three or a seven or some such s i m i l a r number. D i f f e r -ences are s l i g h t l y larger f o r production and value of production because y i e l d s were only put i n cor r e c t to one decimal place. 162 TABLE F . l VERIFICATION OF FEASIBILITY OF FARM PLAN Operation Hours Model Acres of Work Cal c . Acres i n Farm Plan Machine Costs OA 46.5 372. 372. 31.6665 OB 73.125 585. 585. OC 0. 0. OD 16.14286 113. 113. 5.9728582 OE 0. 0. OF 17.0 34. 34. 10.2 OG 35.83333 214.99998 215. 22.933312 OH 0. 0. OI 0. 0. OJ 2.0 14. 14. 0.6 OK 20.0 10. 10. 28.0 OL 16.0 24. 24. 22.4 OM 7.6 38. 38. 10.64 ON 39.0 34. 34. 153.306 OO 12.66667 38.00001 38. 57.114015 OP 61.66667 185.00001 185. 123.33333 OQ OR OS 41.5 83. 83. 13.28 OT 27.66667 83.00001 83. 25.0106696 OU 50.0 50. 50. 32.4 OV 16.66667 50.00001 50. 11.6 OW 10.0 50. 50. 0.24 OX 33.33333 49.999995 50. 1.199999 OY 33.33333 49.999995 50. 1.199999 OZ 100.0 50. 50. 320.0 QA 26.4 132. 132. 10.1376 QB 5.0 10. 10. 2.88 QC QD 17.0 34. 34. 5.1 QE 29.0 116. 116. 4.35 QF 10.4 52. 52. 1.248 QG 10.000002 30.00006 30. 3.0 QH 6.0 24. 24. 1.62 QI 25.5 102. 102. 24.99 QJ 62.5 375. 375. 30.0 QK 2.14286 15.000002 15. 0.642858 QL QM 92.4 462. 462. 55.44 QN 46.5 279. 279. 22.785 QO 52.00001 156.00003 156. 48.308000 QP 12.4994 12.49940 12.49940 12.49940 Source: Solution to l i n e a r programming problem and ca l c u l a t e d from crop plan and input data. TABLE F.2 VERIFICATION OF THE PRODUCTION AND SALES IN THE MODEL Crop Crop Harvested Product Production Value of Production Model Calculated Model Calcu-la t e d Late Potatoes 50 Potatoes 735.0 ton 735.0 ton 58800.0 58800.0 Ea r l y Potatoes 0 Beans 52 Beans 267.4987 267.5 28237.13 28238.0 Ea r l y Peas 15 Peas 31.533 31.533 4428.81 4429.0 Pea Vines 15.0 15.0 789.9 790.0 Late Peas 30 Peas 63.066 63.066 8857.62 8858.0 Pea Vines 30.0 30.0 1577.8 1580.0 Strawberries 5 Strawberries 1515.1515 lb 1515.1515 lb 500.0 500.0 Raspberries 0 Barley 38 Barley 2572.5 bu 2572.5 bu 7768.95 7769.0 Cabbage 10 Cabbage Seed 10763 l b 10763 lb 6434.12 6434.0 Turnip 4 Turnip Seed 5870 lb 5870 lb 3522.0 3522.0 Sugar Beet Seed 20 Sugar Beet Seed 37866 lb 37866 l b 6815.88 6815.0 Source: Solution to the l i n e a r programming problem and calculated from crop plan and input data. 164 TABLE F.3 VERIFICATION OF PURCHASED INPUTS Purchased Quantity Value Input Model Calculated Model Calculated PI01 86.85 86.85 i n . $ 86.85 $ 86.85 PI02 123.0 123 g a l . 1020.90 1020.90 PI03 3.325 3.375 T 675.00 6 75.00 PI04 16.9 16.9 T 1740.70 1740.70 PI05 76 .0 76.0 gal 2216.16 2216.16 PI06 5.15 5.15 T 489.25 489.08 PI07 13.0 13.0 T 3315.00 3315.00 PI08 60.66667 60.66617 pkg 466.67 460.72 PI 09 20000.0 20000.0 1 2000.00 . 2000.00 PI10 4.0 4 u 80.00 80.00 P i l l 4792.0 4792.0 1 458.54 458.60 PI12 10.0 10 u 150.00 150.50 PI13 7770.0 7770 1 726.50 726.50 PI14 -PI15 1.755 1.755 T 296.625 296.625 PI 16 38.0 38 cwt 266.00 276.00 PI17 2.85 2.85 T 570.00 570.00 PI18 - -PI19 30.0 30 T 5610.00 5610.00 PI20 50.0 50 T 6500.00 6500.00 PI21 1.5 1.5 cwt 42.00 42.00 PI22 50.0 50 gal 1050.00 1050.00 PI23 10.0 TO gal 555.52 555.52 Purple Gasoline 1987.17 1984.17 615.09 615.09 Diesel Fuel 1859.li 1857.13 409.00 409.00 Source: Solution to l i n e a r programming problems and ca l c u l a t e d from crop plan and farm input data. TABLE F.4 VERIFICATION OF LABOUR IN THE MODEL Time Labour Hours Labour i n Slack Hired Labour - . «. • Period Calculated Actual Calculated Actual Calculated Actual 0 J r 820.0 810.0 0 Fb 