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Process Planning for Metal Forming OperationsAn Integrated Engineering-Operations
Perspective
Anantaram Balakrishnanand
Stuart Brown
Process Planning for Metal Forming OperationsAn Integrated Engineering-Operations
Perspective
Anantaram Balakrishnanand
Stuart Brown
WP# 3432-92-MSA May, 1992
Process Plann ing for Metal Forming Operat ions
An In tegrated Eng ineer ing— Operat ions Perspect ive 7
Anan taram Balakr ishnan
Sloan School ofManagemen tM. I. T.
Stuar t Brown
D epar tmen t ofMaterials Science and Engineer ing
May 1992
Supported by researchgran ts from MIT'
sLeadersforManufacturi ng program and Alum inum
Company of Amer ica
Abstract
Metal forming Operations such as rolling, extrusion, and drawing offer manyopportunities for operations improvement through better process understandingand improved plannin g practices . This paper addresses short and medium termplanning issues in sheet, plate, and tube manufactu ring operations. First, weidentify certain distinctive characteristics- the inherent process flexibility, closeinterdependence between successive stages, an d economies of scalehof metalform ing operations, and identify the planning an d performance tradeoffs . Wear gue that, just as product design plays a cri tical role in manufactu ring of discretepar ts, process planning has strategic importance in the metal forming context.To be successful, process planning must be closely coupled withprocessengineering efforts, and must simultaneously consider the facility 's entireproduct mix. In contrast, current process engineering efforts are mainly reactive,focusing on
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fixing problems at individual operations, ignoring the interactionsbetween successive stages. Similarly, planning activities are incremental,considering only individual products or orders one at a time rather than theentire range of product sizes to be manufactured . By working together, plannersand engineers can develop principled practi ces and process plans, analyze thesensitivity of production performance to current process constraints, and adopt aproactive process improvement strategy that focuses on critical constraints . Weillustrate these concepts using examples from aluminum tube arid sheetmanufacturing . We present an integrative process engineering- planningframework, and identify several interdisciplinary research opportunitiesspann ing management science, materials science, and mechanical engineering.
Keywords: Manufacturing, process planning, process improvement, metalforming operations, process modeling.
1 . Int roduct i on
The metal forming industry, including rolling facilities, extrusion plants, andtube and wire drawing facilities, plays an important and cri tical role in globalmanufacturing competitiveness . This industry supplies plates and sheets,extrusions, and tubes to most major manufacturin g enterprises including theautomobile, aircraft, housing, and food service and beverage industries . Theseuser industries often perform additional Operations such as stam ping, drill ing,machining
,welding and other finishing operations before assembling the metal
components in fini shed products. In 1987 , shipments of aluminum alone toUnited States ' markets exceeded 15 billion pounds, valued at over $12 billion .
(Aluminum Statistical Review, 1987 and Minerals Year Book, Thecontainers and packaging market segment accounted for approximately 30% ofthe total usage, while building, construction and transportation consumed 20%each. Over 50% of the shipments were sheet, plate and foil products, withextrusions and tube constituting another
This paper addresses planning and process improvement issues in metalforming Operations . Although metal forming has a broad interpretation, for thepur poses of our discussions we exclude "discrete Operations such as stamping,forging, cutting, drilling, welding, and machining operations . Thus, we areconcerned mainly with operations such as hot and cold rolling, extrusion, anddrawing.
The metal forming industry is characterized by large investments in plantand equipment, a wide range of product offerings, the strategic importance ofprocess technology, and universal standards for specifying, measuring, an dtesting product quality. Because of the sign i ficant economies of scale, installingmachines with large capacities
,maintaining high levels of utilization for prime
equ ipment, and improving process yield or recovery are important strategicobjectives for the industry . In tur n, these objectives of improving recovery andutilizati on have led metal forming compan ies to continually upgrade theirequipment to handle larger ingot and lot sizes . In contrast, customers are placingsmaller, more frequent orders as they move towards just-in-time procurementand production. The industry al so faces increasing pressures to improve qual ity,reduce cost and lead times, and meet more stringent specifications . These trendsmake the planning and process engineering functions critical for competitivesurvival .
Despite the metal forming industry's distinctive character istics andconsiderable economic impo rtance, the manufacturing and managemen t scienceliterature does not adequately emphasize planning and process improvementmodels that are tailored to this industry; in contrast, the literatu re on planning,scheduling, process improvement, and product design for discrete partsmanufactur ing and assembly Operations is quite extensive. Likewise, thematerials scien ce and mechanical engin eer ing literature focuses on studyingmaterial proper ties and u nderstan ding individual processing steps from aprocess development rather than a man ufacturability or planning perspective.
This paper attempts to highl ight and explore some of these issues at the interfacebetw een engineer ing and management science using two spedfic examplesaluminum tube manufacturing , and shee t and plate rolling—d eri ved from our
experience in the aluminum industry. The discussions are aimed at a broadaudience including management science researchers concerned with modelingmanufacturing operations an d developing process planning systems,engineer ing researchers dealing w ith deformation processes, and practicingmanagers in the metal forming industry. Specifically, the paper offers thefollowing contributions an d insights:
0 We argue that, just as product designhas considerable impact over themanufacturabili ty of discrete parts (see, for example, Nevins and Whitney
Clark and Fujim oto process planninghas strategic importancefor metal form ing omration s. This importance stems from the wideflexibility, bu t close coupling, between successive metal processing operations,combined with the significant impact that the choice of processing paths hasover manufacturing per formance. The current prevalent practice of treatin gprocess planning mainly as an operational fun ction does not exploit itsstr ategi c potential .
0 Exploitin g the strategi c potential of process planning requires thesimultan eous consideration of mul tiple products rather than the product-byproduct (or order-by-o rder) incremental planning procedure that bothdominates the process plann ing literatu re (see, for example, Alting and"hang and Chang (19901) and is found commonly in practice. A
systems view, incorporating multiple stages as well as multiple products, isessen tial to make appropr iate strategic and tactical decisions regarding productgroupin g, the level of commonality, and capaci ty requirements.
0 We also emphasize the close interrelationship between engineering modelsand planning models to respectively characterize the process constraints and
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capabili ties and choose effective processing paths . We propose an iterativeframework in which the planning model uses as input empirical and modelbased process constraints; in turn, the sensitivity of manufactu ringperformance to these constr aints prioritizes engineering processimprovemen t efforts . This framework represents a departure fromconventi onal process modeling efforts that focus on troubleshooting andexpanding process capability without explicit linkages to the planningfunction . The engineering- planning linkage that we descri be hasimplications both for collaborative, interdisciplinary resear ch withinuniversities and with industry, and for the design of organization stru ctures,incentives, and multi-function coordination processes between engineering,planning, and manufactu ring.
0 Finally, we identify several new problems and issues for further research.
These research issues span topics such as tactical operations modeling andproduction planning, inventory management, and deformation processmodeling .
To summarize, this paper provides an overview of two metal formingoperations, proposes an integrative process engineering and planningframework, and identifies new research issues based on our joint experiencewith several plants in the aluminum industry. We provide only a broaddescription of modeling alternatives, and do not discuss any specific analyticalresults, solution algorithms, or computational results.
Sections 4 an d 5 develop and illustrate the main themes of this paper. Sincethis discussion requires familiar ity with metal form ing processes and operations,Sections 2 and 3 provide the necessary background . Section 2 introduces ageneric two-stage process description that applies to both of our subsequentexamples- tube manufacturing and rolling. We identify the commoncharacteristics and tradeoffs underlying these two examples, and motivate theimportan ce of the process planning function in the metal forming context.Sections 3 and 4 focus on tube manufacturing. Section 3 descr ibes theengineering principles underlying tube man ufactu ring, and discusses typ icalcurrent practices in process engineering and planning. Section 4 characterizesprocess flexibility in tu be manufacturing, identifies the factors affecting extrusionand dr awing workload, and develops an integr ative framework that linksengineering and planning. Section 5 outlines process planning issues related tosheet man ufacturing (rolling), and Section 6 offers concluding remarks. Thepaper places much greater emphasis on tube manufactu ring since this example
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captures most of the principles that we wish tohighlight. We di scuss rollingOperations only briefly in order to emphasize that the same underlyingprinciples apply more broadly to other metal forming operations . Also, theseprinciples im pact both strategic and oper ational decisions . We therefore considera medium-term plann ing problem for tube manufactu ring, and a short-termdecision for rolling operations .
2 . Gener ic Descript ion of Metal Forming Operat i ons
This section presents a generic descri ption of metal forming operationsencompassing the two examples- aluminum tube man ufacturing and rollingoper ations- that we discu ss later. We will limit the discussion to the twoimportant succes sive stages in the metal forming process,hot forming and coldforming, whi ch we refer to as upstream and downstream operations .
A flat (sheet or plate) or tubular prgduct is identifi ed by its al loy, its temperand other mechanical or microstructu ral speci fication s, the physical dimensionsof each piece and their variance, and geometri c toler an ces flatness,eccen tri ci ty). For (hollow) tubu lar products, the physical dimensions are outerdiameter, wall thickness, and tube length. Sheet or pla te products are specified bytheir width, gauge (i .e thickness), and length. Both of ou r subsequent examplesare based on facilities that produce primarily to order, manufacturing severalthousand different product specifications each year .
