"Land and Food Systems, Faculty of"@en . "DSpace"@en . "UBCV"@en . "Short, C. Cameron"@en . "2010-02-19T05:01:49Z"@en . "1977"@en . "Master of Science - MSc"@en . "University of British Columbia"@en . "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 alternative 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 readily adaptable to a wide range of commercial vegetable farmers in Canada but sufficiently flexible to be adaptable to the particular situation of a specific farm. A multiperiod linear programming model was built and validated through its application to a large commercial vegetable farm.\r\nThe relevant theory of the firm was reviewed with special attention made to the theory's application to vegetable farms. The structure of a linear programming problem was discussed and related to the theory of the firm and vegetable farms.\r\nSpecial emphasis was placed on the problem of modeling the machinery used in vegetable production. The work of agricultural engineers was examined to determine the technological relationships involved in machine operation. Other crop budgeting models which involved the construction of similar planning models for a different sector of the agricultural community, especially the Purdue Crop Budgeting Models were reviewed.\r\nThe model constructed was able to deal with machinery constraints by building a number of machine operating activities and tractor transfers so that the time constraint for a particular job would consist of any subset of the predefined set of time periods. Standard coefficients were prepared based on engineering formulae for fuel consumption and repair and maintenance costs for tractors. All inputs in the model except repair and maintenance costs were in physical units. This made it necessary to build several different types of purchasing or renting activities but facilitates the interpretation of data and the use of the model in a large number of different situations.\r\nThe model was validated through its application to a large commercial vegetable farm in British Columbia. The model was run in simulation mode by forcing the model to follow the farm's 1974 crop plan and altering yields and prices to yields and prices that actually occured in that year. In this manner the reliability of the cost coefficients of the input data and the relationships between resources could be evaluated and compared with the results recorded in the farm's CANFARM records.\r\nThe model was run in optimization mode with expected 1976 prices and yields to demonstrate the use of the model in selecting an optimal farm plan. A total of six plans were prepared based on alternate market and risk constraints and yields. These were compared with the plan selected by the farmer without the aid of the model. A detailed report on one of the farm plans v/as also prepared."@en . "https://circle.library.ubc.ca/rest/handle/2429/20494?expand=metadata"@en . "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 \u00C2\u00A9 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\u00C2\u00BB 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' \u00E2\u0080\u00A2 \u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2 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\u00C2\u00BB 183 G.10 E n t e r p r i s e Statement: 20 Acres of Sugar Beets 1976 Optimal 'Plan A\u00C2\u00BB 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' \u00E2\u0080\u00A2. - 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 \u00E2\u0080\u00A2Plan 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 ...,.\u00E2\u0080\u009E.-. 