720.0 720.0 0 Mr 82.10824 697.89176 697.89180 1 Ap 2 27.97077 198.02923 198.02923 35.32665 144.67335 144.67335 3 61.16542 143.83458 143.83459 4 40.95810 40.95811 1 My 82.953 82.953 2 188.49940 188.50000 0.0 3 195.0 195.0 0.0 4 95.23334 114.76666 114.76667 1 Jn 10.28571 169.71429 169.71429 2 1.0 179.0 179.0 3 55.0 55.0 4 55.0 55.0 1 J l 145.0 145.0 2 183.1 183.1 3 47.97651 47.97650 4 41.63112 41.63112 1 Ag 163.61334 16.38666 2 45.92667 45.92667 3 26.66667 26.66667 4 140.43333 51.66667 51.66667 1 Sp 2 3 27.0 436.51899 481.96202 183.0 0.0 0.0 183.0 0.0 0.0 160.51899 159.96202 160.51899 159.96203 4 469.85232 0.0 0.0 193.85232 193.85232 1 Oc 49.53256 160.46744 160.46744 2 13.96774 166.03256 166.03256 3 15.4 194 .6 194.6 4 18.5 161.5 161.5 0 Nv _ 750.0 750.0 0 Dc - 810.0 810.0 Source: Solution to l i n e a r programming problem and c a l c u l a t e d from crop plan and inpu data. TABLE F.5 VERIFICATION OF THE TRACTOR SELECTION BLOCK Tractor Hours Ca l c . 1 1 X O W yJ W \_» JL Level TA TB TC TD TE TF Total T o t a l 14 13 12 11 10 134.6 73.1 52.0 134.6 73.1 52.0 134.6 73.1 52.0 09 08 07 06 05 88.0 43.8 88.0 43.8 88.0 43.8 04 03 02 01 Other 100.0 120.8 32.1 277.2 2.0 10.0 120.8 32.1 277.2 112.0 120.8 32.1 277.2 112.0 To t a l Hours 259.7 231.8 430.1 2.0 10.0 Model Rep. Costs 147.73 91.53 43.84 0.56 2.20 Calculated R & M Costs 147.73 91.53 43.84 0.56 2.20 Source: Solution to l i n e a r programming problem and calculated from crop plan a input data. APPENDIX G THE OPTIMAL FARM PLAN 168 G.l THE NATURE OF THE FARM REPORT From a range of a l t e r n a t i v e s as i n Table 5.5 the farm operator may be able to s e l e c t a farm plan that best s u i t s his subjective evaluation of r i s k and personal preferences with the knowledge of the e f f e c t of his de c i s i o n on his income. I t i s conceivable that i f a workshop approach i s used to u t i l i z e the model i n i t s f i n a l form by CANFARM that the farm operator could specify l e v e l s of crops i n some intermediate range and the model could be run i n simulation mode to provide a de t a i l e d p r o j e c t i o n of the most important physical and f i n a n c i a l records of the farm. For the purposes of the thesis the base plan was selected and a farm report prepared. The nature and scope of the farm report i s of great importance to the usefulness of the planning model. The record system of the.farm may be conceptually divided i n t o four categories. There i s the main d i v i s i o n between physical records and f i n a n c i a l records. Both of these categories may be subdivided according to whether the records are independent of the farm plan or not. This i s most obvious i n the case of the physical records where the input-input, input-output, and the output-output r e l a t i o n s h i p s of the production function and the constraints are independent of the farm plan. I t i s t h i s type of records that have been used to create the documenta-tio n of the case farm. Another series of records can be predicted and/or maintained which r e l a t e d i r e c t l y to i l l u s t r a t i n g the e f f e c t of the choice of a p a r t i c u l a r farm plan (point on the production f u n c t i o n ) . This second set of 169 records c o n s t i t u t e the Farm Report and constitutes the output of the planning model from the perspective of the farm operator. In Table G.l t h i s d i v i s i o n of the record system f o r a farm i s i l l u s t r a t e d . The