Continuous metal forming consists of deforming the shape of the rawmateri al, e.g., rectangular or cylindr ical ingots, into the desired final shape anddimensions. This transformation typically entails successively reducing thecross-sectional dimensions ( for instance, tube diameter or sheet thickness) whileelongating the workpiece. The transformation from ingot to the final productdimensions is achieved through a combination ofhot forming and cold formingprocesses, possibly with intermediate an nealing operations . The process mightalso include some preliminary steps such as cutting, dr illing, or scalping theingot and preheating it, and some finishing oper ations such as stretching,co ating, slitting, and cutting. In tube manufacturi ng, the process of extrusioncorresponds toho t forming, while tube drawing represents cold forming (seeFigure For sheet and plate manufacturing the two corresponding stages arehot and cold roll ing.
All of our subsequent discussions focus on the interactions between the hotand cold forming stages, although the concepts that we discuss al so extend tomore than two stages (including prior stages suchas ingot casting, andsubsequent finishing Operations). An intermediate inventory stocking pointmight decouple these two stages. Each stage can have multiple steps and paral lelworkcen ters, with possible reentrant flows (mul tiple passes at the sameworkcen ter ) in the downstream operation. We will refer to the intermediateproduct produced by the upstream (hot forming) stage as semi-fin ished stock .
Hot and cold forming processes share some similarities, but also haveimportant differences. Hot forming, as the name implies, consists of deformin gthe metal at an elevated temperatur e, while cold forming processes the metal ator near room temperature . Consequently, hot forming is more "efficient" thancold working, i .e ., it permits greater amount of deformation per unit input ofenergy. However, since controlling the process at higher temperatures is moredifficu l t,hot forming cannot achieve very tight dimensional tolerances, and isalso limited in terms of the smal lest size (gauge, outer diameter, wall thickness)that it can produce . Furtherm ore, cold working can introduce some desirablematerial properties such as strength and uniformity .
The process plan for a product is the recipe speci fying its enti re processingpath . This specification includes:( i) the alloy and size of the ingot to be used,( ii) the sequence of processing steps,( iii) the type of equipment required and the processing param eters (machine
setu ps, processing speeds, special Operating instructions) at each step, and( iv) the intermediate and final product dimensions and metallurgical
speci fications .Equipment lim itations, workpiece characteristics and the underlying physics ofthe deformation process together impose upper limits on the amount ofdeformati on that can be achieved in each hot or cold forming step . The limitsdi ffer substantial ly forhot an d cold forming, and depend both on equipment andproduct specifications . In general, the number of processing steps increases as thedi fferential between the geometries of the initial workpiece and final productincreases . For ou r examples, we will express this differential as the differencebetween the cross-sectional ar eas of the workpiece and the finished product.
Let us now describe thr ee important common features that characterize ourtwo metal forming examples .
0 Meta l forming operations perm it a wide range offlexibility, i .e., each fini shedproducthas num erous alternate process plans. In par ticular, for everyproduct, the process planner can choose from a conti nuum of intermediateproduct dimensions (subject to certain process constr aints) at each processingstep . In Section 4, we provide a novel char acterization of processing flexibilityfor tube drawing operations .
0 The upstream and downstream stages ar e highly interdependent, and thechoice of processin g paths has a significant impact on the processing effor t
requ ired at each stage of the manu facturing process. The selected process planfor each product determ ines both the total workload to deform the ingot tothe required final dimensions, and the relative allocat ion of this workloadbetween the upstream and downstream stages .
0 Due to the significant equipment setu p and changeover times and the fixedprocess scr ap requirements, upstream operations strongly favor large lot sizes.
Chan ging over from one product size to another requires changing the roll s,dies , and other tooling, as well as preheating ingots, and processing tes t runs( to stabilize and debug the process). The second factor contri buting to thescal e econom ies is the fixed scrap for each lot or ingot. For instance, a certainfixed length (independent of the ingot size) of the leading and trailing ends ofaho t-rolled sheet must be scrapped because it does not meet materialproperties and dimensional specifications.
These three characteristics processing flexibility, interdependence betweensuccessive stages, and economies of scale create opportunities to improve theplant's effectiveness thr ough principled process planning . In particular, we canexploit the process flexibil ity to achieve economies of scale in the upstreamoperation by lim iting semi-finished stock to a few standard sizes even thoughthe num ber of finished product sizes is very large. This standardization of sizesenables us to either produce to stock in the upstream operation ( if the facilitymaintains semi-finished inventories) or consolidate multiple customer ordersinto a single lot at upstream operations. Both these strategies increase theupstream lo t sizes, thus reducing the number of setups, increasing recovery, andlower in g the un it cost of production. If the upstream Operation produces tostock, limiting the number of standard sizeshas the added advantage of reducingthe safety stock levels due to greater comm onality.
Observe that we have generalized the conventional notion of commonality.
In discrete par ts manufactur ing,commonali ty refers to shar ed raw mater ials or
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components, i .e., overlaps in the bills of material of two or more products (see,for example, Baker et al. and Gerchak and Henig In the metalforming context, however, commonali ty refer s to a shared set of processing stepsfrom the first ( ingot castin g) stage to some intermediatehot or cold formin g step.
The degree of commonality between two products depen ds on the exten t towhichtheir process plans overlap . The inherent flexibili ty in metal formingoperations permits us to intr oduce this commonality. However, selecting a veryhigh degree of commonality might potentially increase the downstream effortsignificantly (since many different finished sizes must be produced from acommon semi-finished size). This tradeo ff between commonal ity and balan cedworkloads will be the main theme of ou r discussions in Sect ions 4 and 5 .
One implication of this tradeoff is that, contr ary to the prevailing practice ofproduct-by-product process planning, we must simultaneously plan theprocessing steps for multiple products . We will argue that resolving the tradeoffeffectively requires not only a principled planning model that judiciously selectsprocess plans for mul tiple products, but also a good understanding of theprocessing constraints . Next, we describe the specific processing steps andconstraints in tube manufacturing.
3. Tube Manufactu r ing:Backg round and Current Pract ice
This section special izes the previous generic two-stage process representationto tube manufactu ring operations . Section outlines the process flow andengineering principles underlying tube drawing and extr usion, and Sectiondescribes current process planning practices and typical process engineeringconcerns .
The process of man ufacturing hollow, seamless cylindrical tubes consists ofan extrusion (ho t forming) step followed by one or more tube drawing (coldforming) passes, possibly with intermediate annealing operations (see FigureEach step of the process reduces the ‘ cr oss-sectional dimensions ou ter diameter
(OD) an d wall thickness (WT) of the workpiece, and increases its length . As wenoted in Section 2, since extrusion is a hot process, it cannot achieve tightdimensional tolerances and is limited in terms of the min imum possible outerdiameter and wall thickness. Subsequent tube drawing operations are, therefore,required to further reduce the cross-sectional dimension s, meet stringent qualitystandards, and achieve desired material properties. We refer to seamlessextruded tubes produced by the extrusion press as blooms , and to drawn tubes,
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i .e . , blooms that have undergone one or more tube drawing passes, as tl rpgg .
Thus, blooms correspond to the semi -finished stock in our previous two-stagerepresentation. Using simple schema tics and a two-dimensional process planrepresentation, the next section descri bes the engineering pr inciples and processlimi tations of extrusion and tu be dr awing. Subsequent sections then indicatehow these constraints bo th interact with and are included directly within processplanning .
Tube Drawing and Ext rus ion:Eng ineer ing Pr inc iples
We will concentrate on the tube dr awing process, di scussing extr usion onlybriefly at the end to indicate the types of processing constraints it imposes .
Tube Drawing
Tube drawing involves pulling a tube, at room temperature, through astationary die with an annular orifice thathas a smaller cross sectional area thanthe tube . The tube consequently decreases in both wall thickness and diameterand increases in len gth. Repeated dr awing steps therefore permits themanu facture of very smal l tubes from initially large bloom sizes . Normal ly, theannular space is formed by a inner mandrel and an outer die as shown in Figur e2. Figure 3 schematically illustrates various types of tube dr awing depending onthe relative sizes and location of the tube, die, and mandrel .
D raw -benchoperat ionPrior to its first drawing pass, each incoming bloom is crimped at one end,
forming a "point" . Each drawing pass starts by threading the tube over themandrel , lubricating the inner and outer surfaces of the tube, and passin g thecrimped end of the tube through the Opening of the die. A set of jaws on theother side of the die grabs the crimped end of the tube, and pulls the tubethrough the annu lus formed by the mandr el and the die. The mandrel is heldplace by a rod that extends past the opposite end of the tube . Notice that thediam eter of the die and the mandrel respectively determine the outside andinside di ameter of the drawn (output) tube.
Graphica l represen ta t ion of t ube draw ingBefore discussing the equipment and workpiece constraints that lim it each
tube drawing pass, let us first introduce a convenient graphical represen tationcalled the Tube Reduction D iagram. The Tube reduction diagram shows thechanges in the tube's dimensions wi th each drawing pass. Since we are focusing
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0physical and operat ional cons iderat ions:for example, the setup operationsof threading the tu be over the mandr el and through the die must berelatively easy .
To deri ve process constr aints that satisfy these condi tions, let us first understandthe important physical principles under lying tube drawing, and descri be therestri ctions qual itatively. Later, we will show how to approximate and expressthese restrictions in terms Of the dimensions of the input and drawn (output)tubes .