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 \u00E2\u0080\u00A2 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. \u00E2\u0080\u00A2 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\u00C2\u00A3- 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 \u00E2\u0080\u00A2 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 \u00C2\u00BB 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) \u00E2\u0080\u00A2 (14) .98 .98 .98 .98 Machine: (1) (2) (3) \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 (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: C \u00E2\u0080\u00A2H JC u ro 2 CQ CU c \u00E2\u0080\u00A2ri 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 + -+ \u00E2\u0080\u00A2= + & + & 0 Labour T r a c t o r A cu -a \u00C2\u00A3 \u00C2\u00B0 T r a c t o r B H [u Machine A a, Machine B + + + + + + + + + + + + \u00E2\u0080\u0094 + H Labour H cu ^ T r a c t o r A B o \u00C2\u00A3 -H T r a c t o r B \u00E2\u0080\u00A2' ^ 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 + + + + + + + + -- + - + + + + + + + + + + + - + - + - + <\u00C2\u00A3+ ^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 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 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 . a a a \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 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 \u00E2\u0080\u00A2 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 \u00C2\u00BB ^ 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 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 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 cu \u00E2\u0080\u00A2H c \u00C2\u00A3} U C in 4J ro EL, s >-> c SH ro CU < < < CQ a > H O -P rH rH rH rH \u00E2\u0080\u00A2H CU CU CU D Cr-3 Ct. \u00E2\u0080\u00A2 3 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 fjLi \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 0 \u00E2\u0080\u00A2 H-> C - r l \u00E2\u0080\u00A2rH 4J Maximum u SI u >i >i >i fd u < 3 3 in (0 CQ CQ CQ CQ IH Objective - - - -Cash + + + + Fuel A January - + + \u00C2\u00A30 Fuel A February - + + 6 0 Fuel A March \u00E2\u0080\u00A2 \u00E2\u0080\u0094 + + 6 0 \u00E2\u0080\u00A2 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 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 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 \u00C2\u00A3! rd 3 rO CU 3 Li \u00E2\u0080\u00A2\"3 C Xi rd CU x: x: CL, w n rd rd x: x: U u w to rd rd U U ro O \u00E2\u0080\u00A2 Li \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 X I XJ Maximum Li LI c c o o cu CU CQ CQ \u00E2\u0080\u00A2J \u00E2\u0080\u00A2J Objective - - + + Cash January - + +^ Cash February + - - + 60 Cash March + - 60 FIGURE 4.7 THE CASH BLOCK OF THE MODEL CO CO CO 0 Li c \u00E2\u0080\u00A2C 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 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 X ro \u00E2\u0080\u00A2H ro \u00E2\u0080\u00A2rH ro \u00E2\u0080\u00A2H 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 - \u00C2\u00A3 0 10 Horsepower - \u00C2\u00A3 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\u00C2\u00A3 + Cash February + *0 Cash March + *0 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 Fixed Costs Control 1.0 = 1.0 \u00E2\u0080\u00A2 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\u00C2\u00A3: 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 \u00C2\u00BB Land 7*-> ( 3 - D Li Purchasedl \u00E2\u0080\u0094> 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 \u00E2\u0080\u00A2Car Gas 1,058 1,058 Diesel Fuel 382 382 \u00E2\u0080\u00A2Oxygen 90 90 Tractor R & M 662 662 \u00E2\u0080\u00A2Truck R & M 504 504 \u00E2\u0080\u00A2Automobile R & M 1,364 1,364 Harvest Equip. R & M 7 7 Gen. Farm Equip. R & M 2,438 2,438 \u00E2\u0080\u00A2Building R & M 4,528 4,528 \u00E2\u0080\u00A2Yard R & M 114 114 \u00E2\u0080\u00A2Structures R & M 367 367 \u00E2\u0080\u00A2Tools 1 1 Part Time Labour 3,346 3,346 \u00E2\u0080\u00A2Custom Work 63 63 \u00E2\u0080\u00A2General Expenses 99 99 \u00E2\u0080\u00A2Handling Charge 120 120 87 TABLE 5.1 continued Cash Accrual $ $ Expenses continued \u00E2\u0080\u00A2Freight & Trucking 288 288 \u00E2\u0080\u00A2Interest 111 111 \u00E2\u0080\u00A2Insurance 857 857 \u00E2\u0080\u00A2Equip. & Machine Insurance 22 22 \u00E2\u0080\u00A2Car Insurance 406 406 \u00E2\u0080\u00A2Truck Insurance 691 691 \u00E2\u0080\u00A2Telephone 118 118 \u00E2\u0080\u00A2H y d r o / E l e c t r i c i t y 692 692 \u00E2\u0080\u00A2Property Tax 6,119 6,119 \u00E2\u0080\u00A2Administration Costs 45 45 \u00E2\u0080\u00A2Fees & Subscriptions 45 45 \u00E2\u0080\u00A2Legal Service 55 55 \u00E2\u0080\u00A2Other Prof. Services 