types of records that should be included i n each section are also i l l u s t r a t e d . The term •S t a t i c Records' used to describe records that are independent of the farm plan i s somewhat misleading i n that i t i s to be expected that the S t a t i c Records may be c o n t i n u a l l y revised based on the r e s u l t s of the farm plan but t h i s i s a r e s u l t of more information and experience becoming a v a i l a b l e to the farm operator rather than the p a r t i c u l a r plan selected. A s u i t a b l e farm report c o n s i s t i n g of the "flow records" fo r the case farm i s given i n Appendix G.2. The CANFARM records were followed as c l o s e l y as possible i n formulating the fi n a n -c i a l records i n the report. Several major di f f e r e n c e s do appear however. A d e t a i l e d Cash Flow Statement was prepared. The Income Statement i s on accrual basis rather than a cash basis. The Enterprise Statements have been abbreviated and an extra column incorporated to i l l u s t r a t e per acre c o s t s . Although the CANFARM system does not include any physical records, t h e i r importance f o r management purposes should not be underestimated. The Farm Report i n Appendix G.3 therefore incorporates U t i l i z a t i o n Reports f o r the resources labour, t r a c t o r s , implements, and purchased inputs. A crop plan, marketing plan, and a production record are also included. As r o t a t i o n , r i s k and marketing c o n s t r a i n t s were so important i n l i m i t i n g the f i n a l p l a n a r e p o r t on the shadow p r i c e s of these c o n s t r a i n t s i s a l s o g i v e n . 171 TABLE G.l THE MAIN CATEGORIES OF THE FARM RECORD SYSTEM Physical Records F i n a n c i a l Records S t a t i c Constraints on Records Resources Prices Machine Operation C o e f f i c i e n t s C u l t u r a l P r a c t i s e s and Associated Y i e l d s Purchase Records Net Worth Statements C a p i t a l Cost Allowance Schedules Depreciation Schedules Flow U t i l i z a t i o n of Records Resources Crop Plan Actual Production, Yields and Sales Shadow Prices Income Statement Cash Flow Statement Enterprise Statements Cost Accounts Tax Records G.2 THE FINANCIAL RECORDS 173 TABLE G.2 INCOME STATEMENT 1976 OPTIMAL 'PLANA' Accrual Crop Sales Straw 10,800 Barley 23,760 F i e l d Beans 16,200 F i e l d Peas 25,920 Potatoes 110,380 Strawberries 6,000 Sugar Beet Seed 18,240 Le a f / F r u i t Seed (Turnip) 4,500 Cabbage Seed 34,000 Pea Vines 2,925 Raspberries 2,800 Total 255,525 Expenses Rent 7,740 Purchased Inputs Twine 87 Premerge 747 Pea F e r t i l i z e r 675 Potash 2,348 Eptam 2,274 F e r t i l i z e r 0-0-22 463 F e r t i l i z e r 11-55-0 1,912 Ben l a t e 266 Beet F e r t i l i z e r 2,000 Turnip F e r t i l i z e r 573 Bees 400 Cabbage F e r t i l i z e r 1,453 Raspberry F e r t i l i z e r 124 Strawberry F e r t i l i z e r 297 Barley Seed 756 Barley F e r t i l i z e r 1,620 Early Potato Seed 2,240 Potato F e r t i l i z e r 9,312 Late Potato Seed 8,190 Bli g h t 53 Sprout I n h i b i t o r 1,323 Monitor I n s e c t i c i d e 700 Total Purchased Inputs 37,814 Purple Gasoline 977 Diesel Fuel 934 Tractor R & M 678 General Farm Equip. R & M 1,906 Part Time Labour 4,478 Interest on Operating C a p i t a l - 662 Total Variable Inputs 53,864 TABLE G.2 continued Fixed Expenses Car Gas Oxygen Truck R & M Automobile R & M Building R & M Yard R & M Structures R & M Tools Custom Work General Expenses