Maximum reduction per drawFirst, drawing a tube requires a certain amount of force to pu ll the tube
throughthe die. The amoun t of force depends on a number of factors in cludingthe required reduction in OD and WT, the deformation resistance of the inputtub'e material, fri ction between the tube, die and mandrel, as well as processingconditions such as ambient temperature, lubri cation, and tooling (for instance,die geometry) . For a given set of processing conditions, the pulling forceincreases as the amount of required reduction increases, and is higher for inputtubes that deform less easily . Higher pu lling forces normally increase fri ctionwhich in turn further increases the force necessary to pull the tube through thedie-mandrel annulus . Beyond a certain limit, increasing the force might breakthe tube, degrade the su rface quali ty, or cause excessive die wear. Fur thermore,the maximum pulling force is al so limited by the machine 's power. Tosummar ize, workpiece failure and equipment capabili ties limit the maximumpulling force and hence the maximum amount of OD and WT reduction thatcan be achieved in a single drawing pass; the actual value of this lim it dependson the deformation resistance of the input tube (which varies with the tube'sprocessin g history), its alloy, and the die-mandrel setu p. We will refer to thi srestriction on the output tube
's relative OD and WT as max reduct ion/draw.
Work hardeningThe other important phenomenon to consider in tube dr aw in g is workharden ing. As we reduce the cr oss-sectional area of a tube, the deformationwi thin the die work-hardens the metal by increasing the average dislocationdensity. By definition, the amount of work-hardening corresponds to increasingthe tube's resistance to deformation. The tube man ufacturi n g process exploitsthis har dening whi le simultaneously limiting its cumulative effect. Workhardening increases the stren gth of the metal, preventing the smaller outputtube from immediately breaking as it pul ls on the remainder of the tube duringthe drawin g process . However, in a mul ti-draw process plan, where the outputfrom one draw becomes the input to the next draw, the tube work-hardens
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successively less with each dr aw, increasing the likelihood of breaking as it exitsthe die. To prevent tube breakage, we impose an upper limit on the totalamount of deformation that a tube can experience before it must be annealed.
Annealin g consists of holding the tube at an elevated temperature for a specifiedtime to resoften the metal, permitting addi tional work-hardening and henceadditional draws to further reduce the cross-sectional dimensions. We refer tothe restriction limiting the cumulative work-hardening before the tube must beannealed as the max work-harden ing constraint .
The third class of constraints stems from a product's temper specification.
Some alloys require a certain minimum am oun t of work-hardening after the lastannealing operation to assure adequate dislocation density so that the productachieves the desired rn icrostru ctur es during subsequent heat treatm ent. Thisrequirement imposes a min final cold work constraint.
The max reduction / draw, min final cold work, and max work-harden ingconstraints effectively restrict the lengthof each line segment in the piecewiselinear representation of a process plan on the tube reduction diagram . Otherfactors in tube drawing act to constrain the orientation the angle) of theseline segments . Notice that the orientation of the line segment connecting theinput and output tubes of a drawing pass ( in the tu be reduction di agram)depends on the relative ratio of reduction in OD to reduction in WT. This ODto—WT reduction ratio impacts the process yield since it affects the surface qualityan d dimensional tolerances of the drawn tube . We will examine two extremeratios corresponding to sinking and ironing operations .
A large diameter-to-wall reduction ratio corresponds to the sinking Operation .
Figur e 3a shows schematically a "pure sinking operation that is unsupported bya mandrel . This mode of operation yields a large reduction in the outerdiameter; the wall thickness may increase or stay the same depending on thestate of stress that develops in the tube during drawing. Notice that sinkingcorresponds to a horizontal (or even upwar d sloping) processing path in the tu bereduction diagram (Figure Sinking operations can cause irregular surfaces onthe inner tube diameter and are, therefore, usually avoided .
At the other extreme, the iron ing operation illustrated in Figure 3chas arelatively small OD -to-WT reduction ratio since it leaves the inner diameterunchan ged while reducing the wal l thickness . Ironing is difficul t to achieve in
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high volume production since it requir es threading the tube's inner diameterover a mandr el with the same outer diameter. D ifficul ties with both sinking andironing therefore impose lower and upper limits on the OD -to-WT reductionratio for each dr awin g pass.
Ma thema tica l represen ta tion of constra in ts
Our previous di scussion identified and justified five di fferent classes of tubedrawing restri ctions-max reduction / draw, max work-hardening, min final coldwork, sinking, an d ironing—due to equipment limitations and process yield orquality considerations . From a process planning perspective, we wish totr anslate these restrictions into limits on the length an d the orientation of theline segments in the process plan 's piecewise linear representation in the tubereduction diagram . Effectively, these limits specify the range of permissibleinput-to-output (dimen sional ) tr ansformations dur ing each draw, and betweenann eal ing steps . Using such limits, we can then easily check if a chosen plan is
feasible, i .e ., if it meets all five restrictions . To convert the original restri ctionsmax work-hardening) into equivalent mathematical constraints on the tube
reduction diagram we will use certain approximations an d su rrogate metri cs thatare functions of the OD and WT of the inpu t and ou tpu t (or drawn) tube at eachdrawing pass, and the star ting and ending dimensions between intermediateann eal ing operations . The subscripts in and ou t denote respectively thedimensions of the input and output tube for a given draw.
First, let us consider the max redu ction ldr aw constraint. This restri ctionlimi ts the drawing force and hence the amount of deformation in each drawingpass to prevent equipment and tube failures . We use the reduction in crosssectional area (CSA) of the tube as a measure for the amount of deformation; theupper limit on CSA reduction is expressed as a proportion of the CSA of theinput tube at each draw. Thus, the max reduct ion/draw constraint becomes:
(CSAin CSAou t) CSA.“ 5 scsamax ,
where the param eter SCSAmaxhas value between 0 and 1 . Recall that the CSA of
a hollow tube is n WT (OD -WT) .
The amoun t of inelastic deformation, whichdictates the amoun t of workhar dening, co rrelates approximately with the CSA reduction. Therefore, we canlim i t the amount work-hardening by specifying an upper limit on the total CSAreduction before an intermediate annealing operation is required . This
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approximation gives the following max work-hardening constr aint (again, weexpress the limit as a of the CSA of the starting tube):
(CSASCSA
e) CsA
ss ACSAmax
where CSAsand CSA
edenote the tube's star ting and ending cross-sectional areas
between annealing steps . The parameter ACSAmaxhas value between 0 and 1,and exceeds SCSAmax.
The actual values of the lim its 8CSAmax and ACSAmax in the maxreduction / draw and max work-hardening constraints are determined by theprocess engineers thr ough process understanding, experience andexperimentation . They vary with the par ticular alloy being drawn. Certainal loys (such as the 6000 series of aluminum alloys) are designed specifically forlarge reductions per draw, and can withstand many draws before requirin g anann ealing treatment, while other alloys are significantly less easily drawn . Thevalues of SCSAmax
and ACSAmaxal so depend on the equipment capabilities, the
die geometry an d setup, and processing conditions lubrication, ambienttemperature), as well as the dimensions of the input tube "thin wall" tubesmight permit only lower CSA reduction per draw) an d its processing history .
work constraint in terms of CSA reduction as follows
(CSAS; CSAf) CSA
S2 1mm,
where the subscript 5 denotes the tube immedi ately after the last annealing step,and f represents the fin ished tube . The parameter 1mmdepends on the alloy andtemper specification.
The sinking and ironing constraints limit the OD -to-WT reduction ratio; wewill interpret and approximate them ‘as lower and upper limits on the angle ofthe line segment connecting the output tube to the input tube (for each drawingpass) in the tube reduction diagram . We will refer to thi s angle as the drawingangle. Let u s first consider the iron ing constrain t which specifies that the innerdiameter or ID OD 2WT) of the output tube must be no greater than the IDof the input tube, i .e.,
2WTin ) 2 (ODou t
2WTou t) '
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Effectively, the constraint imposes an upper limit on the drawing angle. Ironingcorresponds to the limiting case with ID
inID
ou t. We must also provide for
some clearance to thread the mandr el. Recal l that the diameter of the bulb at theend of the mandrel, which equals the inner diameter ID ou t of the output tube,must be first thr eaded through the input tu be before drawing. To convenientlythread the tube, we require a minimum clearance between the bulb and theinner diameter of the input tube. One way to approximate this bulb clearancerequirement is by decreasing the upper limit on the drawing angle. In general,this u ppg r drawing angle constraint has the following form:
(wr - wrou t) (OD 0 0
0m) 5 tan em
Based on their experience, process engineers m ight choose a conservative ( lower)value for the parameter Gmax to ensure good qual ity tubes .
Just as the ironing constraint imposes an upper limit on the dr awing angle,the sinkin g constraint specifies a lower limit. The general form of the lowerdrawi ng angle constraint is
(wi in- wr
om) / (OD 0 00m) 2 tan 9mm .
Sinking corresponds to a dr awing angle 9mmof Again, process engineers
might specify a larger value for this lower dr awing angle to ensure adequateprocess yield.
Ca libra t ing the con strain tsThe constraints described above, with other constraints that capture
limi tations due to process equipment, lubrica tion, or operating conditions, canrepresent a set of rules or standard practices that serve to define bounding processcondi tions on the production of drawn tube . For a parti cular alloy and tubedimensions, the standard practice Specifies the values of the var ious maximumand minimum GSA reduction and draw ing angle parameters. Currently, thesestandar d practices are primarily experience-based, and al though they reflectactual physical processing constraints they have not been derived from firstpr inciples and engineering analysis.
To accurately calibrate these constraints to determine the true values ofthe param eters SCSAmax and so on), we must use a combination of process
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modeling and designed experiments. Process model ing techniques such as fin iteelement methods provide a way to visualize the complicated deformations, dieinteractions, lubricant effects, an d deformation heating effects associated withtube draw ing. Nonlinear finite element programs such as ABAQUS (H ibbett,Kar lsson and Sorenson, In c. and ALPID (Batelle ResearchLaboratories
are sufficiently powerful to model bu lk deformation processes includingthe effects of large deformations, nonlinear constitutive behavior, and coupledthermomechan ical deformations, although particul ar difficul ties sti ll exist withthe model ing of thr ee dimensional contact. While process modeling providesphysical insight, it does not guarantee that all of the relevant factors affecting theprocess are correctly modeled or included wi thin the model . Conversely, inmany cases, designed experiments would be either impossible or too difficult tocapture the range of condi tions that modeling can simulate. Thus, processunderstanding and constraint character ization requires a combined approachemploying modeling, designed experiments, and manufacturing experience.