105 105 \u00E2\u0080\u00A2Office Supplies 18 18 \u00E2\u0080\u00A2Miscellaneous Expense 78 78 Total 53,295 52,395 \u00E2\u0080\u00A2Considered 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_ \u00C2\u00A3_ 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 - \u00E2\u0080\u0094 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 - \u00E2\u0080\u0094 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 - \u00E2\u0080\u0094 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 \u00E2\u0080\u0094T~ $ $ % 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 \u00E2\u0080\u00A2-- 15,883 13,907 .1,976 14.21 Herbicide 3,237 4,170 - 933 - 22.37 \u00E2\u0080\u00A2Other P e s t i c i d e 2,109 - 2,109 Seed 6,766 6,786 - 20 - 0.29 230 - 230 \u00E2\u0080\u00A2Bees Baler Twine 87 1,046 - 959 - 91.68 \u00E2\u0080\u00A2*Lime 388 - 388 221 - 221 106 - 106 \u00E2\u0080\u00A2\u00E2\u0080\u00A2Gen. Crop S & S \u00E2\u0080\u00A2\u00E2\u0080\u00A2Seed 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 \u00E2\u0080\u00A2 . 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 \u00E2\u0080\u00A2Items which are i n the model but do not obviously correspond to items i n CANFARM records. \u00E2\u0080\u00A2\u00E2\u0080\u00A2Items 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 \u00E2\u0080\u00A2 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#\u00C2\u00BB 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 \u00E2\u0080\u00A2OPTIMAL\u00E2\u0080\u00A2PLANS 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. \u00E2\u0080\u0094 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 ^ ^ \u00E2\u0080\u009E T ^ ^ ^ m \u00C2\u00AB Farm Income Acres Harvested Per cent of Total Vegetable Acres Harvested $000's % acres % Potatoes 10,736* 54.5 11,920 47.3 Cucumbers 324 2.0 356 1.5 Lettuce 1,165 6.1 614 2.5 Onions 1,036 5.5 644 2.6 Tomatoes** 439 3.0 240 1.0 Cabbage 818 4.2 802 3.2 Carrots 695 3.6 460 1.8 Processed Peas 1,281 6.0 4,648 18.5 Processed Beans 562 2.8 1,660 6.9 Residual 1,779 12.3 3,730 14.7 Total 18,835 100.0 25,074 100.0 * Average f o r the years 1970-73 only. \u00E2\u0080\u00A2* Average f o r the years 1971-72 only. Source: \"Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s . \" S t a t i s t i c s Canada, 21-003 , A g r i c u l t u r a l D i v i s i o n , Ottawa: Sept.-Dec, 1972, 1973, 1974, 1975. 126 Vegetable TABLE A.5 YIELD PER ACRE COMPARED FOR SELECTED CROPS IN BRITISH COLUMBIA, CANADA, UNITED STATES, AND WASHINGTON STATE: AVERAGES 1970-74 B r i t i s h Columbia Canada Washington tons per acre . . United States Potatoes Carrots Onions 11.18 11.57 12.52 9.1 11.57 11.78 19.10 21.47 18.92 11.65 12.64 14.80 Peas Beans Corn 2.05 3.05 5.60 1.29 2.00 4.01 1.66 3.21 5.80 1.29 2.48 4.78 Lettuce Cabbage Cucumbers 14.45 7.42 6.28 6.39 9.84 6.63 8.57 10.88 n.a. 10.80 10.70 n.a. Source: \"Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s . \" S t a t i s t i c s Canada, 21-003, A g r i c u l t u r e D i v i s i o n , Ottawa: July-Sept., 1971, 1973, 1975 and 1971, 1973, 1975. \" A g r i c u l t u r a l S t a t i s t i c s 1974.\" United States Depart-ment of A g r i c u l t u r e , Chapter IV, pages 149-203, Washington. 127 TABLE A.6 A COMPARISON* OF FARM SIZE IN CANADA, BRITISH COLUMBIA AND WASHINGTON STATE MEASURED IN ACRES AND VALUE OF PRODUCTS SOLD Average Size (acres) Value of Sales ($/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 \u00E2\u0080\u00A2H - r l (0 S-i a a CL) K 5 \u00E2\u0080\u0094 Li \u00E2\u0080\u00A2H 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 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 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 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 > \u00E2\u0080\u00A2z. H3 > CO r o c n 192 TABLE G.17 LABOUR UTILIZATION : 1976 OPTIMAL 'PLAN A\u00C2\u00BB 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 "Thesis/Dissertation"@en . "10.14288/1.0094091"@en . "eng"@en . "Agricultural Economics"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "A vegetable farm planning model for primary producers"@en . "Text"@en . "http://hdl.handle.net/2429/20494"@en .