# Introduction to AMPL

Size: px
Start display at page:

Transcription

1 Math567 (Spring 2019) - AMPL Handout 1 1 Introduction to AMPL A demo version of AMPL could be downloaded from All chapters from the AMPL book are available as a PDF document from the above web page. Go through the first chapter in detail most of the basics necessary to get started are given in Chapter 1. 1 AMPL Basics AMPL is a modeling language which allows the user to represent optimization models in a compact and logical manner. The data (for instance, demand for each month, amount of raw material available, distance between cities, etc.) is handled separately from the optimization model itself (which consists of the decision variables, objective function, and constraints). Thus the user need not alter the original model each time a small change is made in the data. You need to create a model file (for example FarmerJones.mod) and a data file (FarmerJones.dat). The model file declares the data parameters, the variables, objective function, and the constraints in a symbolic fashion. All the numbers (actual data) are provided in the data file. Note the following facts. It is a good convention to name model files as something.mod, and data files as something.dat (AMPL will accept any name for the model and data files though). To help your computer identify the files as text files, it might be a good practice to add a.txt extension to the file names, e.g., something.mod.txt. Every declaration (of a parameter, variables, objective function or a constraint) ends with a ; (semicolon). This is true for both the model and the data files. You can specify values for a parameter in the data file only after it is already declared in the model file. Else, AMPL will give an error. Before solving problems, you need to specify the solver. We will be using CPLEX as the solver. It is a good practice to start each AMPL session by typing option solver cplex; at the ampl: prompt. 1.1 Example: The Farmer Jones problem (Taken from Introduction to Mathematical Programming by Winston and Venkataramanan.) Farmer Jones must decide how many acres of corn and wheat to plant this year. An acre of wheat yields 25 bushels of wheat and requires 10 hours of labor per week. An acre of corn yields 10 bushels of corn and requires 4 hours of labor per week. Wheat can be sold at \$4 per bushel, and corn at \$3 per bushel. Seven acres of land and 40 hours of labor per week are available. Government regulations require that at least 30 bushels of corn need to be produced in each week. Formulate and solve an LP which maximizes the total revenue that Farmer Jones makes. The model and data files are given below. You can use any text editor to create the model and data files. For instance, Notepad works well in Windows. You could use MS Word or WordPad, but make sure you save the files as text only documents (which could be tricky, unfortuntately). Vi or Emacs could be used in Unix/Linux machines.

2 Math567 (Spring 2019) - AMPL Handout 1 2 Model file: FarmerJones.mod # AMPL model file for the Farmer Jones problem # The LP is # max Z = 30 x x2 (total revenue) # s.t x1 + x2 <= 7 (land available) # 4 x x2 <= 40 (labor hrs) # 10 x1 >= 30 (min corn) # x1, x2 >= 0 (non-negativity) set Crops; # corn, wheat param Yield {j in Crops}; # yield per acre param Labor {j in Crops}; # labor hrs per acre param Price {j in Crops}; # selling price per bushel param Min_Crop {j in Crops}; # min levels of corn and wheat (bushels) param Max_Acres; # total land available (acres) param Max_Hours; # total labor hrs available var x {j in Crops} >= 0; # x[corn], x[wheat] = acres of corn, wheat maximize total_revenue: sum {j in Crops} Price[j]*Yield[j]*x[j]; subject to land_constraint: sum {j in Crops} x[j] <= Max_Acres; subject to labor_constraint: sum {j in Crops} Labor[j]*x[j] <= Max_Hours; subject to min_crop_constraint {j in Crops}: Yield[j]*x[j] >= Min_Crop[j]; Data file: FarmerJones.dat set Crops := corn wheat; param Yield := corn 10 wheat 25; param Labor := corn 4 wheat 10; param Price := corn 3 wheat 4; param Min_Crop := corn 30 wheat 0; # No minimum level specified for wheat param Max_Acres := 7; param Max_Hours := 40;