The manufacturing experience component is critical since without thisexperience models can Often represent a process incorrectly, an d processengineers might form incorrect conclusions from experiments .
This sectionhas identified and formulated the deformation limits imposed bythe tube dr awing process . We defer discussion onhow to use these constraintsfor process planning in order to first briefly outline the factors limiting theextrusion operation .
.2 Extrus ion
Extrusion consists of producing a long par t with a given cross section byforcing a hot metal workpiece through a die with a cutout of that cross section(we consider only hot extrusion, although cold extrusion is al so possible).Extrusion is a particu larly efficient forming process since it can produce verycomplicated, and intri cate geometries from large, simple starting workpieces. Forthe production of tubes, the starting extrusion workpieces are simple solid orhollow cylindrical ingots .
Like tube drawing, several processing constr aints limit the bloom sizes thatcan be produced on a given extrusion press (we refer to seamless, cylindricalextruded tubes as blooms). First, as the differential between the cross-sectionalareas of the ingot an d the bloom increases, the requi red ram force to push theingot through the die also increases . The press' capabilities therefore limit themaximum possible cross-sectional reduction. Extrusion engineers might Specify
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this cons traint as an upper limit on the Extrusion Ratio which is defin ed as theratio of cross-sectional areas of the ingot and the bloom. Notice that thisconstr aint is analogous to the max reduction per draw constraint for drawingoperations . The capacity of the extrusion press and its cylinder size also restri ctsthe length and diameter of the starting ingot.
The extrusion process is also con strained by thermal considerat ions . Theingot must be preheated above a certain minimum temperature to achieve therequired deformation with the available ram force . However, the heat dissipatedduring deformation increases the temperature of the metal . Above a cer tainalloy-dependen t maximum temperature the metal becomes too so ft an dpr oduces weak extrusions withpoor surface quali ty . Furthermore, certain al loyscan withstand only a limited amount of deformation before they developinternal defects that either weaken the extruded tube or develop later as surfacedefects . These factors again limit the am ount of cross-sectional reduction .
U sing these extrusion constraints we can develop standard practice rulesanalagous to the tube dr awing guidelines . These rules then determine if apar ticul ar bloom size can be extruded from a specified ingot. We next descri becurrent practices in process planning an d process engineering for tubemanufacturing operations .
Cu rrent Pract ice in Process Eng ineer ing and P lann ing
Process Plann ing
As we mentioned previously, neither the literatu re nor current practiceadequately emphasize the strategic importance of process planning. In stead,
process planning is viewed mainly as an operational function, with much of theemphasis on how to automatically generate the process plan for a given productspeci fication (see, for example, Alting an d "hang CIRP Chang andWysk van 't Erve and Chang In particul ar, the li teraturefocuses on process planning for a single part (primarily non-prismatic parts), andconsiders mainly machining operations; thus, the literature addresses questionssu ch as what is the appropriate computer representation of the product design,how to infer the required processing steps from this representation, and how toprovide computer support for developing the detailed process plan . Resear chershave iden tified two basic methods for process planning-generative methods thatconstr uct process plans from first principles based on the part geometry,tolerances, and material, and var ian t methods that identify simi lar par ts that
— 16
We next describe a typ ical process planning scenario from practice. When thecustomer places an order, the process planner (who is not necessarily a processengineer) receives the product specifications, and is responsible for prepar ing arouting sheet containing the detailed processing steps- from ingot to finishing- toproduce the item. In preparin g this process plan, the planner must operatewithin certain prespecified boundaries. For instance, the extrusion plant mightprespecify a set of stan dard bloom sizes that it can produce, thus limiting theavailable processing path choices from ingot to extrusion. In this case, theplanner must(i) select the best available bloom size (OD andWT) for the product,( ii) speci fy the lot size (number and weight of ingots and blooms) afteraccountin g for extrusion and tube drawing process yields,
( iii) determine the seq uence (and intermediate dimensions) of tube drawingand ann ealing operations to reduce the selected bloom to the requiredfinished size, and
( iv) specify the required finishing operations .
To select the appropr iate bloom size for an order, plan ners often use thevariant method since it uti lizes a previously proven processing path with anacceptable recovery level . Thus, the process planner first identifies a previousproduct with identical or very similar specifications, and chooses the samebloom size for the new order. If the previous product had the same specification,the planner uses the same process plan; otherwise, he applies the draw plan ningprocedure that we descri bed earlier. Occassionally, the previous bloom size mayno longer be available as a stan dard size, in which case the planner chooses asimilar bloom from the available stock sizes . Thus, the process planner isgen erally more concerned with selecting a proven process plan, rather than onethat explicitly considers drawing or extrusion effort . As one example, an analysisof actual process plans over a 3-monthperiod in a tube manufacturing plantrevealed that a potential savings in tube dr awing effort (drawbenchhours) ofapproximately 20% was po ssible
.
by mer ely selectin g, for eachfinished, the closestfeasible bloom from the current list of standard bloom sizes ( this analysis ignoresthe impact on extrusion effort). In part, the process planners
' emphasis onprocess feasibility rather than manufacturing effort and complexity reflects thedi sadvantage of using standar d practi ce ru les that are not completely reliablebecause they are based on experience rather than deep process understanding.
Furthermore, the standar d practice rules do not provide any guidance on howthe product quality varies as the draw param eters drawing angle, CSAreduction per draw) vary.
_ 1g _
How does the extrusion plant decide the standard bloom sizes"This decisionis largely evolutionary. For instance, the extrusion facility is mainly concernedwith maintaining large lot sizes in order to achieve its throughput and efficiencytargets number of pounds extruded per month, effective press util izationand so on ) . Therefore, if the plant receives a large order whose volume ishighenough to justify introducing a new bloom size, the extrusion plant m ight agreeto add this size to its standard list; conversely, sizes that are not active for acertain period of time are discarded from the list. Selecting standard bloom sizesin a pr incipled way is the main theme of Section 4.
Process Engineering
Process engineers typically specialize in individual processes extrusionor tube drawing), focussing on improving the efficiency or yield of that process .Thus, extrusion engineers are concerned with optimizing the extrusion speedand controlling the defect rate for a specified bloom . Similarly, for a givenprocess plan, tu be drawing engineers seek optimum die setups, lubrican ts, anddrawing practices to improve quality .
Setting priorities is a challenge for process engineer ing since the engineermust address immediate process problems while stil l pursuing longer termimprovements . The immediate problems frequently pert ain to a specific lot orpiece of equipment. Due to the pressure to find qui ck solutions to disruptions indaily production, the process engineer becomes preoccupied with"fighting fires",and lacks the guidance necessary to formulate a consistent plan of attack for longterm process improvement. Furthermore, the engineer seeks ways toincrementally modify the current practice without considering morefundamental changes in the process .
Even when the opportun ity exists for broader process improvement, it maybe difficult to select the most critical part of the process to address. What mayappear to be the most di fficult problem on a local process scale may not beeconomically the most important constraint on the process . To increasemanufacturing flexibility without sacrificing either manufacturing efficiency orquality, the engineer needs to know both which process constraints, if relaxed,would offer the most benefit and which constraints are most amenable torelaxation . In many cases the rationale for one set of constraint parameter valueshas been lost due to chan ges in technology and product mix, and the standar dpractices Specified for a given process may be the result of habit rather than
en gineering knowledge. The next section provides a framework to incorporatemanufacturing an d process constraints directly into the planning process, whichthen feeds back sensitivi ty analysis to the engineerin g activity to identify"critical " constraints .
4 . Tact ical Process Plann ing for Tube Manufactur ing
This section deal s withhow to use the inherent process flexibility of tubemanufacturi ng wisely to medi ate between the conf licting Objectives of extrusionand tube drawin g. We first develop a char acterization of processing flexibilityusing the dr awing and extrusion constraints descri bed in Section and brieflydiscuss the factors affecting the workload in extrusion and tube drawing. Thisdiscussion leads naturally to the tradeoffs and constraints of a medium-termplanning model to select standar d bloom sizes. We descri be an iterativeengineering-planning framework using this model, and identify several relatedresearch issues .
We define process flexibili ty as the opportunity to choose from a range ofal ternate proces s plans for each product. Tube drawing and extrusion operationspermit wide flexibil i ty, and the processing path choices greatly influence both thetotal workload and its relative distribution between extrusion an d drawing.
Exploiting process flexibility to balance and contro l the workload requires amedium to long-term systems view that closely coordinates engineering andplanning activ iti es . However, as we have noted, process planning is oftentreated as an on -line, operational function; it is typically myopic considersone product at a time) and is largely based on pasthistory. Correspondingly,process engin eering efforts are mainly reactive, addressing cu rrent difficul ties inindividual processing steps . We motivate an d formal ize a medium-term processengineering and plan ning framework to systematically address extru siondr awing tradeoffs .
