Farm Plan Whole-Farm Planning (LP)
Whole Farm Planning Whole-farm planning is largely a matter of enterprise selection. What crops and livestock enterprises will be produced on this farm in the next year?
Background: Enterprise Combinations Economic theory behind whole-farm planning.
Production Possibility Curve Definition: A Production Possibility Curve (PPC) is the geometric representation of the combination of products that can be produced with a given set of inputs. It can be defined for an entire economy or for a single firm.
Graph of PPC enterprise 2 enterprise 1
Types of Enterprise Relationships • Competitive with constant substitution • Competitive with increasing substitution • Supplementary • Complementary
Competitive with Constant Substitution enterprise 2 These enterprises use the same inputs, in the same ratios. enterprise 1
Competitive with Increasing Substitution enterprise 2 The enterprises use different ratios of inputs and inputs experience diminishing marginal returns in each case. enterprise 1
Supplementary enterprise 1 makes use of some inputs that are not needed for enterprise 2 enterprise 2 supplementary range enterprise 1
Complementary enterprise 2 as we produce more of enterprise 1, we can also produce more of enterprise 2 enterprise 1
Examples Competitive Constant Sub: Competitive Increasing Sub: Supplementary: Complementary corn and milo corn and cotton soybeans and winter stockers broilers and cattle
Terms • Physical substitution ratio: • Profit Ratio Quantity of Output Lost Quantity of Output Gained Profit per unit of gained output Profit per unit of lost output
Physical Substitution Ratio The physical substitution ratio is the slope of the Production Possibility Curve.
Profit Ratio Profit Ratio is the slope of the isoprofit line: = 1* Y1 + 2 *Y2 where 1 is profit per unit of enterprise 1, Y1 is the number of units (e.g. acres) produced, 2 is the profit per unit of enterprise 2 and Y2 is the number of units produced.
Decision Rule Physical Substitution Ratio = Price Ratio
Graph: Point of Tangency enterprise 2 isoprofit lines and PPC enterprise 1
In real life We don't know the PPC. We are going to approximate this process using a technique called "Linear Programming."
Linear Programming Linear programming maximizes or minimizes a particular linear objective function, subject to linear restrictions. Here our objective function is to maximize the returns over variable costs. This is a one-year or short-run plan.
Returns over variable costs The returns over variable costs come from the enterprise budgets.
Farm Planning Process • Inventory available resources • Select enterprises to be considered. • Obtain appropriate Enterprise Budgets. • Figure out the "technical coefficients" and "RHS" (limits) • Develop linear programming tableau. • Find optimal enterprise combination.
Resource Inventory The resource inventory tells you how much of each resource (e.g. land, labor, other inputs) you have on the farm. Labor resources is usually calculated for several periods of the year. Land may be of several different types.
Technical Coefficients Technical Coefficients tell you how much of each resource you need to produce one unit of a given enterprise. For example, it takes one acre of row-crop land to produce one acre of cotton.
Restrictions in LP Each limited resource requires one linear restriction in the LP model. They are normally "inequality constraints."
Consider a simple example: Vegetable production in Zaire. Possible enterprises: Lettuce and tomatoes. Each bed of lettuce makes a profit of 30 "Zaires" (local currency). Each bed of tomatoes makes a profit of 40 Zaires.
Marketing Restrictions Marketing: The local market will absorb no more than the output of: 16 beds of tomatoes 8 beds of lettuce
Labor Restriction The student who wants to grow vegetables can work up to 24 hours per week on his garden. Tomatoes require 1 hour per week. Lettuce requires 2 hours per week.
Setting up the LP: Objective Function = 1 Y1 + 2 Y2 Y1 is the number of tomato beds Y2 is the number of lettuce beds = 40Y1 + 30 Y2
Restrictions Y1 ≤ 16 (marketing restriction for tomatoes) Y2 ≤ 8 (marketing restriction for lettuce) Y1 + 2Y2 ≤24 (labor) So we can produce no more than 16 beds of tomatoes and 8 beds of lettuce. And we must limit our labor so that the amount expended is less than 24 hours per week.
All Together in Equation Form Objective max 40Y1 + 30 Y2 = Subject to: Y1 ≤ 16 Y2 ≤8 Y1 + 2Y2 ≤24
Graphing the constraints lettuce (mktg 1) 12 (labor) 8 (mktg 2) 24 16 tomatoes
Creating The "PPC" lettuce (mktg 1) 12 (labor) 8 (mktg 2) Feasible Region 24 16 tomatoes
Feasible Region lettuce (8,8) 8 Feasible Region (16,4) 16 tomatoes
Optimizing: Max profit $760 lettuce isoprofit lines slope = -30/40 Profit-Max Combination (16,4) 8 Feasible Region 16 tomatoes
With more enterprises With more than two enterprises, we can't graph the solution. We will use some software to find our answer. First we must put the problem in proper form.
Equation Form Again Objective max 40Y1 + 30 Y2 = Subject to: Y1 ≤ 16 Y2 ≤8 Y1 + 2Y2 ≤24
The LP "tableau" Y1 Y2 Type RHS OBJ 40 30 MT1 1 0 LE 16 MT2 0 1 LE 8 LBR 1 2 LE 24 Where LE means less than or equal to and RHS stands for "right hand side"
The RHS The RHS (right-hand side) contains the amount of the constrained resource you have available.
Technical Coefficients The numerical values in the constraint rows, other than the RHS entries, are the technical coefficients.
Objective Function The values in the OBJ row are the amount of profit per unit of enterprise produced. In your farm plan, you will get these values from the Enterprise Budgets. For your OBJ values: Use Returns above Variable Costs.
Using Excel to Solve the LP I took the tableau for the vegetable example, and solved it using Excel Solver (a tool in Excel). I get the answers 16 beds of tomatoes, 4 beds of lettuce, and profit of $760. If you pop this page open, you can see the formulas I used. You'll learn how to use Solver in the following slides.
LP Example for Farm Plan You have 7 possible enterprises on the farm: cotton, peanuts, corn, soybeans, winter stockers, summer stockers, and cow-calf. Enterprise budgets for these three crops are available on my class site.
Restrictions come from your data • cropland: how much cropland? • pasture: how much pasture? • labor: how many hours of labor per month from permanent employees (operators' labor plus year-round hired labor)?
LAND The sample farm has 625 acres cropland and 411 acres of pasture. These will be RHS values in the LP.
LABOR This farm has 2.5 permanent employees, 1 operator plus 1.5 year-round hired. With about 4.33 weeks per month and 60 hours per person per week, monthly labor available in hours is: 2.5x4.33x60 =649.5
SEASONS If you plant soybeans or peanuts over the summer, you can follow those crops with winter grazing. For the most part, you can't do that with cotton or corn. (Some people do, but it is more complicated.) So corn and cotton take up land all year. Soybeans or peanuts leave land available for winter grazing.
Putting together the tableau • use the enterprise budgets • the information on resource limits that you obtain from your data • the labor requirements by month spreadsheet
LP Objective function • Maximize returns above variable costs • Copy in the returns above variable costs for each acre of crops and each head of livestock. • The correct cell in each Enterprise Budget is shaded in yellow.
Corn Budget for LP objective
Make an Excel Table • One row for objective • One row for cropland (summer season) • One row for cropland available for winter grazing • 12 rows for labor, one for each month • One row for "Level" (part of the solution) • One column for each enterprise (7) • One column for "type" • One column for RHS • One column for "Used" (more of the solution)