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E20-0127-0_Linear_Programming_-_Aluminum_Alloy_Blending


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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



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