Character izing Tube D rawing and Ext rus ion Flexibility
Our discussion of tube drawing constraints in Section had the implici tpurpose of determining the set of finished tube sizes that can be produced from agiven bloom. Indeed, current standard practi ce ru les were developed primarilyto support this "
top-down" view, with planners usin g the rules to verify if they
can produce a par ticular product from a specified bloom, and to construct asatisfactory process plan . Most computer aided process plann ing systems
_ 20 _
reinforce this view of the planning function by automating the feasibilityverification tasks . However, the mathematical representation of the constraintsin the context of the tube reduction diagram is very powerful, an d enables us toaddress the conver se question, namely,
"given a desired target point i .e., finishedtube, what are the possible bloom sizes that can produce this tube"" This"bottom-up
" view of processing constraints provides substan tial latitude to theprocess planner in selecting an appropriate bloom size, and designing a tubedr awing plan from first principles without the restri ction of prior processinghistory .
To characterize the flexibility of the tube drawing process, we partition thefeasible bloom sizes that can produce a given finished tube size according to thenumber of drawing passes and intermediate annealing operations they requ ire.
Consider, first, the subset of blooms that can produce the finished tube in a singledr aw. This subset, shown in Figure 5, consists of all sizes that satisfy the lowerand upper drawing angle constraints and the minimum final coldwork constraint and the maximum reduction per draw constraint Werefer to the ar ea contained within the Iso-CSA l ines representing the rn inumum
cold work limit Tmin and the maximum reduction per draw limit SCSAmax, and
the lines defining the upper and lower drawing angles as the 1-draw region . As
shown in Figure 5, we can recursively construct the feasible ar eas for multipledraws, introducing intermediate annealing steps as necessary.
The feasible area rgpresen tat ion conveniently character izes the inherentflexibility of tu be drawing operations, with larger areas denoting greaterflexibility. (This type of flexibility is sometimes called range flexibility; see Slack
Upton Process engineers can increase flexibility in di fferentdirections by exploring the limiting values for each of the constraint parametersSCSAmax, ACSAmax, Omax, and firm“
. The feasible ar ea representation also verifiesou r previous observation that blooms that are farther away from the finishedtube require more number of draws, and hence more drawing effort.
The tube drawing feasible area is analogous to the concept of processing mapsthat have been popularized in materials manufacturing. Woodyatt et al . [1992]
use a graphical representation to show the range of mechan ical propertiestensile and yield strength) and chemistries carbon, manganese, and sulfurcontent) corresponding to different grades of steel . Frost and Ashby [1982] andAshby [1985] have developed deformation maps andho t-isostatic pressing mapsthat assist the process engineer to Operate witha desired range of materialbehavior. Forming limit diagrams have been applied to the shaping of sheet
_ 21 _
materials thr ough stamping and shee t dr awing (Wagoner, et al .However, these concepts have not been extensively implemented within othermetal working processes, such as tube form ing or rolling. As we will show
,they
can be di rectly coupled to the plannin g process, providing both engineeringinput directly to the planning operation and economic information to theactivity Of process improvement.
Just as we used the tu be dr awing constr aints to define feasible bloom sizesthat can produce a given tube, we can also use the extru sion constraints to defin efeasible ingot sizes that can produce a given bloom size. Alternatively, given aset of standar d ingot sizes, we can use the extr usion constraints to define the setor area Of bloom sizes that the press can produce from these ingots. Byoverlapping this area withthe feasible drawing area for a particular tube we canidentify bloom sizes that are feasible for both extrusion and drawing.
We should note that the process flexibility demonstrated by feasible areasrepresents a double-edged sword. Exploited systematically, we can use thisflexibility to enhan ce competitive advantage. Exploited piecemeal, the practice ofincremental planning can resul t in contradictory process plans over time sincesim ilar tu bes can have dramatically different processing paths . Furthermore,without a consistent set of practices, process engineers cannot rely upon eitherhi storical data or implement system-wide improvements .
Determinants of Extrusion and Tube D rawing Effort
Given the wide spectrum of bloom size and dr aw planning choices facing theprocess planner, we are interested in understanding the effects of these choiceson extr usion and tube drawing effort in order to balance the workload.
Ext rusion effo r tTo understand extrusion workload, we wil l focus on how the effect ive
extrusion speed, a common performan ce metric for extrusion managers, varieswith bloom dimensions and lot size. Effective speed is the number Of "good"
pounds extr uded per hour of press usage ( incl uding batch setup time); it dependson the total processing time for a batch and its recovery rate. The total time toextrude a batch of blooms with specified length and CSA consists of:( i) the presssetup or chan geover time, which might be sequence-dependent, and includes thetim e to preheat the ingot, and change the tooling (dies, mandrel, and possibly thecylinder), and ( ii) the actu al extrusion tim e whichequals the batch size
( including scrap) times the extrusion rate . The extrusion rate ram 5
decreases as the cross-sectional area of the bloom decreases .
The recovn rate good pounds as a of total pounds extruded) inextrusion also depends on the batch size and bloom dimensions . Plann ed scrap,consisting of fixed lengths ( largely independent of bloom dimensions) from theleading and trailing ends of each bloom or batch of blooms, decreases as a of
total extruded weight when the batch size increases. The extrusion process alsointroduces random defects (surface defects and dimensional variations) whichtend to increase as the bloom's CSA decreases .
Because effective extrusion speed and recovery increase with batch size,extrusion man agers strongly prefer to produce fewer and preferably large GSAbloom sizes in large batches .
Tube draw ing effo rt
Tube drawing workload increases directly with the number of drawing passes .
The batch size and dimensions of the tube affect the time requ ired for eachdr awing pass . We can broadly decompose the total time required for eachdrawing pass into two components:( i) batchsetup time:consisting of the time toload and unload racks of tubes (using, say, cranes or forklift trucks), to change thedie set on the draw bench, and to draw one or more trial tubes to validate an ddebug the drawing pass; and ( iii) the processing time for eachtube:consisting ofthe time to set up the tube on the draw bench thread the mandrel throughthe tube, and the actu al drawing time. The drawing time is proportional tothe length of the output tube (which increases from one draw to the next), andthe drawing speed; this speed depends on the draw bench's capabilities an d therequired CSA reduction per draw. In addition to draw-bench time, we must alsoconsider the time required for materials handling and intermediate annealingOperations . More importantly, material s handling and anneal ing in troduceadditional defects surface defects) and might severely degrade process yield;the batch size (and hence workload) correspondingly increases to produce therequired number of good finished tubes for a given process plan . To summ arize,the various ingredients of tube dr awing workload lead managers in the drawingfacility to strongly prefer process plan s that require very few drawing passes andno in termediate annealing steps so that they can improve their performancemetrics such as recovery rate, throughput total pounds or feet of gooddr awn tubes produced per month), and productivity.
The Bloom Sizing Problem
Flexibili ty in tube manufacturing impacts long-term capacity plam i ing,
medium -term tooling, and short-term lot planning decisions . In this section, wefocus on a medium-term ( say, annual) tactical planning decision, n amely, theproblem of selecting a set of standard bloom sizes . We refer to this decision asbloom sizing.
The interdependen ce and tradeoffs between extrusion and tu be dr awingworkloads motivates the bloom sizing problem . The downstream ( tubedr awing) stage prefers to select a tailored bloom size for eachof its finished tubesizes in order to minimize the number of draws and eliminate intermediateannealing steps. In terms of the tube reduction diagram, this draw-effor t
min imizing strategy would select, for each fin ished size, a bloom belonging tothe 1-draw feasible region for that tube; yield variations and extrusion feasibilitydetermine the exact bloom size within (or even beyond) this area . This strategyrequires a large number of bloom sizes ( in the worst case, as many bloom sizes asthe number of finished products), withrelatively low annual demand for eachbloom size and possibly low extrusion rates .
Conversely, the extrusion plant prefers to exploit commonality in order tolimit the number of blooms to a set of standard sizes that it can produceefficen tly. Conceptually, the same bloom can
"serve" k different finishedproducts if it lies in the intersection of the feasible drawing areas for these kproducts . Even within this intersection, the drawing facility might prefer a sizethat has the smal lest weighted distance ( in terms of number of draws) to the ktar get points, whi le the extrusion plan t might choose a differen t size tomaximize effective extrusion speed . Observe that as k increases, the totalvolume of finished products served by the bloom increases, improving extrusionperformance; however, the area of intersection decr eases, possibly increasing theweighted distances and hence the total drawing effort .
This tradeo ff between extrusion an d dr aw ing effort is the crux of the bloomsizing problem . Given the projected product mix and volumes, the bloom sizing
prgblem consists of selecting a se t of standard bloom sizes (and deciding thedraw plan for each product) to "effectively" resolve the extrusion-drawingtradeoff. As we shall see later, we can represent the tr adeoff in variousal ternative ways by including the extrusion and dr awing effort either in theobjective function or as constraints . Observe that selecting standar d bloom sizesis a special case of the more general commonality selection problem of choosing
(u) Processing constrain t parameters:To select bloom sizes and dr awing plan sthat are feasible, we require:( i) standar d practice rules defining the feasibleextrusion area, and ( ii) the parameters OCSAmax, ACSAm ax,
0m “,
and 9mm) defining the tube dr awi ng restrictions . We assume that either
these constraint parameters define preferred Operating regions withacceptable yield, or the process engineer characterizes yield as a function ofthe drawing plan's param eters variations of yield with draw angleand CSA reduction per dr aw).
( iii) Procmsing effort par am eters:To quan tify extrusion and drawing effort,we require formulae and procedures to calculate the total extrusion anddr awin g effort (expressed, say, in monetary values) as a function of thebloom dimensions and drawing plans. The extrusion and drawing effortmodels require speed and yield parameters based on process engineering.
The planning model has two sets of deci sions:( i) selectin g standard bloomsizes (OD andWT), and ( ii) assign ing each fin ished product to a selected bloom.
specify the preferred process plan for all the products in the medium-term .