3 Math567 (Spring 2019) - AMPL Handout 1 3 More points to note: Comments are given using the symbol #. Everything after a # in a line are ignored by AMPL. Symbolic parameters are declared for data, whose actual values are specified in the data file. Any parameter is declared using the keyword param. Variables are declared using the keyword var. The objective function starts with a maximize or a minimize, followed by a name, and then a colon (:). The actual expression of the objective function then follows. Each (set of) constraint(s) begins with the keyword subject to followed by a constraint name, possible indexing, and then a colon (:). The expression for the constraint(s) follows. Each constraint and objective function must have a unique name. Nonnegativity and other sign restrictions are declared along with the variable declarations. If no sign restrictions are provided, the variable(s) are considered unrestricted in sign (urs). 1.2 Running AMPL, Output from AMPL session To start an AMPL session in Windows, double-click on the executable names sw.exe. A scrollable window will open with the prompt sw:. Type ampl and press enter to get the ampl: prompt. In Unix/Linux machines, run the ampl executable to get the ampl: prompt. Here are the commands and output from an AMPL session to solve the Farmer Jones LP. sw: ampl ampl: option solver cplex; ampl: model FarmerJones.mod; data FarmerJones.dat; ampl: expand land_constraint; subject to land_constraint: x[ corn ] + x[ wheat ] <= 7; ampl: expand min_crop_constraint; subject to min_crop_constraint[ corn ]: 10*x[ corn ] >= 30; subject to min_crop_constraint[ wheat ]: 25*x[ wheat ] >= 0; ampl: solve; CPLEX : optimal solution; objective dual simplex iterations (1 in phase I) ampl: display x; x [*] := corn 3 wheat 2.8; ampl: display total_revenue; total_revenue = 370 ampl:

4 Math567 (Spring 2019) - AMPL Handout 1 4 If there is any error in the model file, AMPL will point it out. You will have to make the appropriate corrections in your.mod file (model file) and save it. In order to re-read the model file, you first need to give the command reset; at the ampl: prompt. Then say model FarmerJones.mod; again. If there was no error in the model file, but there is an error in the data file, you could reset just the data part by typing reset data;. This commands leaves the model file in tact. The modified data file could then be read in using the data command. The command display can be used to display the value(s) of a (set of) variables or the objective function. In the above LP, if you give the command display land constraint; after solving the LP, AMPL will display the value of the dual variable corresponding to the constraint (which is 0 in this case). The command expand is used to display the actual expression of a constraint or an objective function. 1.3 Another Example: Inventory problem (Taken from Introduction to Mathematical Programming by Winston and Venkataramanan.) A customer requires 50, 65, 100, and 70 units of a commodity during the next four months (no backlogging is allowed). Production costs are 5,8,4, and 7 dollars per unit during these months. The storage cost from one month to the next is \$2 per unit (assessed on ending inventory). Each unit at the end of month 4 could be sold at \$6. Use LP to minimize the net cost incurred by the customer in meeting the demands for the next four months. Model file: InventoryModel Pr1 Pg104.mod # AMPL model file for the inventory model # (WV-IMP problem 1 from page 104: discussed in class) # # min z = 5 x1 + 8 x2 + 4 x3 + 7 x4 + 2 (s1+s2+s3) - 6 s4 (net cost) # # s.t. s1 = x1-50 (inventory month 1) # s2 = x2+s1-65 (inventory month 2) # s3 = x3+s2-100 (inventory month 3) # s4 = x4+s3-70 (inventory month 4) # all vars >= 0 (non-negativity) param n; # No. of months param Demand {i in 1..n}; # demand for each month param Cost {i in 1..n}; # production cost for each month param Store_Cost; # storage cost (same for each month) param Price; # selling price (at the end of month n) var x {j in 1..n} >= 0; # No. units made in month j var s {j in 0..n} >= 0; # inventory at the end of month j # s[0] - inventory at the start of month 1 = 0

5 Math567 (Spring 2019) - AMPL Handout 1 5 minimize net_cost: sum {k in 1..n} Cost[k]*x[k] + Store_Cost*(sum{j in 0..n-1} s[j]) - Price*s[n]; subject to inventory_balance {i in 1..n}: s[i] = x[i] + s[i-1] - Demand[i]; subject to set_initial_inventory: s[0] = 0; Data file: InventoryModel Pr1 Pg104.dat param n := 4; param Demand := ; param Cost := ; param Store_Cost := 2; param Price := 6; Notice how all the inventory balance constraints are represented in a single line (under inventory balance). Here is the output from AMPL where the above LP is solved. ampl ampl: option solver scplex; ampl: model InventoryModel_Pr1_Pg104.mod; ampl: data InventoryModel_Pr1_Pg104.dat; ampl: solve; display x,s; CPLEX : optimal solution; objective dual simplex iterations (0 in phase I) : x s := ; ampl:

6 Math567 (Spring 2019) - AMPL Handout An integer programming example Binary and integer variables can be declared by adding the keyword binary or integer to the variable declaration. This keyword is included (usually) after possible bounds (separated by commas) before the final semi-colon (;). Here is an example. (Taken from Introduction to Mathematical Programming by Winston and Venkataramanan.) Because of excess pollution on the Momiss river, the state of Momiss is going to build pollution control stations. Three sites (1,2, and 3) are under consideration. Momiss wants to control the levels of two pollutants (1 and 2). The state legislature requires that at least 80,000 tons of pollutant 1 and at least 50,000 tons of pollutant 2 be removed from the river. The relevant data for the problem is shown in the table. Formulate and solve an IP to minimize the cost of meeting the state legislature s goals. Amt removed per ton of water site station building cost (\$) cost of treating 1 ton of water (\$) pollutant 1 pollutant , , , Model File:MomissIP.mod # model file for Momiss river MIP - problem 2 from page 502 param n_sites; param n_polut; param Cost_Treat {j in 1..n_Sites}; param Cost_Build {j in 1..n_Sites}; param Polut_Removed {i in 1..n_Polut, j in 1..n_Sites}; param Min_Polut {i in 1..n_Polut}; var x {j in 1..n_Sites} >= 0; var y {j in 1..n_Sites} binary; #var y {j in 1..n_Sites} >=0, <=1, integer; # this declaration works too param M; minimize total_cost: sum {j in 1..n_Sites} Cost_Treat[j]*x[j] + sum {j in 1..n_Sites} Cost_Build[j]*y[j]; subject to min_polut_removed {i in 1..n_Polut}: sum {j in 1..n_Sites} Polut_Removed[i,j]*x[j] >= Min_Polut[i]; subject to forcing_cons {j in 1..n_Sites}: x[j] <= M*y[j];

7 Math567 (Spring 2019) - AMPL Handout 1 7 Data File:MomissIP.dat # data file for Momiss river MIP - problem 2 from page 502 param n_sites := 3; param n_polut := 2; param Cost_Treat := ; param Cost_Build := ; param Polut_Removed : := ; param Min_Polut := ; param M := ; Output from AMPL session ampl ampl: option solver scplex; ampl: model MomissIP.mod.txt; ampl: data MomissIP.dat.txt; ampl: solve; CPLEX : optimal integer solution; objective MIP simplex iterations 0 branch-and-bound nodes ampl: display x,y; : x y := 1 2e ; 2 For more You should read the AMPL book to learn more about AMPL. Several examples are available for free download from the AMPL web page too.

### Linear Programs: Variables, Objectives and Constraints

8 Linear Programs: Variables, Objectives and Constraints The best-known kind of optimization model, which has served for all of our examples so far, is the linear program. The variables of a linear program

### Basic Components of an LP:

1 Linear Programming Optimization is an important and fascinating area of management science and operations research. It helps to do less work, but gain more. Linear programming (LP) is a central topic

### Solving Linear Programs using Microsoft EXCEL Solver

Solving Linear Programs using Microsoft EXCEL Solver By Andrew J. Mason, University of Auckland To illustrate how we can use Microsoft EXCEL to solve linear programming problems, consider the following

### Chapter 13: Binary and Mixed-Integer Programming

Chapter 3: Binary and Mixed-Integer Programming The general branch and bound approach described in the previous chapter can be customized for special situations. This chapter addresses two special situations:

### Using CPLEX. =5 has objective value 150.

Using CPLEX CPLEX is optimization software developed and sold by ILOG, Inc. It can be used to solve a variety of different optimization problems in a variety of computing environments. Here we will discuss

### EXCEL SOLVER TUTORIAL

ENGR62/MS&E111 Autumn 2003 2004 Prof. Ben Van Roy October 1, 2003 EXCEL SOLVER TUTORIAL This tutorial will introduce you to some essential features of Excel and its plug-in, Solver, that we will be using

### Optimization Modeling for Mining Engineers

Optimization Modeling for Mining Engineers Alexandra M. Newman Division of Economics and Business Slide 1 Colorado School of Mines Seminar Outline Linear Programming Integer Linear Programming Slide 2

### CPLEX Tutorial Handout

CPLEX Tutorial Handout What Is ILOG CPLEX? ILOG CPLEX is a tool for solving linear optimization problems, commonly referred to as Linear Programming (LP) problems, of the form: Maximize (or Minimize) c

### Linear Programming. March 14, 2014

Linear Programming March 1, 01 Parts of this introduction to linear programming were adapted from Chapter 9 of Introduction to Algorithms, Second Edition, by Cormen, Leiserson, Rivest and Stein [1]. 1

### Chapter 2 Solving Linear Programs

Chapter 2 Solving Linear Programs Companion slides of Applied Mathematical Programming by Bradley, Hax, and Magnanti (Addison-Wesley, 1977) prepared by José Fernando Oliveira Maria Antónia Carravilla A

### INTEGER PROGRAMMING. Integer Programming. Prototype example. BIP model. BIP models

Integer Programming INTEGER PROGRAMMING In many problems the decision variables must have integer values. Example: assign people, machines, and vehicles to activities in integer quantities. If this is

