Optimisation of Manganese Alloy Multi-plant Production Planning

165 Pages·2017·13.72 MB·English

Optimisation of Manganese Alloy Multi-
plant Production Planning
Martin Naterstad Digernes
Lars Rudi
Industrial Economics and Technology Management
Submission date: June 2017
Supervisor: Magnus Stålhane, IØT
Co-supervisor: Brage Rugstad Knudsen, ITK
Henrik Andersson, IØT
Norwegian University of Science and Technology
Department of Industrial Economics and Technology Management

Problem Description
ThepurposeofthisMaster’sThesisistodevelopanoptimisationmodeltomanagemanganesealloy
production. Efficient allocation of resources across multiple plants is essential to ensure optimal
production. The primary objectives of this thesis are to formulate a model that handles complex
chemicalandpoolingrestrictionsandtoapplyasolutionmethodtoverifytheglobaloptimum.
Maincontents:
1. Descriptionoftheproblem.
2. Presentationofthemathematicalformulationdevelopedfortheproblem.
3. Presentationofthesolutionmethodappliedtosolvetheproblem.
4. Implementationandtestingofthemathematicalformulationusingtheappropriatesoftware.
5. Presentationanddiscussionoftheresultsandanevaluationoftheapplicabilityofthemodel.
I

Preface
ThisMaster’sThesisistheconcludingpartofourMasterofScienceinIndustrialEconomicsand
Technology Management with a degree specialisation in Managerial Economics and Operations
ResearchattheNorwegianUniversityofScienceandTechnology(NTNU),spring2017.TheMas-
ter’sThesisisacontinuationoftheworkdonebyDigernesandRudi(2016)inthespecialisation
projectinManagerialEconomicsandOperationsResearch,Fall2016.
We would like to thank our supervisors Associate Professor Magnus Stålhane (Department of
Industrial Economics and Technology Management, NTNU), Professor Henrik Andersson (De-
partmentofIndustrialEconomicsandTechnologyManagement,NTNU),andPostdoctoralBrage
Rugstad Knudsen (Department of Engineering Cybernetics, NTNU) for their valuable guidance
throughoutthework. WewouldalsoliketothankourindustrialpartnerErametNorwayforpro-
vidinguswithindustrialdata.
Trondheim,June7,2017
MartinNaterstadDigernes LarsRudi
III