Handling Charge , Freight and Trucking Interest Insurance Equipment & Machine Insurance Car Insurance Truck Insurance Telephone H y d r o / E l e c t r i c i t y Property Tax Administration Costs Fees & Subscriptions Legal Services Other Professional Services O f f i c e Supplies Miscellaneous Expense Total Fixed Expenses Total Expenses Income les s Expenses 174 Accrual $ 1,058 90 504 1,364 4,528 114 367 1 63 99 120 288 111 857 22 406 691 118 695 6,119 45 45 55 105 18 78 17,961 71,825 183,700 Source: Solution to farm planning model i n optimization mode and CANFARM records. TABLE G.3 CASH FLOW STATEMENT : 1976 OPTIMAL 'PLAN A' Jan. $ Crop Sales Barley Straw F i e l d Beans F i e l s Peas Potatoes Strawberries Sugar Beet Sd Le a f / F r u i t Sd Cabbage Seed Pea Vines Raspberries Crop Expenses Purchased Inputs Twine Premerge Pea F e r t . Potash Eptam F e r t . 0-0-22 F e r t . 11-55-0 Ben^late Beet F e r t . Turnip F e r t . Bees Cabbage F e r t . Rasp. F e r t . Straw. F e r t . Barley Seed Barley F e r t . E. Pot. Seed Potato F e r t . Feb. $ Mar. $ Apr, $ 2000 573 756 2240 May $ 87 747 675 2348 2274 463 1912 266 1453 124 297 1620 9312 June $ July $ Aug, $ Sep. $ Oct. $ Nov. $ Dec. $ 23760 5400 5400 8400 7800 12960 12960 19200 10080 13602 13603 3000 3000 31215 18240 4500 34000 2800 1462 146 1462 "3001) 5800 24600 62062 35825 13603 87955 400 r-i O TABLE G.3 continued Jan. Feb. Mar. Apr. May $ $ $ $ $ Crop Exes cont. L. Pot. Seed 8190 B l i g h t 53 Sprout I n h i b i t o r Monitor Insect. Tot a l Purch. Inputs Purple Gasoline Di e s e l Fuel Rent Tractor R & M Gen.Farm Equip R & M Part Time Lab. Int. on Op. C a p i t a l 3 7 Total Var. Exes 3 7 Total Exes Car Gas 70 80 Oxygen Truck R & M 7. 80 80 Auto. R&M 26 30 30 121 121 B u i l d . R&M 1150 1150 Yard R&M Struc. R&M 30 31 31 Tools Custom Work Gen. Exes 33 33 Handling Ch. 40 40 Fre i g h t & Tr. Interest Insurance Equip. & Mach. Insur. June $ July Aug. $ Sep. $ Oct, $ Nov. $ 1323 700 40 76 121 1214 31 33 66 76 1 63 103 857 121 58 10 160 128 8 Dec, $ 93 293 39 3 91 305 153 130 337 204 5 133 32 22 71 7740 67 189 95 4 113 73 112 25 80 369 223 7 221 559 427 20 215 762 3501 183 230 348 359 333 201 -225 -474 -508 3179 4414 30892 2801 891 1932 3990 -358 7232 80 63 63 63 283 15 110 113 118 42 37 11 9 677 90 29 275 100 114 924 8 TABLE G.3 concluded Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Total Exes cont $ $ $ $ $ $ $ $ $ $ $ • Car Insur. 406 Truck Insur. 691 8 15 19 Telephone 9 10 10 8 9 10 11 9 Hydro/Elec. 150 151 151 43 43 43 32 29 25 28 Property Tax 51 51 51 5966 Admin. Costs 15 15 15 Fees & Subs 15 15 15 Legal Serv. 15 20 20 Other Prof. 105 Services 8 O f f i c e Sup. 2 8 •7 O Misc. Exes / O T o t a l Fixed Expenses 421 445 1547 1505 1514 1568 1534 6027 379 455 1428 To t a l Expenses 424 452 4726 5919 32406 4369 2425 7959 4369 97 8660 Cash Surplus 424 -452 -4726 -5919 -32406 -1369 3375 16641 57693 35728 4943 Accum. Cash Surplus -•424 -876 -5602 -11521 -43927 -45296 -41921 -25280 32413 68141 73084 Dec. 1138 19 87936 Source: Solution to farm planning model i n optimization mode and CANFARM records. H i TABLE G.4 178 ENTERPRISE STATEMENT 63 ACRES OF LATE POTATOES : 1976 OPTIMAL 'PLAN A Revenue Crop Sales Bi-product Sales T o t a l Sales Units Per Acre 15.59 ton Costs Per Acre . $ 1,447 T o t a l Costs $ 91,130 Expenses Purchased Inputs Chemical F e r t i l i z e r Potato F e r t i l i z e r 1,200 lb. 112 7,056 Herbicide Eptam Sprout I n h i b i t o r Other Chemical