Service Manuals, User Guides, Schematic Diagrams or docs for : IBM generalInfo E20-0147-0_Linear_Programming_-_Electric-Arc_Furnace_Steelmaking
<< Back | HomeMost service manuals and schematics are PDF files, so You will need Adobre Acrobat Reader to view : Acrobat Download Some of the files are DjVu format. Readers and resources available here : DjVu Resources
For the compressed files, most common are zip and rar. Please, extract files with Your favorite compression software ( WinZip, WinRAR ... ) before viewing. If a document has multiple parts, You should download all, before extracting.
Good luck. Repair on Your own risk. Make sure You know what You are doing.
Image preview - the first page of the document
>> Download E20-0147-0_Linear_Programming_-_Electric-Arc_Furnace_Steelmaking documenatation <<
Text preview - extract from the document
Linear Programming-
Electric-Arc Furnace Steelmaking
Data Processing' Application
CONTENTS
Introduction . . . . . . . 1
Problem Profile. . . 2
Problem Economics 3
Single- Furnace Model Formulation 3
Input Data Requirements. 4
Example Problem . . . . . . . . . 4
Cost Constraint. . . . . . . . . 8
Charge Material Supply Equations . 9
Specification and Control Constraints 10
Multifurnace Model Formulation . 19
Summary . . . . . . . . . . . 21
Output Reports. . . . . . . . 21
Basis Variables Report 22
Slacks Report. . . . 24
DO. D/J Report . . . . . . . . . 26
Cost Range Report . 27
Summary . . 28
Bibliography. . . . . . . 29
Copies of this arid other IBM publications can be obtained through IBM branch
offices. Address comments concerning the contents of this publication to
IBM, Technical Publications Department, 112 East Post Road, White Plains, N. Y. 10601
INTRODUCTION
The introduction of linear programming (LP) has produced remarkable
and diverse benefits in a number of industries. Recent applications of
LP techniques by metal producers -- notably to control costs and quality
in alloy blending -- suggest a variety of new applications. The purpose
of this manual is to demonstrate the application of LP in the production of
steel in electric-arc furnaces -- a process which, because it involves
complex blending and quality control, is particularly responsive to LP
techniques. The immediate and more obvious LP results enable the steel
producer to:
1. Minimize the cost of both initial and supplemental furnace charges
2. Minimize and possibly eliminate off-compositions
3. Maintain accurate scrap inventory records
4. Purchase and sell most economically
5. Evaluate plant operating changes
6. Interpret historical charge data in terms of operating relationships
to develop more efficient operation
Contrary to popular belief, little mathematical knowledge or skill is
required to formulate an LP model. Nor does the operation of the com-
puter and the analysis of computer results require any advanced technical
skill. Linear programming requires nothing more than the expression of
all the elements in the process -- plant operating practices, charge
materials, specifications, etc. -- in the form of simple linear equations.
A general explanation of basic linear programming appears in the IBM
data processing application manual An Introduction to Linear Pro-
gramming (E20-8171), which should be read in conjunction with this
manual.
To demonstrate the methods and advantages of LP in steel production, we
shall present a typical production problem as a basis for the development
of an LP model which can be solved by the IBM 1620/1311 Linear Pro-
gramming System. With minor modifications the model can be run on
any of IBM's LP systems.
1
PROBLEM PROFILE
The basic process consists of the following phases:
1. An initial charge of sc rap and alloying material is melted in a
furnace by electrical energy supplied through carbon or graphite
electrodes.
2. Oxygen, supplied through lances, is blown through the molten bath to
burn off impurities. As a consequence, a slag forms which contains,
in addition to the oxidized impurities, a significant quantity of iron
oxide and oxides of expensive alloying metals (such as chromium).
3. In alloy steelmaking much of the metallic oxide in the slag is reduced
by the addition of silicon -- for example, in the form of high-silicon,
low-impurity chrome silicides.
4. In medium-Iow-, and low-carbon steelmaking, the initial slag is
raked and poured off, and a second slag is either formed or placed
on the bath. This slag serves to eliminate remaining contaminants
and protect the metal bath from contamination by reaction with the
furnace atmosphere.
5. When the metal bath is brought to end specifications and temperature,
the steel is poured out into ingots, molds, etc.
Because the electric furnace allows close control of both composition and
temperature, it is in widespread use in medium -low-carbon steel produc-
tion and has become the primary producer in stainless and alloy st~el
production.
The fundamental problem is to produce a specified steel at the lowest
possible cost. In order to achieve least-cost production, the producer
must consider a complex variety of fa.ctors which, immediately or
ultimately, contribute to the costs of production. The more obvious
variable factors include price, grade, and availability of initial charge
scraps,price and quantity of required additives, and heat time (that is,
price and quantity of required energy). Less obvious factors that
markedly affect costs include refractory erosion, oxygen rate and lance
position, and quality control. The least tangible, and possibly the most
important, factor that contributes to the formulation of consistently
accurate bids (especially for steel orders) is an accurate log of heat
histories -- to serve as the basis for predicting operating efficiency and
revising operating practices.
2
PROBLEM ECONOMICS
In most cases a wide variety of scraps, differing in composition, physical
condition, and price, are available for the initial charge in the electric-
arc furnace. Further, the available quantity of each scrap, as well as
its price, fluctuates. The primary economic problem, then, is to deter-
mine the composition of an initial charge that will produce the specified
steel at least cost. The nature of the initial charge will affect the cost of
furnace operation (since different scraps will require different optimum
furnace temperature and blow time). Further, the nature of the initial
charge, in conjunction with the furnace operation during the melt and
decarburization of the charge, affects the cost in terms of relatively
expensive reducing and finishing additives.
