On Best Corrected Mixture Problems in Metallurgy: A Case Study

F Dubeau,M E Ntigura Habingabwa

doi:10.1155/2017/2742540

Abstract

We consider three simple mixture problems occurring in metallurgy. The first problem considered is the classic minimum cost mixture problem. For the second problem, we consider finding a correction to a given mixture, a premix, without considering the cost of this premix. We only consider the cost and the weight of the quantity used as a correction. We show that the minimum cost correction does not correspond to the minimum weight correction, and we built the Pareto curve that gives all intermediate solutions between these two extreme solutions. Finally, the third problem is the correction problem for a nonfree premix. The correction is done to obtain a minimum cost corrected mixture.

Highlights

Using materials, such as scrap metal for recycling, in order to form blends with desired specifications on some basic chemical elements is a well-known mixture problem met in foundries
We show that the minimum cost correction does not correspond to the minimum weight correction, and we built the Pareto curve that gives all intermediate solutions between these two extreme solutions
This problem is an example of a bicriteria linear programming problem, and we are going to identify its Pareto set which gives the link between minimum cost solution and minimum weight solution

Summary

Introduction

Using materials, such as scrap metal for recycling, in order to form blends with desired specifications on some basic chemical elements is a well-known mixture problem met in foundries. People working in these fields bring to our attention the three different but related problems that we are going to consider in this paper. The first problem, called the basic problem, is to make a minimum cost mixture while checking the constraints on the specifications. We look for a minimum unit cost corrected mixture This is an example of a linear-fractional programming problem. Other approaches could be used to analyze similar mixture problems; for example, the fuzzy approach could be used to introduce uncertainties on the data [9]

Basic Problem

Conclusion