Blight Control Monitor I n s e c t i c i d e Seed Other 1 gal. 1 gal, 3 lb. ,2 gal. 1 ton 29 21 1 11 130 1,827 1,323 53 700 8,190 T o t a l Purchased Inputs Purple Gasoline ) Diesel Fuel ) Repair & Maintenance Costs Tractors General Farm Equipment Part Time Labour T o t a l V a r i a b l e Expenses A l l o c a t e d Overheads Tot a l Costs ' Revenue l e s s Expenses 7.4 3.8 10.9 59 385 56 441 1,006 466 239 674 3,716 24,244 3,528 27,772 63,408 Source: Solu t i o n to farm planning model i n optimization mode 179 TABLE G.5 ' ENTERPRISE STATEMENT 20 ACRES OF EARLY POTATOES : 1976 OPTIMAL •PLAN A' Revenue Crop Sales Bi-product Sales T o t a l Sales Expenses Purchased Inputs Chemical F e r t i l i z e r Potatoe F e r t i l i z e r Units Per Acre 6 ton Costs Per Acre $ 960.00 1,200 lb. 96.00 T o t a l Costs — J 19,200.00 1,920.00 Herbicide Other Chemical Seed Other 1,400 l b . 112.00 2,240.00 Total Purchased Inputs Purple Gasoline ) Diesel Fuel ) Repair & Maintenance Costs Tractors General Farm Equipment Part Time Labour To t a l V a r i a b l e Expenses Allocated Overheads Tot a l Costs Revenue l e s s Expenses 18.33 7.28 12.47 246.08 59.00 305.08 654.92 366.60 145.60 249.40 4,921.60 1,180.00 6,101.60 13,098.40 Source: Solution to farm planning model i n optimization mode 180 TABLE G.6 ENTERPRISE STATEMENT 30 ACRES OF BEANS : 1976 OPTIMAL 'PLAN A' Units Per Costs Per T o t a l Revenue Crop Sales Bi-product Sales T o t a l Sales Expenses Purchased Inputs Chemical F e r t i l i z e r Potash 0-0-22 Bean F e r t i l i z e r Herbicide Eptam Premerge Other Chemical Benelate Seed Other Total Purchased Inputs Purple Gasoline , ) Diesel Fuel ) Repair & Maintenance Costs Tractors Acre Acre Costs • $ $ 4 ton 540.00 16,200 200 l b . 100 l b . 500 l b . 10.30 4.75 63.75 309 143 1,913 0.5 g a l . 1.5 gal.-14.58 12.45 437 374 3.5 units 8.86 266 114.69 3,442 3.35 100.5 1.57 47 General Farm Equipment 2.24 67 Part Time Labour To t a l V a r i a b l e Expenses 121.85 3,656 Allo c a t e d Overheads 59.00 1,770 Total Costs 181.00 5,430 Revenue l e s s Expenses 359.00 10,770 Source: S o l u t i o n to farm planning model i n optimization mode 181 TABLE G.7 ENTERPRISE STATEMENT 15 ACRES OF LATE PEAS : 1976 OPTIMAL 'PLAN A' Units Per Acre Costs Per Acre $ Tot a l Costs Revenue Crop Sales Bi-product Sales T o t a l Sales 2.4 ton 1.0 ton 576.00 65.00 641.00 8,640.00 975.00  9,615.00' Expenses Purchased Inputs Chemical F e r t i l i z e r F e r t i l i z e r Potash 150 lb, 200 lb. 15.00 10.30 225.00 155.00 Herbicide Premerge 1 gal 8.30 124.5 Other Chemical Seed Other Twine 1.93 Tota l Purchased Inputs Purple Gasoline ) Diesel Fuel ) Repair & Maintenance Costs Tractors General Farm Equipment Part Time Labour T o t a l V a r i a b l e Expenses A l l o c a t e d Overheads T o t a l Costs Revenue l e s s Expenses units 1.93 28.9 35.53 532.95 3.27 49.05 1.83 27.45 3.33 49.95 43.96 659.40 59.00 885.00 112.96 1,544.40 528.00 7,071.00 Source: Solution to farm planning model i n optimization mode. TABLE G.8 ENTERPRISE STATEMENT 30 ACRES OF EARLY PEAS : 1976 OPTIMAL 'PLAN A» 182 Revenue Crop Sales Bi-product Sales T o t a l Sales Units Per Acre 2.4 ton 1.0 ton Costs Per Acre 576.00 65.00  641.00 Tota l Costs t 17,280.0 1.950.0  19.230.0 Expenses Purchased Inputs Chemical F e r t i l i z e r F e r t i l i z e r Potash Herbicide Premerge Other Chemical 150 lb. 200 lb. 1 gal, 15.00 10.30 8.30 450.0 309.0 249.0 Seed Other Twine 1.93 units T o t a l Purchased Inputs Purple