The crucial interrelation among the several phases of steel production
makes it exceedingly difficult to determine the least-cost initial charge,
optimum furnace operation, and least-co.st supplemental charge. This
difficulty is vastly compounded by commo.n fluctuations in the availability
of specific scraps, since the alteration of anyone component in the initial
charge will alter all the relationships required for least-cost production.
Heretofore, steel producers employing manual calculation to determine
initial furnace charge often used expensive scrap that came close to
matching the alloy specification requirements together with expensive
pure metals and additives. An increasing number of steelmakers, how-
ever, are profiting from the application of linear programming, which
enables the producer to examine all possible combinations and quickly
determine the most economical furnace charge. Further, by serving to
"force" overstocked scrap types in least-cost charges, LP can contribute
to the achievement and maintenance of ideal inventory procedures.
SINGLE-FURNACE MODEL FORMULATION
A linear programming model for steel production is a mathematical
representation, in the form of linear equations, of all lmown and esti-
mated factors relevant to the production of the specified steel. To
demonstrate the method for formulating such a model, we postulate a .
specific problem and relatively ideal conditions -- the production of
20,000 lbs. of low-carbon stainless steel from four initially available
charge materials. In actual practice a larger number of materials are
available to the furnace operator; regardless of their variety and compo-
sition (the factors that complicate manual calculation), they can easily
be included in the LP model, increasing the model's size'but not its
complexity.
3
Input Data Requirements
The following basic data is required to formulate the LP model:
1. Specifications of alloy to be produced
2. Pounds of alloy required
3. Composition analysis of all raw materials
4. Per-pound cost of all raw materials
5. Inventory levels of all raw materials (scrap and reducing and
finishing additives)
6. Special raw-material restrictions (for example, ingot weights)
7. Current operating practices (for example, basicity levels)
8. Furnace characteristics (for example, maximum permissible
temperature)
Most of this information is available from purchasing, cost accounting,
inventory accounting, or other sources and is probably used in existing
systems for computing furnace charges. Where exact information cannot
be readily obtained, estimates should be made, since it is an easy matter
to change the input data and re-solve the problem once an optimal solu-
tion has been obtained .. Indeed, the rapid calculation of the effect of
changes in the input is a prime advantage of the LP approach. Moreover,
the accumulation of a log of heat histories will result in increasingly
precise estimates.
Example Problem
We wish to produce 20,000 lbs. of steel with the specifications shown in
Figure 1. The four initial charge materials available are steel scrap,
430 grade steel scrap, high-carbon ferrochrome, and low-carbon ferro-
chrome. They may be priced and analyzed as shown in Figure 2.
Since market variations frequently influence the choice of initial charge
materials, our model must be responsive to the fifth element in the list
of input data requirements: inventory levels. Hence we will assume that
the availability of 430 grade scrap and high- and low-carbon ferrochrome
is limited to 2000 lbs. each. We can invoke similar limitations, depend-
ing on market conditions, to vary the quantities of any of the charge
elements at any phase of the process.
We will not postulate here any special raw-material restrictions, though
forcing the use of ingot weights may be an important production problem.
(This aspect of the problem will be discussed in the section on output
basis variables.)
4
Chromium minimum 16.0%
Silicon maximum 1. 0%
Manganese maximum 1. 0%
Carbon maximum 0.05%
Figure 1. Problem specifications
Steel 430 Grade High-Carbon Low-Carbon
Scrap Scrap Ferrochrome Ferrochrome
Cost per lb. $0.02 $0.075 $0.27 $0.40
Chromium 0 16.0% 55.6% 65.0%
Manganese 1.0% 1. 0% 0 0
Silicon 0.2% 0.95% 2.0% 1. 0%
Carbon 0.6% 0.12% 8.0% 0.09%
Iron 98.2% 81. 43% 34.4% 33.91%
Figure 2. Analysis of materials
The complex thermochemistry and tight controls required in the production
of the specified steel introduce problems best handled by an adaptive
rather than a static model, especially when the scrap analysis is uncertain.
1. The composition of the initial charge and the amount and variety of
reducing and finishing additives are established by a linear program,
based on final metal specifications, cost and composition of available
charge materials, and plant capacity.
2. Based on carbometer analysis and spectograph analysis of the melt,
a new linear program is formulated to determine accurately the
quantities of reducing and finishing additives required to achieve the
specified steel at least-cost.
For our purposes we need develop only the first of these programs. In
practice, the second model can be developed quite easily from the first.
The schematic of the LP model matrix (Figure 3) graphically illustrates
the steelmaking process. The detailed model matrix is shown in Figure 4.
Every source of the various elements which make up the final alloy
appears at the head of a matrix column, which is called a problem activity.
Cost, maximum and minimum specifications, and symbolic designations
for the processes which alter the element quantities provided by the
sources appear at the ends of the matrix rows, called problem constraints.
Consider the first four columns of the blending section of the matrix in
5
Column Activity Names
/ r__________________________~I~--------------------------~,
;
◦ Jabse Service Manual Search 2024 ◦ Jabse Pravopis ◦ onTap.bg ◦ Other service manual resources online : Fixya ◦ eServiceinfo