Abstract
The average concentration of manganese in the earth’s crust is nearly 0.1%, making it the fourth
mostabundantofthemetalsincommercialuse. Manganesealloysaremainlyconsumedasalloy-
ing elements in the steel industry. Manganese ores are extracted at mining sites and smelted to
manganesealloysatsmeltingsites. Intheproductionofmanganesealloys,theproblemistofind
theoptimalcombinationofores,fluxes,coke,andslagtofeedthefurnacesthatyieldsalloysthat
meet customer specifications and to optimally decide the volume, composition, and allocation of
theproducedslagbetweenfurnaces.Thealloysareeithersoldorfurtherrefinedandthensold.The
authorsnametheproblemasthemanganesealloymulti-plantproductionproblem.
Currentdecisionsintheindustryarebasedonexperienceandprocessknowledgeandaredenoted
assinglefurnaceoptimisation. Singlefurnaceoptimisationisthepracticeofoptimisingtheprofit
for each single furnace without considering the overall production. A multi-plant optimisation
modelcanprovidedecisionsupporttotheindustryandimprovethecurrentpractice.
Apoolingproblemformulationispresentedtosolvetheproblem. Totheauthors’knowledge,little
workhasbeendoneonformulatingthepoolingproblemforproductionofmanganesealloys,and
noformulationsformulti-plantproductionexistinthisindustry. Theformulationpresentedisflow
andqualitybasedandisahybridbetweenthestandardandthegeneralpoolingproblem.Themodel
is,however,subjecttosimplifyingassumptionsthatmaylimithowrealisticitisinitscurrentstate.
ThebilineartermsinthemathematicalformulationarelinearisedusingtheMultiparametricDis-
aggregation Technique (MDT) and the formulation is implemented in the linear solver FICO(cid:13)R
Xpress. To the authors’ knowledge, this is the first model that applies the MDT to solve large-
scale,realinstances. ThemodelisappliedtotestinstancesbasedontheindustrialpartnerEramet
Norway’splantlayoutandsolvedtoaglobaloptimalitywithin3%usingtheMDT-algorithm. The
computationalstudyshowsthattheoptimisationmodelpresentedcansolveproblemsizesofupto
ten furnaces to a global optimality gap within 8% for the allotted run time, that the MDT scales
well with the problem sizes tested, and that our model outperforms single furnace optimisation.
It should be noted that the single furnace optimisation practice is based on mimicking the actual
practicebyusingourmodelandnotactualpracticeresults. Comparingthemodeltorealproduc-
tiondataremainsanobjective,buttheresultsindicatethatmulti-plantproductionplanningcanbe
ofconsiderablevaluetomanganesealloyproduction.
Apaperbasedonthecontentsofthisthesishasbeenwrittenincooperationwiththesupervisors.
Thispaper,withthetitle"OptimisationofManganeseAlloyProduction",isappendedtotheendof
thethesis. Asthepaperisbasedonthisthesis,thereisoverlappingcontent.
V
Sammendrag
Gjennomsnittligmangankonsentrasjonijordskorpenerrundt0.1%. Manganerdermeddetfjerde
mest forekommende metallet blant metaller i kommersiell bruk. Manganlegeringer blir hoved-
sakelig konsumert som legeringselementer i stålindustri. Manganmalm blir utvunnet gjennom
gruvedrift og legeringer produseres i smelteverk ved å smelte malm sammen med andre råstof-
fer i ovner. Legeringene har gitte kvalitetsspesifikasjoner og kan selges som de er, eller videre
raffineresogselges.
Problemetimanganlegeringsproduksjoneråfinneenoptimalkombinasjonavmalmer,flussmiddel,
koksogslaggåbenytteiovnenetilåproduseredesluttproduktenesomtilfredsstillerkundeneskrav,
samt å bestemme volum, komposisjon og transport av slaggstoff som kommer fra ovnene. Dette
problemet blir betegnet som multifabrikks-manganlegeringproduksjons-problemet. I dag baseres
produksjonsbeslutninger på erfaring og prosesskunnskap, dette blir betegnet som enkeltovnsopti-
mering. Enkeltovnsoptimeringerpraksisenmedåoptimereprofittforhverenkeltovnogtarikke
hensyntildenhelhetligeproduksjonen. Enmultifabrikkmodellkanbidrasombeslutningsstøttetil
industrienogforbedredennåværendepraksisen.
Enoptimeringsmodellbasertpåpoolingproblemetpresenteresforåløseproblemet. Etterdetfor-
fatternekjennertil,erlitearbeidgjortforåformulereetpoolingproblemformanganlegeringspro-
duksjonogingenmultifabrikkmodelleksistererfordenneindustrien.Modellenerflyt-ogkvalitets-
basertogerenkombinasjonavenstandardogengenerellpoolingproblemformulering. Modellen
inneholderforenklingerogantagelsersombegrenserhvorrealistiskdenerisinnåværendetilstand.
Debilineæreleddeneidenmatematiskeformuleringenerlineærisertvedbrukavmultiparametrisk
disaggregeringsteknikk (MDT). Formuleringen er deretter implementert i det lineære optimer-
ingsprogrammetFICO(cid:13)R Xpress. Tilforfatterneskunnskapermodellensompresenteresdenførste
hvor MDT benyttes til å løse store, reelle probleminstanser. Modellen benyttes til å teste prob-
leminstanserbasertpåErametNorgesittfabrikkoppsettogdisseløsestiletglobaltoptimalitetsgap
innenfor3%vedbrukavMDT-algoritmen. Enberegningsstudieviseratoptimeringsmodellenkan
løse probleminstanser på størrelser opp til ti ovner til et globalt optimalitetsgap innenfor 8% på
tillatt kjøretid, at MDT skalerer godt med størrelsen på probleminstansene som testes og at vår
modell presterer bedre enn enkeltovnsoptimering. Det gjøres oppmerksom på at praksisen med
enkeltovnsoptimering er basert på en etterligning av den virkelige produksjonen ved å bruke vår
optimeringsmodellogikkeresultaterfraenfaktiskproduksjon. Sammenligningavmodellenmot
reelledatagjenstårfremdelessometmål,menresultateneindikereratbrukavvåroptimeringsmod-