Gasoline ) Die s e l Fuel ) Repair & Maintenance Costs Tractors General Farm Equipment Part Time Labour T o t a l V a r i a b l e Expenses A l l o c a t e d Overheads To t a l Costs Revenue l e s s Expenses 1.93 35.53 3.00 1.60 2.29 42.42 59.00 101.42 540.00 58.0 1.066.0 90.0 48.0 68.7 1,272.6 1,770.0 3,042.6 16,200.0 Source: Solu t i o n to farm planning model i n optimization mode. 183 TABLE G.9 ENTERPRISE STATEMENT 108 ACRES OF BARLEY : 1976 OPTIMAL 'PLAN A' Revenue Crop Sales Bi-product Sales T o t a l Sales Units Per Acre 2 ton 80 bales Costs Per Acre $ 220.00 100.00  320.00 Tota l Costs $ 23,760 10,800  34.560 Expenses Purchased Inputs Chemical F e r t i l i z e r F e r t i l i z e r Potash 150 l b . 200 l b . 15.00 10.30 1,620 1,112 Herbicide Other Chemical Seed 1 Other To t a l Purchased Inputs Purple Gasoline ) Diesel Fuel ) Repair & Maintenance Costs Tractors General Farm Equipment Part Time Labour To t a l V a r i a b l e Expenses A l l o c a t e d Overheads Tot a l Costs Revenue l e s s Expenses cwt 7.00 756 32.30 3,488 3.43 370 1.27 137 3.47 375 7.06 762 47.53 5,133 59.00 6,372 107.00 11,505 213.00 23.004 Source: Solution to farm planning model i n optimization mode 184 TABLE G.10 ' ENTERPRISE STATEMENT 20 ACRES OF SUGAR BEETS : 1976 OPTIMAL 'PLAN A' Revenue Crop Sales Bi-product Sales T o t a l Sales Units Per Acre 2,400 lb, Costs Per Acre 912.00 To t a l Costs $ 18,240.00 Expenses Purchased Inputs Chemical F e r t i l i z e r Beet F e r t i l i z e r 0-0-22 Potash Herbicide 1,000 lb. 150 lb. 200 lb. 100.00 7.12 10.30 2,000.00 142.40 206.00 Other Chemical Seed Other T o t a l Purchased Inputs Purple Gasoline ) Diesel Fuel ) Repair & Maintenance Costs Tractors General Farm Equipment Part Time Labour T o t a l V a r i a b l e Expenses Al l o c a t e d Overheads Tot a l Costs Revenue l e s s Expenses 117.42 4.96 1.51 7.13 131.02 59.00 290.00 622.00 2,348.4 99.20 30.20 142.60 2,620.4 1,180.0 5,800.00 12,440.00 Source: Solution to farm planning model i n optimization mode. TABLE G . l l ENTERPRISE STATEMENT 5 ACRES OF TURNIP : 1976 OPTIMAL 'PLAN A» 185 Revenue Crop Sales Bi-product Sales To t a l Sales Units Per Acre 2,000 lb, Costs Per Acre $ 900.00 Tota l Costs $ 4,500 Expenses Purchased Inputs Chemical F e r t i l i z e r Turnip F e r t i l i z e r 0-0-22 Potash Herbicide 1,198 l b . 150 l b . 200 l b . 114.65 7.12 10.30 573 36 52 Other Chemical Seed Other Bees Total Purchased Inputs Purple Gasoline ) Diesel Fuel ) Repair & Maintenance Costs Tractors General Farm Equipment Part Time Labour To t a l V a r i a b l e Expenses A l l o c a t e d Overheads Total Costs Revenue l e s s Expenses 1.0 unit 20.00 152.07 4.73 1.39 7.07 165.26 59.00 224.00 676.00 100 760 24 7 35 826 295 1,121 3,379 Source: S o l u t i o n to farm planning model i n optimization mode. 186 TABLE G.12 ENTERPRISE STATEMENT 20 ACRES OF CABBAGE : 1976 OPTIMAL 'PLAN A' U n i t s Per Acre Revenue Crop S a l e s B i - p r o d u c t S a l e s T o t a l S a l e s C o s t s Per Acre $ 2,000 l b . 1,700.00 T o t a l C o s t s $ 34,000 Expenses Purchased I n p u t s Chemical F e r t i l i z e r Cabbage F e r t i l i z e r 0-0-22 Potash H e r b i c i d e 777 l b . 150 l b . 200 l b . 