Given the projected demand for each finished size, the tube-to-bloomassignments determine the total required production volum e of eachstandardbloom size, and hence the total extrusion effort. For each fin ished product, thedr awin g plan is a function of the bloom that is assigned to that product; hence,the tube to-bloom assignment determines the total tube dr awing effort. Thisassignment also determ ines whether the tube requi res intermediate annealing
To ta l cost m in im izing model
First, let us describe a simplified planning model that minimizes the sum of
the annual extrusion and drawing effort. For this model, we assume lot-for-lotextrusion, i .e each extrusion lot produces blooms for a single dr awing lot which,in turn, corresponds to a unique customer order. Our basic planning model al soign ores the sequence-dependence of setup times in extrusion. Since cylinderchangeovers are the most time-consuming activities, assumin g that setup timesdo not depend on production sequence is reasonable if blooms and presses arepartitioned (using, say, group technology) so that blooms requi ring differentcylinders are assign ed to different presses ( the plant that we studied followed thisstrategy). These two assum ptions simplify the model by enablin g u s to express
26
both tube drawing and extrusion effort as separable, additive functions of thedecision variables .
We assume that a set of m candidate bloom sizes is prespecified . Thecandidate blooms might consist of all sizes that can be produced using thecurrent tooling (dies and mandrels), or might correspond to all the feasibleproducible by extrusion) grid points of a rectangular grid superimposed on thetube reduction diagram. Alternatively, we might use a
"feasible areaoverlapping procedure" (Loucks that determ ines the inter section of thefeasible dr awing regions for closely clustered fin ished products to identify a list ofpromising bloom sizes that can serve several end products . We index thecandidate bloom sizes from 1 to m, and the finished tube sizes from 1 to n.
Suppose we assign bloom j to tube i, i .e., the process plan for product i consistsof extruding bloom j, and drawing it down to product i
'
s OD andWT. Using theassociated drawing plan, and the annual demand and average lot size for producti, we can calculate the total drawing effort to manufacture product i using bloomj . We convert this total drawing effort into an j-to-i drawing cost which wedenote as dii ' Note that this drawing cost can readily incorporate the costs ofmaterial handling, annealing, and scrap reprocessing. For notationalconvenience, we assume that diihas a very large value if bloom j does not lie inproduct i's feasible area. Because we have assumed lot-for-lot extrusion, we canalso compute the j-to-i extrusion cost ei’ to produce bloom j to meet product i
's
annual demand . This cost includes the cost of setup and actual usage of theextrusion press, as well as the cost of reprocessing extru sion scrap.
Using these costs, we can formul ate the medium-term planning task as anassignment problem. For all i and j the model containsbinary decision variables x
iirepresenting the tube-to-bloom assignment
decisions. The variable xiitakes the value 1 if we assign product i to bloom j, and
the value 0 Otherwise. In terms of these decision variables, the basic planningmodel has the following form:
minimize E] ; [e + dlll x1j
for all i and
0 or 1 for all
27
The objecti ve function minimizes the total annual production cost which,under our assumption of lot-for-lot extrusion, is the sum of the drawing andextrusion costs over all the selected tube-to-bloom assignments . The constraints(42 ) an d ensure that every product is assigned to one bloom. Observe that,in this simple form, the planning model is easy to solve:assign each product i tothe bloom j that minimizes (eii di j
k
Model Var ian ts, and Enhan cemen t sThe assignm en t model considers all products simultaneously, and
captur es the variations in extrusion speed and drawing effort with bloom size;however, its main disadvantage is the lot-for-lot extr usion assumption. Thus,the model ignores the savings in setup time at the extru sion press when wecombine multiple customer orders requiring the same bloom into a singleextrusion lot. To capture the setup savings, extrusion managers might eitherspeci fy a sur rogate constraint that limits the number of standard bloom sizes, orprefer to include an estimate of the annual setup cost in the objective function.
We next outline some of these modeling options
Impose an upper limit on the number of selected bloom sizes .To model this restri ction, we introduce another set of binary variables yj, foreach bloom j The bloom select ion variable yi takes the value 1 ifwe select bloom j, and the value 0 otherwise. The model contains twoadditional sets of constraints:( i) the forcing constraints:
x" yi
for all
which specify that we can assign a tube i to a bloom j on ly if we select bloom j,and the upper limit, say p, on the number of stan dar d bloom sizes:
at
E y.
p,
i=1
Note that addin g constraints and to transforms theassignment model into a p-median model (see , for example, Mirchandanian d Francis
(u) Include an implicit fixed cost, say FYfor selecting each bloom size j.
For in stan ce, if we assume that the facility produces each bloom size onceevery week, the fixed cost P
imight represen t the annual setup cost to produce
bloom j . We dr op constraint from the p-median formu lation, an dchange the objective fu nction to
n m m
minimize 2 2 le a d“) xii
"i i°
i= 1 j=1 j=1
This formulation corresponds to a plant location model, with bloomsrepresenting plants, and products representing cu stomers. By parametrical lyincreasing the fixed costs P
i’we can generate an entire family of solutions
with decreasing number of standard bloom sizes.
(iii) Estimate of the number of setups for eachbloom (as a function of its tubeassignments) and include an explicit setup cost in the objective function .
For instance, we might approximate the number of setups by assuming thatthe extrusion facility selects lot sizes using the economic order quanti tyformula (see, for example, Nahmias In this square root formula, theannual demand for bloom j, say, D i depends on the tube
-to—bloomn
assignments, i .e ., D i21
di xii’where di denotes the known annual demand
1:
for tube i . Observe that introducing the EOQ-based setup cost creates a nonlinear, non-separable objective function in the optimization model .Alternatively, we might assume that the extrusion facility accumulates allorders for a week, and consolidates al l orders requi ring the sam e bloom into asingle extrusion batch; thus, the production frequency of each bloom dependson the demand pattern for the finished tubes it serves . To estimate thenumber of blooms produced each week (and hence the setups) under thispolicy we require additional information an d assumptions regarding theorder arrival process for each product . Again, a probabilistic model forestimating the number of setups as a function of the tube-to-bloomassignment variables introduces non-lineari ties in the objective function .
By redi stributing the workload between extrusion and tube drawing operations,the bloom sizing and tube-to-bloom assignment decisions also affect the relativecongestion in the two stages . The basic planning model does not capture theincreased lead times and inventory costs due to this congestion . Thus, anotheruseful model enhancement consists of including the effects of congestion usingqueueing approximations (see, for example, Bitran and Tirupati Not andBarash [1980] emphasize the role of the process planning function to judiciou slyselect alternate routes and manage the relative congestion at differentworkcen ters of a flexible manufacturing system.
Modeling Alterna t ivesThe basic planning model that we have just described seeks feasible tu be-to
bloom assignm ents that minimize the total extrusion and drawing cost . This
_ 29 _
total cost minimizingmodel represents a centralized decision-making process, orassumes close Cooperation between the extr usion and tube dr awing facili ties toachieve the global cost minimization obje ctive . We can also extend this modelto contexts where the extrusion and tube drawing facil ities are separ ate cost orprofit centers, an d the extrusion facili ty specifies the
"transfer price" (possiblywith volume di scounts) for each of its stan dard bloom sizes, or offers is capacityat a negoti ated rate per hour of usage ( including setup time). Indeed, we caneven tr ansform the model to a "profit maximizing" form if the extrusion facilityis free to accept external orders, and the tube drawing facility can use externalextrusion sou rces and also selectively reject customer orders that are relativelyunprofitable .
Other organiza tional structures might requi re different models . We descri betwo al ternative models- an extrusion constrained model , and a bloom coveragemodel- that represents more appropriately the tu be drawing facility's viewpoint.We descri be only the aggregate structure of the models instead of providingdetailed mathematical formulations . For both models, the decision variables arethe binary bloom selection and assignment variables (yi and xii) .
Extrusign -cons trained model:
This model has the following form
minimize total drawing costsubject to
Extr usion capacity constraint, i .e., upper limit on total extrusion hours toproduce the required blooms, and
Upper limit on number of stan dard bloom sizes chosen (optional ).
Instead of including extrusion cost in the objective function, this model treatsextru sion effort as a capacity constraint. By param etrically changing the availableextrusion capaci ty, we can generate a set of par eto-optimal solutions that vary intheir tube drawing and extrusion processing requ irements. Figure 6 illustrates atradeoff cu rve between extrusion and dr awing effort; managers might fin d thesetradeo ff curves more appealing than the sin gle solution generated by ourprevious total cost min imizing model.
B oom covera e model:
This model focuses on selecting a subset of blooms that maximizes the totalvolum e of drawn tu bes that are "easy to produce" . Since annealing costs aretypically much higher than drawing coss , producs that do not require
- 30
intermediate anneals might be considered easy to produce. Correspondingly, wedefine the coverage of a bloom as the total annual volume ( in pounds or feet) offinished products drawn from that bloom withou t any in termediate anneals (or
within a prespecified number of dr awing passes). The model then becomes:
maximize total bloom coveragesubject to
Upper limit p on the number of standard bloom sizes.
The model does not explicitly consider extrusion and drawing effort, and doesnot require that every product should be assigned to some bloom. Instead themodel seeks, say, the top 5 or 10 p 5 or 10) blooms that together cover,without intermediate anneals, a large portion of the total end-product demand;the annual demand (feet or pounds) of each product serves as its weight incomputing this coverage. We can enhance the model, for instance, by includingan extrusion capacity constraint similar to the previous model . Sectionoutlines other relevant modeling options including multi-objective problemformulations, and models to select a "robust" set of bloom sizes ( to provideprimary and secondary coverage, or to meet shi fting demand patterns).