ellkanværeavbetrakteligverdiformanganlegeringsproduksjon.
Enartikkelbasertpåinnholdetidennemasteroppgavenharblittskrevetisamarbeidmedveilederene.
Denneartikkelen,medtittelen"OptimisationofManganeseAlloyProduction",erlagtvedislutten
avoppgaven. Sidenartikkelenerbasertpåmasteroppgaven,erdetoverlappendeinnhold.
VI
Table of Contents
ProblemDescription I
Preface III
Abstract V
Sammendrag VI
TableofContents VII
ListofTables XI
ListofFigures XIII
Dictionary XV
1 Introduction 1
2 IndustryInsight 3
2.1 MarketOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 MarketSupplyandDemand . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 TheSupplyChain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 TheProductionProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3.1 TheFeMnProduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.2 TheSiMnProduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.3 Ores,Fluxes,Quartz,andCoke . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.4 TheFurnace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.5 TheMOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.6 TheLCSiMnRefiningStation . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.7 TheCrushingProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.8 By-products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 TheProductionMethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.1 TheDiscardSlagPractice . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.2 TheDuplexMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.5 FurnacePowerConsumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.6 ChemicalReactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.7 ErametNorway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 ProblemDescription 15
3.1 TheManganeseAlloyMulti-plantProductionProblem . . . . . . . . . . . . . . . 15
VII
TABLEOFCONTENTS
4 LiteratureReview 17
4.1 TheBlendingProblemVersusthePoolingProblem . . . . . . . . . . . . . . . . . 18
4.2 ThePoolingProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3 ClassificationsofthePoolingProblem . . . . . . . . . . . . . . . . . . . . . . . . 19
4.4 PoolingProblemFormulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.5 ThePoolingProbleminDifferentIndustries . . . . . . . . . . . . . . . . . . . . . 23
4.6 SolutionMethodsforthePoolingProblem . . . . . . . . . . . . . . . . . . . . . . 25
4.7 TheMulti-periodPoolingProblem . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.8 OurContribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 ModelFormulation 31
5.1 ModellingChoicesandModelAssumptions . . . . . . . . . . . . . . . . . . . . . 31
5.1.1 ProblemStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.1.2 RawMaterialSupplyandCosts . . . . . . . . . . . . . . . . . . . . . . . 32
5.1.3 ChemicalConsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.1.4 SlagProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.1.5 By-products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.1.6 End-productContentSpecifications . . . . . . . . . . . . . . . . . . . . . 34
5.1.7 FurnaceSetup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.1.8 ProcessTemperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.1.9 RecoveryofThermalEnergy . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.2 DefinitionofSets,Indices,Parameters,andVariables . . . . . . . . . . . . . . . . 35
5.3 PoolingProblemStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.4 MathematicalModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.4.1 ObjectiveFunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.4.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
ResourceInventoryConstraints . . . . . . . . . . . . . . . . . . . . . . . 41
FurnaceConstraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
FurnacePowerConsumptionConstraints . . . . . . . . . . . . . . . . . . 42
Furnace-SlagConnectionConstraints. . . . . . . . . . . . . . . . . . . . 44
MORConstraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
LCSiMnRefiningStationConstraints . . . . . . . . . . . . . . . . . . . . 46
CrushingConstraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
FinalInventoryandDemandConstraints . . . . . . . . . . . . . . . . . . 48
ChemicalBalanceConstraints . . . . . . . . . . . . . . . . . . . . . . . . 48
BoudouardReactionConstraints . . . . . . . . . . . . . . . . . . . . . . . 50
ChemicalContentConstraints . . . . . . . . . . . . . . . . . . . . . . . . 50
Non-negativityConstraints . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.5 Multi-periodModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6 SolutionMethod 55
6.1 DefinitionofSets,Indices,Parameters,andVariables . . . . . . . . . . . . . . . . 55
6.2 TheMultiparametricDisaggregationTechnique . . . . . . . . . . . . . . . . . . . 57
6.3 TheLowerBoundProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.3.1 HCFeMnFurnace-SlagConnection . . . . . . . . . . . . . . . . . . . . 57
6.3.2 MCSiMnFurnace-SlagConnection . . . . . . . . . . . . . . . . . . . . 59
6.4 TheUpperBoundProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4.1 HCFeMnFurnace-SlagConnection . . . . . . . . . . . . . . . . . . . . 60
6.4.2 MCSiMnFurnace-SlagConnection . . . . . . . . . . . . . . . . . . . . 62
6.5 TheGlobalOptimalityAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 64
VIII