72.65 7.12 10.30 1,453 142 206 Other C h e m i c a l Seed Other ^ n n Bees 1.0 u n i t 15.00 300 T o t a l Purchased Inputs 105.07 2,101 P u r p l e G a s o l i n e ) A ac aa D i e s e l F u e l ) Re p a i r & Maintenance C o s t s T r a c t o r s General Farm Equipment P a r t Time Labour 1.18 24 8.79 176 T o t a l V a r i a b l e Expenses 119.99 2,400 A l l o c a t e d Overheads 59.00 1,180 T o t a l C o s t s 179.00 3,580 Revenue l e s s Expenses 1,521.00 30,420 Sour c e : S o l u t i o n t o farm p l a n n i n g model i n o p t i m i z a t i o n mode 187 TABLE G.13 ' ENTERPRISE STATEMENT 5 ACRES OF STRAWBERRIES : 1976 OPTIMAL 'PLAN A 1 Revenue Crop Sales Bi-product Sales T o t a l Sales Expenses Purchased Inputs Chemical F e r t i l i z e r Strawberry F e r t . Units Per Acre 702 lb, Costs Per Acre $ 4,000 l b . 1,200.00 59.50 Tota l Costs $ 6,000.00 297.50 Herbicide Other Chemical Seed Other T o t a l Purchased Inputs Purple Gasoline ) Diesel Fuel ) Repair & Maintenance Costs Tractors General Farm Equipment Part Time Labour T o t a l V a r i a b l e Expenses A l l o c a t e d Overheads T o t a l Costs Revenue l e s s Expenses 59.50 297.50 0.90 1.01 1.42 62.83 59.00 122.00 1,078.00 4.50 5.05 7.10 314.00 295.00 609.00 5,391.00 Source: S o l u t i o n to farm planning model i n op t i m i z a t i o n mode TABLE G.14 ENTERPRISE STATEMENT 2 ACRES OF RASPBERRIES : 1976 OPTIMAL 'PLAN A« Revenue Crop Sales Bi-product Sales Total Sales Expenses Purchased Inputs Chemical F e r t i l i z e r Raspberry F e r t . Units Per Acre 3,500 l b . 750 lb. Costs Per Acre $ 1,400.00 61.88 Total Costs $ 2,800.00 123.76 Herbicide Other Chemical Seed Other Total Purchased Inputs Purple Gasoline ) Diesel Fuel ) Repair & Maintenance Costs Tractors General Farm Equipment Part Time Labour Total V a r i a b l e Expenses Allocated Overheads Total Costs Revenue less Expenses 1.75 1.96 3.34 68.93 59.00 128.83 1,271.17 3.50 2.92 6.68 137.86 118.00 255.86 2,542.34 Source: Solution to farm planning model i n optimization mode. G.3 THE PHYSICAL RECORDS TABLE G.15 UTILIZATION REPORT FOR LAND : 1976 OPTIMAL 'PLAN A' Crop Amount Land A Early Land B Summer Rented Amount Land A Late Summer Land B Rented Opportunity Land A Land B Cost Rented Late Potatoes Ear l y Potatoes 35 0 23 0 5 20 35 0 23 0 5 0 0.0 161.5 0.0 161.5 0.0 0.0 Late Peas Ear l y Peas Beans 6 0 0 9 30 30 0 0 0 6 0 0 9 0 30 0 0 20 0.0 0.0 0.0 0.0 0.0 0.0 65.4 65.4 65.4 Barley 47 0 61 0 0 0 0.0 0.0 0.0 Strawberries Raspberries 5 2 - - 5 2 - -0.0 0.0 -Sugar Beet Seed Cabbage Seed Turnip Seed 20 20 5 : - 40 40 10 - - 0.0 0.0 0.0 - -T o t a l Cropped 140 92 86 138 62 5 Tot a l Unused 0 0 14 2 30 95 Shadow Price f o r Land 124.00 124.00 91.30 0.0 0.0 0.0 Source: Solution to farm planning model i n optimization mode. CO o c n <D cn o h-1 c rt H-O 3 rt O Hi 0) t i 3 TJ i— 1 OJ 3 3 H-3 i£> 3 O a CD 3 O TJ rt H* 3 H* N CU rt H-O 3 3 O a CD fD o o 3 U) r t t j Cu H* 3 (D a c 3 O o 3 cn r t t j CO H*" 3 (D a ^ c , H 3 : o , ^ n a n c D > x X X X X • • • n o 3 M r t t j D> H> 3 r t Late 1 Potatoes Early Potatoes Beans Late Peas Early Peas Barley Sugar Beet Seedf^ Turnip Seed Cabbage Seed Strawberries Raspberries Unused II II b h * r o r o i r o u i o u i o l I c o U l I I I I I I I I I I ro to l i I I I I l l l I ro u i t|\ IN ir. Il\ IN l i t r o OJ J> c o r o i u i o u i o o H i H i H i r o o o> cr> c n v o ~ j v o c o c o l l l l c n oo r o c n u i l I I I I I l I l I l l c n oo c n oo U l H i c n U l CO Hi H i c o r o I o ^ r o o O 0 Land A Land B Rented Land A l l Land co o c 3 a Land A Land B Rented Land A l l Land n o 3 cn rti t | 0) H" 3 rt CO 3" OJ a o n fD n po o > CO H CO H r H H3 Hi VO -J c n O T3 H H > no > •z. H3 > CO r o c n 192 TABLE G.17 LABOUR UTILIZATION : 1976 OPTIMAL 'PLAN A» Date Hours Available Own Family To t a l Hours Unused U t i l i z e d Used Hired January 1 - January 31 810 0 810 810 0 February 1 - February 28 720 0 720 720 0 March 1 -March 31 780 0 780 589 191 A p r i l 1 - A p r i l 8 210 26 226 98 128 A p r i l 9 - A p r i l 15 180 0 180 14 166 A p r i l 16 - A p r i l 23 210 0 210 93 117 A p r i l 24 - A p r i l 30 180 48 . 