### Linear Programming Notes V Problem Transformations

Linear Programming Notes V Problem Transformations 1 Introduction Any linear programming problem can be rewritten in either of two standard forms. In the first form, the objective is to maximize, the material

### Linear Program Solver

Linear Program Solver Help Manual prepared for Forest Management course by Bogdan Strimbu 1 Introduction The Linear Program Solver (LiPS) Help manual was developed to help students enrolled in the senior

### Cloud Branching. Timo Berthold. joint work with Domenico Salvagnin (Università degli Studi di Padova)

Cloud Branching Timo Berthold Zuse Institute Berlin joint work with Domenico Salvagnin (Università degli Studi di Padova) DFG Research Center MATHEON Mathematics for key technologies 21/May/13, CPAIOR

### Using EXCEL Solver October, 2000

Using EXCEL Solver October, 2000 2 The Solver option in EXCEL may be used to solve linear and nonlinear optimization problems. Integer restrictions may be placed on the decision variables. Solver may be

### Linear Programming. Solving LP Models Using MS Excel, 18

SUPPLEMENT TO CHAPTER SIX Linear Programming SUPPLEMENT OUTLINE Introduction, 2 Linear Programming Models, 2 Model Formulation, 4 Graphical Linear Programming, 5 Outline of Graphical Procedure, 5 Plotting

### Tennessee Agricultural Production and Rural Infrastructure

Tennessee Trends in Agricultural Production and Infrastructure Highlights - In many states the percentage of the state population designated by the U.S. Census Bureau as living in rural areas has declined,

### Linear Programming Supplement E

Linear Programming Supplement E Linear Programming Linear programming: A technique that is useful for allocating scarce resources among competing demands. Objective function: An expression in linear programming

### Journal of Sustainable Development in Africa (Volume 12, No.2, 2010)

Journal of Sustainable Development in Africa (Volume 12, No.2, 2010) ISSN: 1520-5509 Clarion University of Pennsylvania, Clarion, Pennsylvania A FARM RESOURCE ALLOCATION PROBLEM: CASE STUDY OF SMALL SCALE-

### Rain on Planting Protection. Help Guide

Rain on Planting Protection Help Guide overview Rain on Planting Protection allows growers to protect themselves from losses if rain prevents planting from being completed on schedule. Coverage is highly

### Linear Programming. April 12, 2005

Linear Programming April 1, 005 Parts of this were adapted from Chapter 9 of i Introduction to Algorithms (Second Edition) /i by Cormen, Leiserson, Rivest and Stein. 1 What is linear programming? The first

Approximation Algorithms Chapter Approximation Algorithms Q. Suppose I need to solve an NP-hard problem. What should I do? A. Theory says you're unlikely to find a poly-time algorithm. Must sacrifice one

### How Crop Insurance Works. The Basics

How Crop Insurance Works The Basics Behind the Policy Federal Crop Insurance Corporation Board of Directors Approve Policies Policy changes General direction of program Risk Management Agency Administers

### Airport Planning and Design. Excel Solver

Airport Planning and Design Excel Solver Dr. Antonio A. Trani Professor of Civil and Environmental Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia Spring 2012 1 of

### IBM ILOG CPLEX for Microsoft Excel User's Manual

IBM ILOG CPLEX V12.1 IBM ILOG CPLEX for Microsoft Excel User's Manual Copyright International Business Machines Corporation 1987, 2009 US Government Users Restricted Rights - Use, duplication or disclosure

### Parameters and Expressions

7 Parameters and Expressions A large optimization model invariably uses many numerical values. As we have explained before, only a concise symbolic description of these values need appear in an AMPL model,

### Dantzig-Wolfe bound and Dantzig-Wolfe cookbook

Dantzig-Wolfe bound and Dantzig-Wolfe cookbook thst@man.dtu.dk DTU-Management Technical University of Denmark 1 Outline LP strength of the Dantzig-Wolfe The exercise from last week... The Dantzig-Wolfe

### A Weighted-Sum Mixed Integer Program for Bi-Objective Dynamic Portfolio Optimization

AUTOMATYKA 2009 Tom 3 Zeszyt 2 Bartosz Sawik* A Weighted-Sum Mixed Integer Program for Bi-Objective Dynamic Portfolio Optimization. Introduction The optimal security selection is a classical portfolio

### ! Solve problem to optimality. ! Solve problem in poly-time. ! Solve arbitrary instances of the problem. !-approximation algorithm.