In summary, we can model the medium-term bloom selection problem invarious al ternative ways, depending on the organization structure, the relativecosts and equipment utilization in extrusion an d drawing, and the availability ofdata and methods to quan tify production effort and inventory cost. The modelmight u se various approximations or surrogate measu res of performance, andcapture extrusion and drawing considerations via either the objective fu nctionor constraints. Some models are well-known optimization problemsassignment, plant location, p-median) with proven solution methods, whileothers require new optimal or heuristic methods that exploit the problemstructure. In Section we describe some interesting generic optimizationproblems that are motivated by the medium-term planning model .
The models we have described in this section represent an improvementover current practice. They recognize the strategic value of simultaneouslyconsidering all products that the facility expects to produce; by incorporating theimpact on both upstream an d downstream operations , these models provide aprincipled way to select common processing paths and bal ance the workloads.We remark that the underlying principle of exploiting process flexibility toestablish upstream commonal ity extends to the ingot casting stage as well . Thus,we might consider a comprehensive long and medium-term planning model
_ 31 _
that selecs standard ingot sizes an d standard bloom dimensions , including notonly standard OU—WT ggmbin ations but also standard lengths for each OD —WT
combin ation, to effectively produce the projected mix and volumes of fin i shedtubes . Vasko,Wolf and Stott [1989] and Vasko et al . [1989] address relatedproblems of selecting optimal ingot sizes and choosing comm on metallurgical
grades for steel rolling operations .
Plann ing-Eng ineer ing Iterat ions
The planning model requ ires the process constrains as input. Theseconstr ains impact both the feasibility of the tube-to-bloom assignmen ts, and thecal cul ation of drawing and annealing effort. Since the process planningdecisions ar e sensitive to the accu racy of these constraints, the planning modelrequires good process understanding, i .e., an accurate representation ofconstraints, and characterization of processing speeds. This section explains thereverse effect, i .e., the planning model can provide valuable in formation toguide process engineering efforts. Thus, in addition to providing support fortactical planning decisions, the plannin g model plays an import ant role incontinuous improvement efforts by generating sensitivity analysis informationwith respect to various constraints . This information identifies promisingdirections for process improvement or further refinement of process cons trains .
As we noted in Section the process variables controlling the tube dr awingconstraints are not well-understood cur rently, and the standard practiceguidel ines ar e based primarily on experience . To fur ther explore and cal ibratethese constraints requires extensive experimentation and detailed processmodeling. To effec tively direct process modeling and improvement efforts, theprocess engineer requires some principled method to determine whichconstraints are cri tical in terms of improvement in manufactu ring performan ce
cost, lead time, quality), and to prioritize the various improvem ent optionsfor fur ther exploration . Consider, for instance, two of the five tube dr awingconstraint classes- the max reduction per draw constraint, and the lower drawingangle-descri bed in Section Shou ld the process engineer first explore thepossibility of increasing the GSA limit 8CSAmax in the max reduction per draw
constr aint, or should he study the effect on tube quality of reducing the lowerdrawing angle" Should the CSA limit be increased through better processunderstanding and more precise parameter estimation, or by redes igning thetooling die geometry, lubrication)"What is the economic impact ofincreasing the CSA limit by, say, 1 percentage point, and how does this impact
_ 32 _
process constraint parameters . In effect, the planning-engineering iterationsdrive the plant's continuous improvement efforts . This complementary use ofplanning and process engineering models represents a new par adigm for bothengineers and planners . This paradigm explicitly recogn izes that good processunderstanding is a prereq uisite for effective planning, while the economicconsiderations derived from planning must drive process engineering. Weemphasize that the planning-engineering iterations are ongoing activities , andgo well beyond the normal consu ltations between engin eers and the modelbuilder during the ini tial stages of validating and testing the basic planningmodel Vasko et al .
ResearchIssues
The tube manufacturing context we have descri bed provides a rich set ofmanagemen t and engineering research opportunities . We limit our discussionsto three promising areas for further resear ch .
Plann ing (Bloom Select ion ) Methodologies:We have described the elements of medium-term plannin g, and posed the
essential tradeoffs in terms of an optimization problem that can be modeled invar ious ways. By discretizin g the space of possible bloom and tube sizes, we canformu late the planning models as integer programs; however, these problemsar e difficult to solve optimally (most models we have considered are NPcomplete or NP-hard) . Developing effective solution methods for these modelsis important, especially since the iterative plan ning-engineering frameworkrequ ires repeated application with varying constraint parameter s . The basicplanning model an d some of its varians are well-known optimization problems(assignment, plan t location, or p-median problems). However, other modelssuchas the extrusion-constrained model and the bloom coverage models arenew, and solving them effectively requires tailored optimization-based heuristicsolution approaches that exploit their special structure using, say, decompositiontechniques or polyhedral approaches (see, for example, Nemhauser and Wolsey
Since bloom sizing decisions must consider mu ltiple conflicting objectives,the formulation and soluti on of multi-objective models to identify a robust set ofstandard bloom sizes is another important area to investigate . Instead ofcombining all the factors into a single objective function or co nstraint,practi tioners might prefer a mul ti-objective optimization framework thatconsiders a hierarchy of metri cs . For instance, the multiple objectives might
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consist of ( i) minimiz ing the total annealing effort or the weighted number ofproducts requir ing intermediate anneals, ( ii) minimizing the number ofstandar d bloom sizes, and ( iii) minimizing the total tube drawing effort.Furthermore, selecting a
"robust" set of blooms sizes might be an importan tpractical consideration . Robustness of the bloom set might be defined as theabili ty to provide, for each product, both a good primary or preferred bloom aswell as a feasible secondary or alternate bloom (for contingencies when theprimary bloom is in short supply). Del Cal lar [1992] attemps to solve this modelusing genetic algorithms. Al ternatively, we might define robustn ess in terms ofthe sensitivity of the bloom set's performance total extrusion and dr awingeffort) to shifs in the product mix and demand pattern increasingproportion of thinner wall tubes). Finally, all of our previous models implicitlyassum e that product qual ity is at an acceptable level as long as the drawing planmeets the max draw, work hardening, and draw angle constrains . In practice,however, the process yield an d product quali ty vary even within this feasibleregion. If we can characterize this variation using engineering models (seeSection then we can either include an explicit qual ity cost in the plann ingmodel 's objective function, or employ techniques such as fuzzy set theory (see,for example, Woodyatt et al . [1992] for an application to selecting metallurgicalgrades) to captur e the qual ity and yield var iations.
The medium-term process plan ning framework also motivates some genericOptimiza tion problems that might interest researchers in location theory andcomputational geometry . Consider, for instance, the following generic problemmotivated by the feasible area overlapping procedure to identify prom isingcandidate bloom sizes:Given a set of points (tubes) on the plan e, a weight (demand) for eachpoint,and a feasible ar ea (defined by inequali ty constrains ) associated with eachpoint, find a location (bloom) belonging to the intersection of these areas thatmin imizes the sum of the weighted distances to all the poins .
We can extend this problem to select a prespecified number (say, p 1) oflocations to minimize total weighted distance assum ing each original point isassigned to its closest location. Computer scientists and location theorists haveanalyzed simple versions of this problem for certain special metrics (see, forexam ple, Shamos Franci s, McGinn is an d White
The tube manufacturing context also motivates a new class of or ientedlocat ion problems dealing with the optimal location of facilities that can servedemand only in a certain direction on the plane . Gopalan [1992] analyzes theperformance of heuristics for certain special types of oriented location problems .
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As an example, consider the bloom coverage model and assume, for simplici ty,that the lower drawing angle is 0° and the upper drawing angle is 90° abloom can produce any tube lying to is south-west). The following question isone of man y interesting oriented location problems related to bloom coverage:Given a set of poins on the plan e and a prespecified radius r, find theminimum number of locations that can cover all the given poins assumingthat each location can only cover poins to its southwest and lying at most runis away .
D eveloping tailored solution methods to exploit the special structure of theseoriented location problems is a promising researchdi rection.
Invgn tory Policies for Systems withCommonality and Subst itu tabilitg:
We have already discussed issues associated with approximating the benefisof commonali ty in terms of reduced setup times and improved recovery. Ourprevious model assumed , however, that both extr usion and tube drawing weremake-to-order activities . The benefits of commonal ity become magn ified whenthe upstream stage (extrusion) produces to stock since having fewer standardbloom sizes reduces the num ber of part numbers" to monitor, and moreimportantly reduces the safety stock (of blooms) due to r isk pooling. In suchsystem s, the planning model requ ires an estimate or approximation of thesebenefits associated with managing bloom inventor ies as a function of the bloomselection and tu be-to-bloom assignment decision variables . To identify a goodapproximation, we must first decide what inventory po licy to u se in the presenceof commonality multiple produ cs using the sam e bloom size as startingstock) and substi tutability if the assigned bloom is not available ininventory, we can produce the tube from a different bloom size albeit withapossibly higher drawing effort ). The tube manufacturing context intr oduces newdimensions that differentiate it from previous resear ch on optimal inventorypolicies for systems having common components o r substitutable produ cs ( see,for example, Collier Baker Baker et ai . Gerchak and Henig
Gerchak et ai . Bitran and Dasu Bassok et al . andOu and Wein
Consider, for instan ce, the following short-term production/ inventory policyfor a given set of standard bloom sizes . Eachtubu lar producthas a prespecified"
preferr bloom size to use as starting stock. When an order arrives, if thecorresponding preferred bloom is no t available in stock, the plannerhas theoption of selecting a prespecified "alternate" bloom thathas a proven, but moreexpensive, dr awing plan . If the al ternate bloom is al so not available in stock, theplanner must expedite an extrusion lot for the preferred bloom . Given the
36
distri bution of demand for various tube sizes, what is the optimal inventorypolicy and the expected inventory level for this system" Observe that optimalityis defined with respect to a composite objective function that includes theexpected expediting coss in extrusion, and the excess (extrusion, drawing, andscrap) costs of using al ternate blooms, in addi tion to the conventional ordering,setup and inventory carrying coss . We must first understand the per formanceof this system, for a given set of standard bloom sizes and tube to-bloomassignmens , before we can incorporate the related economies of scale and scopein the medium-term planning model .
