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Linear Programming-
Aluminum Alloy Blending




Data Processing Application
CONTENTS

Introduction . . . . . 1 Post-Optimal Output . 14
Problem Profile . . . 2 DO. D/J . 14
Problem Economics 2 COST. R . 14
Historical Conditions 2 Applying the Problem Answers 14
Problem Complexity 2 Furnace Charge s 15
The Manual Approach 3 Quality Control 15
LP Model Formulation . . . 3 Inventory. 16
Input Data Requirements 3 Purchasing and Cost Analysis. 16
Single-Furnace Problem .... 3 Product Research and Pricing 16
Activities (Matrix Columns) 4 Management Studies . 16
Constraints (Matrix Rows) . 4 Summary. 16
Summary . . . . . . . . 7 Postoptimal Operations and
Multifurnace Model . . . . . 7 General Procedures 17
Special Constraints and Formulations 8 Operating Modes 17
Example 1 - Equivalence 8 Ingot Constraints . 17
Example 2 - Substitution 11 Inventory Constraints 18
Problem Answers . . . . 13 Frequency of Solution 18
Optimal Solution. . . . 13 Continuous Pouring 18
Other Optimal Output . 13




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INTRODUCTION

This manual explores the use of linear programming and the often astounding economical advantages it
(LP) in the aluminum alloying industry. It discusses imparts, the technique as an everyday management
the nature of the industry, the decisions involved in aid remains in its infancy. There are two reasons
producing an alloy, the mechanics of alloying, and for this.
the techniques and advantages of applying LP to the First, there has been both ignorance and fear
industry. Particular emphasis is placed on explaining regarding the mathematical aspects of LP problem
how linear programming can be used to: formulation. Many people have felt that a staff of