Approximation Algorithms Chapter Approximation Algorithms Q Suppose I need to solve an NP-hard problem What should I do? A Theory says you're unlikely to find a poly-time algorithm Must sacrifice one of

### Cash to Accrual Income Approximation

Cash to Accrual Income Approximation With this program, the user can estimate accrual income using the Schedule F from his/her federal income tax return. Fast Tools & Resources Farmers typically report

### Bachelors of Computer Application Programming Principle & Algorithm (BCA-S102T)

Unit- I Introduction to c Language: C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating

### Quick Cash Flow Projections

Quick Cash Flow Projections The Quick Cash Flow Projections tool assists farm operators in projecting cash needs, farm profitability, and debt servicing capabilities. The program also aids users in performing

### GENERALIZED INTEGER PROGRAMMING

Professor S. S. CHADHA, PhD University of Wisconsin, Eau Claire, USA E-mail: schadha@uwec.edu Professor Veena CHADHA University of Wisconsin, Eau Claire, USA E-mail: chadhav@uwec.edu GENERALIZED INTEGER

### Grain Inventory Management

Grain Inventory Management With this program, the user can manage and track grain inventories by landowner, production location, storage site and field. Transactions can be recorded for: Production Grain

### Name: Class: Date: 9. The compiler ignores all comments they are there strictly for the convenience of anyone reading the program.

Name: Class: Date: Exam #1 - Prep True/False Indicate whether the statement is true or false. 1. Programming is the process of writing a computer program in a language that the computer can respond to

### Breakeven Analysis. Takes the user to the data input worksheet of the tool.

Breakeven Analysis This program allows the user to calculate breakeven price and yield levels and prepare projected net farm income and cash flow statements. The Breakeven Analysis program assists farm

### Lecture 3. Linear Programming. 3B1B Optimization Michaelmas 2015 A. Zisserman. Extreme solutions. Simplex method. Interior point method

Lecture 3 3B1B Optimization Michaelmas 2015 A. Zisserman Linear Programming Extreme solutions Simplex method Interior point method Integer programming and relaxation The Optimization Tree Linear Programming

### A Production Planning Problem

A Production Planning Problem Suppose a production manager is responsible for scheduling the monthly production levels of a certain product for a planning horizon of twelve months. For planning purposes,

### Dynamic Programming 11.1 AN ELEMENTARY EXAMPLE

Dynamic Programming Dynamic programming is an optimization approach that transforms a complex problem into a sequence of simpler problems; its essential characteristic is the multistage nature of the optimization

### Energy capacity planning and modeling

Andras Herczeg: Energy capacity planning and modeling - with Open Source Energy Modeling System (OSeMOSYS) (Final Report) Rensselaer Polytechnic Institute MANE-6960H01 Mathematical Modeling of Energy and

### PROMOTION MIX OPTIMIZATION

WII UCM MODELLING WEEK, 9-13 JUNE 2014 PROMOTION MIX OPTIMIZATION Accenture COORDINATOR: Liberatore, Federico PARTICIPANTS Bermúdez Gallardo, José Carlos Fossi, Margherita Pérez García, Lucía CONTENTS:

### A Reference Point Method to Triple-Objective Assignment of Supporting Services in a Healthcare Institution. Bartosz Sawik

Decision Making in Manufacturing and Services Vol. 4 2010 No. 1 2 pp. 37 46 A Reference Point Method to Triple-Objective Assignment of Supporting Services in a Healthcare Institution Bartosz Sawik Abstract.

### Spreadsheets have become the principal software application for teaching decision models in most business

Vol. 8, No. 2, January 2008, pp. 89 95 issn 1532-0545 08 0802 0089 informs I N F O R M S Transactions on Education Teaching Note Some Practical Issues with Excel Solver: Lessons for Students and Instructors

### Diet and Other Input Models: Minimizing Costs

2 Diet and Other Input Models: Minimizing Costs To complement the profit-maximizing models of Chapter 1, we now consider linear programming models in which the objective is to minimize costs. Where the

### Solving Math Programs with LINGO

2 Solving Math Programs with LINGO 2.1 Introduction The process of solving a math program requires a large number of calculations and is, therefore, best performed by a computer program. The computer program

### 56:171 Operations Research Midterm Exam Solutions Fall 2001

56:171 Operations Research Midterm Exam Solutions Fall 2001 True/False: Indicate by "+" or "o" whether each statement is "true" or "false", respectively: o_ 1. If a primal LP constraint is slack at the

### Command Scripts. 13.1 Running scripts: include and commands

13 Command Scripts You will probably find that your most intensive use of AMPL s command environment occurs during the initial development of a model, when the results are unfamiliar and changes are frequent.

