Acceptability Index and Interval Linear Programming

Introduction

This chapter defines an interval linear programming problem as an extension of the classical linear programming problem to an inexact environment. Let’s refer here a very good example (Tong (1994)) of using interval numbers in an optimization problem:

There are 1000 chickens raised in a chicken farm and they are raised with two kinds of forages - soya and millet. It is known that each chicken eats 1 - 1.3 kg of forage every day and that for good weight gain it needs at least 0.21 - 0.23 kg of protein and 0.004 - 0.006 kg of calcium everyday. Per kg of soya contains 48 - 52% protein and 0.5 - 0.8% calcium and its price is 0.38 - 0.42 Yuan. Per kg of millet contains 8.5 - 11.5% protein and 0.3% calcium and its price is 0.20 Yuan. How should the forage be mixed in order to minimize expense on forage?

Most of the parameters used in this problem are inexact and perhaps appropriately given in terms of simple intervals. In reality inexactness of this kind can be cited in countless numbers (Huang et al (1995), Ida (2000), Giove et al (2006), Riverol et al (2006) etc.).