Linear Programming in Agriculture: Maximizing Profit in a Simple Crop Farm, Study notes of Agricultural economics

Download Linear Programming in Agriculture: Maximizing Profit in a Simple Crop Farm and more Study notes Agricultural economics in PDF only on Docsity! 1 ABM 332 OPTIMIZATION MODEL --- LINEAR PROGRAMMING 2 User Interface Decision Maker Strategic Models Tactical Models Operational Models Model Building Blocks and Subroutines Data Base Management System Model Base Management System Finance Production Marketing Personnel Research Other Other Internal Data External Data T R A N S A C T I O N D A T A Data Base Model Base COMPONENTS OF A MODERN DECISION SUPPORT SYSTEM SOURCE: Sprague and Watson (House, Ed.) 3 DATA ORIENTED vs. MODEL ORIENTED Analysis Info. System Data Analysis System File Drawer System Suggestion Models Accounting Models Representaion System Optimization Models Data OrientedA A A Data Retrieval Data Analysis Simulation Suggestion A Model OrientedA 4 P A coomon tool used by managers in addressing operational and tactical decisions < Standard algorithm readily available (Solver in Excel) < Post optimality information is very valuable in making business adjustments < Easy to cheat on the assumptions < Easy to incorporate traditional economic concepts P Three main parts: LINEAR PROGRAMMING CONCEPTS 1. Have activities or process available as alternatives 2. Desire to maximize or minimize something 3. Have constraints or restrictions 9 Corn (x1) Soys (x2)Economic situation: Gross Income 260 200 Direct Expenses 110 60 Net Income 150 140 ----per acre figures ----- SIMPLE CROP FARM (only two crops) Resources required: Land (Ac) 1 1 Harvest Labor (Hr) 0.45 0.60 Capital ($) 110 60 Resources available: Land (Ac) 400 Harvest Labor (Hr) 225 Capital ($) 35,000 Also a minimum of 70 acres of corn to be grown 10 (Simple Crop Farm Continued) Considering only one resource at a time, what is the maximum acres that can be grown of corn and soybeans? HINT: Divide the amount of resource available by the amount needed by the activity Corn Soys Cropland 400/1 = 400 400/1 = 400 Harvest Labor 225/0.45 = 500 225/0.60 = 375 Capital 35000/110 = 318 35000/60 = 583 11 (Simple Crop Farm Continued) Adding in the desire to maximize or minimize something, need to consider the relative profits of the two crops Slope of Iso-Revenue Line = - ————————— Net Inc. X1 (Corn) Net Inc. X2 (Soys) = - ———— 150 140 = - 1.071 How many acres of soybeans does it take to generate the same income as 500 acres of corn? 500 * 1.071 = 535.5 12 SIMPLE FARM GRAPHIC SOLUTION 600200 300 400 500100 700 Acres Corn (X1) 100 200 600 300 400 500 Max. Land Max. Labor Max. Capital Min. Corn Iso-Revenue Line 220 180 a b c d e Feasible Region 13 (Simple Crop Farm Continued) Solution Comparisons: D(Opt.) B C E Acres Corn 220.0 70.0 100.0 318.0 Acres Soys 180.0 322.5 300.0 0.0 Total Net Inc. 58200 55650 57000 47700 Land Used (Ac) 400.0 392.5 400.0 318.0 Labor Used (Hr) 207.0 225.0 225.0 143.1 Capital Used ($) 35000 27050 29000 35000 14 (Simple Crop Farm Continued) 179 218 180 181 182 183 184 223219 220 221 222217 Acres corn (X1) Impact of Adding One Acre of Land Max. Land (400 Ac.) Max. Capital Max. Land (401 Ac.) 182.2 218.8 19 P For more complex problems, it is not possible to solve linear programming problems with graphical methods P Can use one of several linear programming algorithms < SOLVER in Excel – Can handle limited sized problems < Special linear programming packages using the Simplex method – AELP for a smaller problems – LINDO (with What’sBest) for very large problems P How is it done with SOLVER < Works fine but it take some extra time to set up the problem in the proper structure SOLVING THE SIMPLE CROP FARM WITH AN ALGORITHM 20 P It finds the maximun profit (net income) P Overall profit < This is in the “Target Cell” & Answer Report – Profit = $58,200 (return to fixed resources) P Level of activities that maximize the profit < This is found in the “Changing Cells” and Answer Report – Corn = 220 acres – Soys = 180 acres P Utilization of fixed resources (contraints) < This is found in the “Constraints Cell” or the Answer Report – Land and capital totally utilized – 18 hours excess harvest labor – Minimum corn exceed by 150 acres UNDERSTANDING THE RESULTS FROM SOLVER 21 (Understanding SOLVER Results Continued) P Cost of forcing in non-optimal activities < Found in the Sensitivity Report – There are none for this problem P Cost of the meeting the constrains < Found in the Sensitivity Report – Land = $128/acre – Capital = $0.20/dollar – Harvest labor and minimum corn acres are not binding, thus their values are zero P Also given with SOLVER are: < Price range over which the solution holds < Resource range over which the solution holds