### Minimizing costs for transport buyers using integer programming and column generation. Eser Esirgen

MASTER STHESIS Minimizing costs for transport buyers using integer programming and column generation Eser Esirgen DepartmentofMathematicalSciences CHALMERS UNIVERSITY OF TECHNOLOGY UNIVERSITY OF GOTHENBURG

### Agricultural Production and Research in Heilongjiang Province, China. Jiang Enchen. Professor, Department of Agricultural Engineering, Northeast

1 Agricultural Production and Research in Heilongjiang Province, China Jiang Enchen Professor, Department of Agricultural Engineering, Northeast Agricultural University, Harbin, China. Post code: 150030

### Coordinating Supply Chains: a Bilevel Programming. Approach

Coordinating Supply Chains: a Bilevel Programming Approach Ton G. de Kok, Gabriella Muratore IEIS, Technische Universiteit, 5600 MB Eindhoven, The Netherlands April 2009 Abstract In this paper we formulate

### Specifying Data. 9.1 Formatted data: the data command

9 Specifying Data As we emphasize throughout this book, there is a distinction between an AMPL model for an optimization problem, and the data values that define a particular instance of the problem. Chapters

### Models in Transportation. Tim Nieberg

Models in Transportation Tim Nieberg Transportation Models large variety of models due to the many modes of transportation roads railroad shipping airlines as a consequence different type of equipment

### > DO IT! Chapter 6. CVP Income Statement D-1. Solution. Action Plan

Chapter 6 CVP Income Statement Use the CVP income statement format. Use the formula for contribution margin per unit. Use the formula for the contribution margin ratio. Garner Inc. sold 20,000 units and

### COST & BREAKEVEN ANALYSIS

COST & BREAKEVEN ANALYSIS http://www.tutorialspoint.com/managerial_economics/cost_and_breakeven_analysis.htm Copyright tutorialspoint.com In managerial economics another area which is of great importance

### Sensitivity Analysis 3.1 AN EXAMPLE FOR ANALYSIS

Sensitivity Analysis 3 We have already been introduced to sensitivity analysis in Chapter via the geometry of a simple example. We saw that the values of the decision variables and those of the slack and

### Solving Linear Programs in Excel

Notes for AGEC 622 Bruce McCarl Regents Professor of Agricultural Economics Texas A&M University Thanks to Michael Lau for his efforts to prepare the earlier copies of this. 1 http://ageco.tamu.edu/faculty/mccarl/622class/

### Database Access. 10.1 General principles of data correspondence

10 Database Access The structure of indexed data in AMPL has much in common with the structure of the relational tables widely used in database applications. The AMPL table declaration lets you take advantage

### Two objective functions for a real life Split Delivery Vehicle Routing Problem

International Conference on Industrial Engineering and Systems Management IESM 2011 May 25 - May 27 METZ - FRANCE Two objective functions for a real life Split Delivery Vehicle Routing Problem Marc Uldry

### Agricultural Commodity Marketing: Futures, Options, Insurance

Agricultural Commodity Marketing: Futures, Options, Insurance By: Dillon M. Feuz Utah State University Funding and Support Provided by: On-Line Workshop Outline A series of 12 lectures with slides Accompanying

### Lecture 10 Scheduling 1

Lecture 10 Scheduling 1 Transportation Models -1- large variety of models due to the many modes of transportation roads railroad shipping airlines as a consequence different type of equipment and resources

### Discrete Optimization

Discrete Optimization [Chen, Batson, Dang: Applied integer Programming] Chapter 3 and 4.1-4.3 by Johan Högdahl and Victoria Svedberg Seminar 2, 2015-03-31 Todays presentation Chapter 3 Transforms using

### Evaluating Taking Prevented Planting Payments for Corn

May 30, 2013 Evaluating Taking Prevented Planting Payments for Corn Permalink URL http://farmdocdaily.illinois.edu/2013/05/evaluating-prevented-planting-corn.html Due to continuing wet weather, some farmers

### A Branch and Bound Algorithm for Solving the Binary Bi-level Linear Programming Problem

A Branch and Bound Algorithm for Solving the Binary Bi-level Linear Programming Problem John Karlof and Peter Hocking Mathematics and Statistics Department University of North Carolina Wilmington Wilmington,

### Farmland Lease Analysis: Program Overview. Navigating the Farmland Lease Analysis program

Farmland Lease Analysis: Program Overview The farmland lease analysis program is used to aid tenants and landlords in determining the returns and risks from different farmland leases. The program offers

### Price, Yield and Enterprise Revenue Risk Management Analysis Using Combo Insurance Plans, Futures and/or Options Markets

Price, Yield and Enterprise Revenue Risk Management Analysis Using Combo Insurance Plans, Futures and/or Options Markets Authors: Duane Griffith, Montana State University, Extension Farm Management Specialist

### Personal Study Assignment #1: Inventory Assessment

The purpose of this activity is for you to conduct an inventory of your farm business assets. Think about your farm business and list all of the assets you own and/or control that make up the farm business.