228 174 54 May 1 - May 8 210 48 258 130 128 May 9 - May 15 180 48 228 0 228 11 May 16 - May 23 : 195 0 195 0 195 43 May 24 -May 31 210 0 210 127 83 June 1 - June 8 180 0 180 167 13 June 9 - June 15, 180 0 180 175 5 June 16 - June 23 210 54 264 210 54 June 24 - June 30 180 54 234 180 54 July 1 - July 8 210 54 264 0 264 July 9 - July 16 210 54 264 0 264 July 17 - July 23 180 54 234 0 234 July 24 - July 31 210 54 264 33 231 August 1 - August 7 180 0 180 0 180 190 August 8 - August 15 210 0 210 114 96 August 16 - August 23 210 0 210 190 20 August 24 -August 31 180 0 180 96 84 Sept. 1 - Sept. 8 210 0 210 175 35 Sept. 9 -Sept. 15 180 96 276 0 276 310 Sept. 16 - Sept. 23 210 112 322 0 322 214 Sept. 24 - Sept. 30 180 96 276 0 276 352 October 1 - October 8 210 0 210 156 54 October 9 - October 16 180 0 180 180 0 October 17 - October 24 210 0 210 210 0 October 25 - October 31 180 0 180 164 16 Nov. 1 -Nov. 30 750 0 750 750 0 Dec. 1 -Dec. 31 810 0 810 810 0 Source: Solution to farm planning model i n optimization mode. TABLE G.18 UTILIZATION REPORT FOR TRACTORS : 1976 OPTIMAL 'PLAN A' Power Tractor Hours 1370 Case TA D19 TB D17 TC D16 TD Massy TE JD & DB TF Total Hours Maximum Shadow Pri c e 130 120 110 100 90 80 70 60 50 40 30 20 10 0 Unspec 140 130 120 110 100 90 80 70 60 50 40 30 20 10 i f ied 0 0 166 0 118 0 0 0 0 0 46 0 0 0 189 70 0 14 0 0 152 Tota l Hours per Tractor T o t a l R & M Costs Average R & M Costs 284 46 425 $169 $35 $295 59<t 76<t 69<t — — 0 0 158 0 0 55 0 60 391 13 0 5 10 60 609 23 $6 $171 $5 10tt 28<t 22<t 0 0 166 0 118 0 0 0 235 70 0 172 55 464 167 Maximum Shadow Pr i c e $3.75 $0.00 $0.00 $0.12 $0.15 $0.00 1447 $681 47ct 0 0 $7.55 0 $7.18 0 0 0 $3.09 $2.31 0 $0.91 $0.96 $0.57 Source: Solution to farm planning model i n optimization mode. TABLE G.19 UTILIZATION REPORT FOR IMPLEMENTS : 1976 OPTIMAL •PLAN A' Implement Code Name Hours of Use Cost/ Hour Total Costs Maximum Shadow Price IA 17 f t . C u l t i v a t o r 55.75 .681 37.97 0.0 IB Packer Mulch 143.62 .9768 140.29 2.66 IC Harrow 25.52 .12 3.06 0.0 ID Packer 19.27 .30 5.73 0.0 IG Stan H Seeder 22.5 .60 13.50 0.0 IH Seed D r i l l 52.25 .64 33.44 0.0 II F e r t i l i z e r Spreader 10.70 .30 3.21 0.0 I J Swather 73.27 1.40 109.58 0.0 IK Seed Combine 81.00 4.509 365.23 0.0 IL Plow 88.67 2.00 177.33 0.0 IN Sprayer 126.78 .6.0 76.07 0.0 10 Tedder 76.5 .32 24.48 347.0 IP Baler 51.0 .868 44.27 0.0 IQ Potato Planter 83.0 .648 53.78 0.0 IR Ridger 27.67 .096 2.66 0.0 IS Floa t 16.6 .024 0.40 0.0 IT Wagons 161.67 .036 5.82 0.0 IU Potato Combine 166.0 3.20 531.20 0.0 IV Subsoiler 21.6 .387 8.24 0.0 IW Rotovator 5.0 .576 2.88 0.0 IX R o t o t i l l e r 16.0 .384 6.30 0.0 IZ Disc C u l t i v a t o r 22.5 .30 6.75 0.0 JA DT C u l t i v a t o r 35.0 .15 5.26 0.0 JB Row C u l t i v a t o r 6.0 .12 0.72 0.0 JC J Deer Row C u l t i v a t o r 10.0 .30 3.00 0.0 JD Disc 106.91 .48 51.37 0.0 IE Rake 79.0 .49 38.71 0.0 IF Power Mulch 71.36 .929 66.34 0.0 JG Truck 20.75 3.20 66.40 0.0 1889.09 Source: Solution to farm planning model i n optimization mode. 

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