Case Study: The Herd Feeding Problem

Submitted: 18 Feb 2008

Operations Research Topics: LinearProgramming, BlendingModels

Application Areas: Farm Management


Problem Description

Adapted from a real-world problem

When determining how to feed a herd of dairy cows, farmers need to take into account many different parameters, e.g.,

  • How much milk they want the cows to produce;
  • The price of the various feed types;
  • If the cows are pregnant and how far through their pregnancy are they;
  • How much pasture their farm currently has for grazing.

Farmers will often turn to farm consultants to help them make the best decision. In this case study we are going to analyse the decision suggested by a farm consultant.

The following table gives some typical amounts of MJME (megajoules of metabolisable energy) required for a cow each day in order for it to produce various amounts of milk that day.


Cows get MJME from their feed, or more specifically the amount of DM (dry matter) in their feed. The next table gives a list of possible feed types, their cost, %DM, MJME per kgDM as well as their percentage of protein and NDF (neutral detergent fibre).


This month, a consultant has estimated that a herd of 350 cows each require 180 MJME per day to produce 23 L of milk. For nutrition they need their feed to contain at least 17% protein and 32% NDF.

He also estimates the farm has 1920 kg of usable pasture.

His feed solution for each cow is given below.


The farmer wants to know if this is the best possible solution.

For more information on MJME, DM, etc see - Straggle Muster 113.

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Student Tasks

1. Write AMPL files herd.mod, herd.dat and to find a feeding solution.Write a management summary of your feeding solution. Be sure to compare it to the consultant's solution.

What to hand in Your new AMPL files herd.mod, herd.dat and Your management summary.

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Topic attachments
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Microsoft Excel Spreadsheetxls herd.xls r1 manage 22.0 K 2008-02-29 - 23:01 TWikiAdminUser  
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Topic revision: r16 - 2009-10-06 - MichaelOSullivan
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