### CAPACITY UTILIZATION FOR PRODUCT MIX USING OPERATION BASED TIME STANDARD EVALUATION

CAPACITY UTILIZATION FOR PRODUCT MIX USING OPERATION BASED TIME STANDARD EVALUATION Sandeep A. Chowriwar 1, Ishan P. Lade 2, Pranay B. Sawaitul 3, Sachin M. Kamble 4 1 Department of Mechanical Engineering,

### Branch-and-Price Approach to the Vehicle Routing Problem with Time Windows

TECHNISCHE UNIVERSITEIT EINDHOVEN Branch-and-Price Approach to the Vehicle Routing Problem with Time Windows Lloyd A. Fasting May 2014 Supervisors: dr. M. Firat dr.ir. M.A.A. Boon J. van Twist MSc. Contents

### Chapter 4. Systems Design: Process Costing. Types of Costing Systems Used to Determine Product Costs

4-1 Types of Systems Used to Determine Product Costs Chapter 4 Process Job-order Systems Design: Many units of a single, homogeneous product flow evenly through a continuous production process. One unit

MS Excel Handout: Level 2 elearning Department 2016 Page 1 of 11 Contents Excel Environment:... 3 To create a new blank workbook:...3 To insert text:...4 Cell addresses:...4 To save the workbook:... 5

### A BULLISH CASE FOR CORN AND SOYBEANS IN 2016

A BULLISH CASE FOR CORN AND SOYBEANS IN 2016 Probabilities for higher prices, and the factors that could spur price rallies. Commodity markets tend to move on three variables: perception, momentum and

### CROP BUDGETS, ILLINOIS, 2015

CROP BUDGETS Department of Agricultural and Consumer Economics University of Illinois CROP BUDGETS, ILLINOIS, 2015 Department of Agricultural and Consumer Economics University of Illinois September 2015

### USING EXCEL SOLVER IN OPTIMIZATION PROBLEMS

USING EXCEL SOLVER IN OPTIMIZATION PROBLEMS Leslie Chandrakantha John Jay College of Criminal Justice of CUNY Mathematics and Computer Science Department 445 West 59 th Street, New York, NY 10019 lchandra@jjay.cuny.edu

### LocalSolver: black-box local search for combinatorial optimization

LocalSolver: black-box local search for combinatorial optimization Frédéric Gardi Bouygues e-lab, Paris fgardi@bouygues.com Joint work with T. Benoist, J. Darlay, B. Estellon, R. Megel, K. Nouioua Bouygues

### Section IV.1: Recursive Algorithms and Recursion Trees

Section IV.1: Recursive Algorithms and Recursion Trees Definition IV.1.1: A recursive algorithm is an algorithm that solves a problem by (1) reducing it to an instance of the same problem with smaller

### Chapter 3 INTEGER PROGRAMMING 3.1 INTRODUCTION. Robert Bosch. Michael Trick

Chapter 3 INTEGER PROGRAMMING Robert Bosch Oberlin College Oberlin OH, USA Michael Trick Carnegie Mellon University Pittsburgh PA, USA 3.1 INTRODUCTION Over the last 20 years, the combination of faster

### Computers. An Introduction to Programming with Python. Programming Languages. Programs and Programming. CCHSG Visit June 2014. Dr.-Ing.

Computers An Introduction to Programming with Python CCHSG Visit June 2014 Dr.-Ing. Norbert Völker Many computing devices are embedded Can you think of computers/ computing devices you may have in your

### Mathematical finance and linear programming (optimization)

Mathematical finance and linear programming (optimization) Geir Dahl September 15, 2009 1 Introduction The purpose of this short note is to explain how linear programming (LP) (=linear optimization) may

### Standard Form of a Linear Programming Problem

494 CHAPTER 9 LINEAR PROGRAMMING 9. THE SIMPLEX METHOD: MAXIMIZATION For linear programming problems involving two variables, the graphical solution method introduced in Section 9. is convenient. However,

### Maximizing volume given a surface area constraint

Maximizing volume given a surface area constraint Math 8 Department of Mathematics Dartmouth College Maximizing volume given a surface area constraint p.1/9 Maximizing wih a constraint We wish to solve

### SBB: A New Solver for Mixed Integer Nonlinear Programming

SBB: A New Solver for Mixed Integer Nonlinear Programming Michael R. Bussieck GAMS Development Corp. Arne S. Drud ARKI Consulting & Development A/S OR2001, Duisburg Overview! SBB = Simple Branch & Bound!

### 3.3 Real Returns Above Variable Costs

3.3 Real Returns Above Variable Costs Several factors can impact the returns above variable costs for crop producers. Over a long period of time, sustained increases in the growth rate for purchased inputs

### Chapter 11 Monte Carlo Simulation

Chapter 11 Monte Carlo Simulation 11.1 Introduction The basic idea of simulation is to build an experimental device, or simulator, that will act like (simulate) the system of interest in certain important

### Revenue and Costs for Corn, Soybeans, Wheat, and Double-Crop Soybeans, Actual for 2009 through 2015, Projected 2016

CROP COSTS Department of Agricultural and Consumer Economics University of Illinois Revenue and Costs for Corn, Soybeans, Wheat, and Double-Crop Soybeans, Actual for 2009 through 2015, Projected 2016 Department

### Blending petroleum products at NZ Refining Company

Blending petroleum products at NZ Refining Company Geoffrey B. W. Gill Commercial Department NZ Refining Company New Zealand ggill@nzrc.co.nz Abstract There are many petroleum products which New Zealand

### AGRICULTURE CREDIT CORPORATION CASH WHEN YOU NEED IT MOST

AGRICULTURE CREDIT CORPORATION CASH WHEN YOU NEED IT MOST OVERVIEW 1) Observations on Farm Debt in Canada 2) Overview of the APP and Changes 3) Overview of the Commodity Loan Program (CLP) 90000000 Total

### GUROBI OPTIMIZER QUICK START GUIDE. Version 6.0, Copyright c 2014, Gurobi Optimization, Inc.

GUROBI OPTIMIZER QUICK START GUIDE Version 6.0, Copyright c 2014, Gurobi Optimization, Inc. Contents 1 Introduction 4 2 Obtaining a Gurobi License 6 2.1 Creating a new academic license.............................

### Click on the links below to jump directly to the relevant section

Click on the links below to jump directly to the relevant section What is algebra? Operations with algebraic terms Mathematical properties of real numbers Order of operations What is Algebra? Algebra is

### 298,320 3,041 107,825. Missouri Economic Research Brief FARM AND AGRIBUSINESS. Employment. Number of Agribusinesses.

Missouri Economic Research Brief FARM AND AGRIBUSINESS Missouri s Farm and Agribusiness Missouri s farm and agribusiness sectors include crops, livestock, industries supporting farm production and farm-related

### Optimal Scheduling for Dependent Details Processing Using MS Excel Solver

BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 8, No 2 Sofia 2008 Optimal Scheduling for Dependent Details Processing Using MS Excel Solver Daniela Borissova Institute of

### Approximation Algorithms

Approximation Algorithms or: How I Learned to Stop Worrying and Deal with NP-Completeness Ong Jit Sheng, Jonathan (A0073924B) March, 2012 Overview Key Results (I) General techniques: Greedy algorithms

### 1 Mathematical Models of Cost, Revenue and Profit

Section 1.: Mathematical Modeling Math 14 Business Mathematics II Minh Kha Goals: to understand what a mathematical model is, and some of its examples in business. Definition 0.1. Mathematical Modeling

### Linear Programming: Theory and Applications

Linear Programming: Theory and Applications Catherine Lewis May 11, 2008 1 Contents 1 Introduction to Linear Programming 3 1.1 What is a linear program?...................... 3 1.2 Assumptions.............................

### Crop-Share and Cash Rent Lease Comparisons Version 1.6. Introduction

Crop-Share and Cash Rent Lease Comparisons Version 1.6 Alan Miller and Craig L. Dobbins Spreadsheet can be found at http://www.agecon.purdue.edu/extension/pubs/farmland_values.asp Introduction This spreadsheet

### Linear Programming: Chapter 11 Game Theory

Linear Programming: Chapter 11 Game Theory Robert J. Vanderbei October 17, 2007 Operations Research and Financial Engineering Princeton University Princeton, NJ 08544 http://www.princeton.edu/ rvdb Rock-Paper-Scissors

### 2+2 Just type and press enter and the answer comes up ans = 4

Demonstration Red text = commands entered in the command window Black text = Matlab responses Blue text = comments 2+2 Just type and press enter and the answer comes up 4 sin(4)^2.5728 The elementary functions

### The University of Georgia

The University of Georgia Center for Agribusiness and Economic Development College of Agricultural and Environmental Sciences Estimating a Business Opportunity s Economic Vitality DRAFT Prepared by: Kent