Long-term Process Developmen t and Improvemen t
We have argued for a proactive process engineering strategy to real ize longterm process improvements with potential ly greater economi c benefit comparedto the current reactive mode of problem-solving that is driven by day-to-dayprocess difficulties . The short term solutions normally encompass a narrowerscope of change, accomplished through incremental adjustments andexperimentation around the current operating parameters . Longer termimprovements offer greater economic advantage, but require deeper processknowledge and understanding of the underlying principles. In particular, ou rintegrative approach requires the definition and cal ibration of explicit constraintsthat can be then relaxed or tightened to investigate the effect on processingflexibility. As we mentioned in Section the true underlying constrains arecurrently not well-understood, presenting a rich set of research opportunities .Designed experiments and accumulated experience can provide guidance on thevar iables governing a particular process, but the results are oftenphenomenological rather than fundamental. We must complementexperimentation and experience with methods such as finite element analysis tobetter understand the effects of die geometries, machine setups, materialproperties, and process path. We also require guidelines or a structured approachto combine these model-based and experimental methods so that processengineers can identify and address process improvement opportuni tiesefficiently. Dorah [1992] uses a fin ite element model to study the tube drawingprocess, and repot s results from a set of designed experimens to investigate theeffecs of die setups and geometry on process yield .
The current state-of-the-art in modeling metal working processes sti ll haslimitations associated with interfaces. Friction, lubrication, and the effect ofsurface condition ar e all imperfectly accomodated within simulation models,and computational capabilities limit the model size if we wish to represent threedimensional forming operations . Another ar ena concerns the formulation of
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inexpensive lubricants that provide maximum lubrication with the leastenvironm ental irnpact . Lar ge quanti ties of lubricants ar e required for co ldrolling and tube drawing, and their handl ing, cleaning, and disposal in man ycases is not resolved . These lubricants al so depen d on and influence the sur facecondi tion of the metal , and appropriate practi ces to produce the proper sur facecondi tion are still in their infancy.
Characterizing product qual ity within the feasible area is an importan t an dvery promising research thrust. Tube quality varies as a function of the processparameters drawing angle), bu t cur rent understanding of this relation ship isimperfect. Indeed, the constraint approximations and limiting parameter sspecified in current standard practice rules ar e often conservative estimates thatsupposedly ensure a prespecified yield and acceptable quality level. However, theiterative planning-engineering framework that we have proposed can expli ci tlyaccount for the cost of quality; it does not require a prior specification of a qual itytarget, but instead determines the appropriate level by formally incorporating thetr adeoffs between poor quality and lower effort. For instance, the planningmodel might possibly choose a processing path with lower recovery if this pathhas lower manufacturing complexi ty or requires less effort (inspite of the lowerrecovery). Therefore, to exploit this feature, we require a functional descri ptionofhow recovery varies as we select different trajectories within the tube drawingfeasible area recovery as a function of drawing angle, and GSA reduction perdraw). Notice that, contrary to many process improvement efforts that dealprimarily with parameter optimiza tion, we require a characterization of theresponse su rface rather than a point solution . An important research issueconcernshow to design parsimon ious exper imen ts to provide adequate accuracyfor the response function, similar to recent schem es that reduce the number ofexper imens required to optimize a process‘ operating parameters (see, forexample, Alkhai ry and Staelin [1992a],
Fina lly, a fru itful and novel research direction concerns the direct integrationof the cost of process engineering analysis within the plann ing model . In Sectionwe proposed an iterative framework, withsequential engineering and
planning activities . Consider instead an integrated model where, instead ofspecifying hard process con straints in the plann ing model, we permit relaxingthe constraints at a cost. For instance, instead of specifying a fixed lower dr awingangle of 25° we permit even lower values for this constraint; reducing the value,however, entai ls additional coss for process analysis and exper imentation, andlower yield . Using this type of model, we can evaluate the return on investmentfor different types of process engineering efforts, and directly identify constraints
38
that are critical or cost effective from a planning perspective. We are not awareof any similar effort to include quality metri cs an d process engineering costwithin a planning model .
Next, we briefly descri be process planning and engineerin g issues associatedwith rolling operations, and identi fy similar opportu nities for modeling andcollaboration .
5 . Short-term Plann ing of Rol l ing Operat ions:Comb in ingAl uminum Sheet Orders
This section briefly describes the interactions between upstream anddownstream operations in aluminum sheet and plate rolling operations, an daddresses short-term decisions concerning how to plan production for a set ofconfirmed orders . Our main purpose in this section is to i llustrate how theprevious concepts— simul taneously planning the processing paths for mul tipleorders, accounting for the impact of these decisions on both the upstream anddownstream stages, an d integrating process engineering activities withplanning— apply to other metal forming operations besides tube man ufacturi ng,and are also relevant for short-term planning. We discuss the process flow inrolling operations and outline the underlying engineering principles, describethe economics of rolling and market characteristics, and identify short-termplanning issues an d modeling requ iremens . Our description is based on arolling facility that largely produces special ty sheet produ cs to order ( theindustry di stinguishes betiveen flat plates an d sheets based on thickness, withplate products being muchthicker).
Process Flow and Eng ineering Princ iples of Rol l ing
Roll ing operations consist of processing a rectangular ingot of the requ iredalloy and dimensions at synchronized hot rolling mi lls, followed by one or morecold rolling passes . The process flow might also include preprocessing steps,intermediate thermal operations, and a final finishing stage . We focus on theinteractions between hot rolling ( the upstream stage) and cold rolling ( thedownstream stage) . Each step of the process successively decreases theworkpiece's gauge thickness) an d increases its length; normally the widthremains relatively constant. Thus, the decrease in cross-sectional are a equal sthe decrease in gauge .
A hot line consists of one or more rever sing or multi-stand rolling millsarranged in series and operating synchronously ( to avoid the need to reheat themetal between stations). The relea se of ingots into the line and the workloaddis tri bution among the m ills is contr olled so that the workpiece does not waitbetween stations (due to blocking) . Like extrusion, hot rolling can achievegreater reduction per un it energy input (since the metal deforms more easily atelevated temperatur es) compared to cold rolling, but is limited in terms of thesmal lest possible gauge and the dimensional tolerances it can achieve. Shee tsfrom the hot line are processed at cold mills to further reduce the gauge, andmee t temper an d other material properties. If thehot rolled sheethas asignificantly larger gauge relative to the required fin ished product, the materialmust undergo mul tiple cold rolling passes sin ce the process constrains that wedescri be next limit the amount of reduction in each pass .
Engineer ing pr inciplesThe dominance of rolling in the production of formed metal produ cs has led
to more advanced technical understanding of the rolling process relative to, say,tu be drawing. Wusatow ski [1969] and Robers [1978] provide comprehensivereviews of the fun damentals of rolling processes . Both hot and cold rollingprocesses impose constr ains similar to extrusion and dr awing. This sectionintroduces a few essential characteristi cs of metal rolling, and descri bes one classof process constraints, namely, the maximum gauge reduction per roll in g pass .
The amount of gauge reduction in each pass depends on the type and powerof the rolling mill, the thickness and width of the incoming plate, the type andcondition of the metal alloy, the work rolls
’ diameter, the metal temperature, thenature of the lubricant, and the desired manufactu ring tolerances. Becauserolling deformation induces dynamic recrystallization (Sakai and Jonasthe amount of reduction achieved byho t rolling also influences the evolution ofmicrostructure in the metal, and hence its properties and subsequent processing.
This tight coupling between the complicated deformation fields and di stri butionof mechanical properties throughout the plate makes the design ofhot rollingpractices particularly chal lenging.
To increase productivity, rolling mill s attempt to achieve as large a gaugereduction as possible, as quickly as possible, during every pass of the metalthroughthe rolls. However, the amount of reduction in each pass is limited byseveral factors including:
Rol l ing Economics - and Market Character ist ics
Like extrusion, rolling operations are char acterized by considerable economiesof scale. The per pound production cost is lower for lar ger rolling mills thansmaller rolling mills, and decreases as the ingot size increases (due to reductionsin scrap and setups). Typical performance metrics for rolling operations includerecovery rate (good poun ds as a percentage of total pounds rolled) and
product ivity or ou tpu t rate (good pounds produced per hour of press operation) .
The processing speeds and costs of rolling vary widely depending on the sizeof the mill , the requir ed reduction in gauge, and the al loy and temper. Theproductivi ty of rolling operations is determined by the rolling Speed, machinesetup and changeover time, and planned scr ap. Rolling speed decreases as theamount of required gauge reduction increases, and total setup time increases asthe product diversity (number of different gauges and widths) increases. Finally,the plan ned scrap—d u e to ingot scalping, head and tail scrap (material removedfrom the leading and trail ing ends of a shee t due to quali ty considerations), andside trim- as a percentage of ingot weight decreases as the ingot weight increases,i .e., larger ingos have better recovery rate. Scrap al sohas a di rect impact on totalproduction cost since it represents un productive use of rolling capacity, andentail s a reprocessing cost ( the energy cost and vapor loss dur ing the meltin goper ation) to recycle the metal for ingot casting.
Thus, con siderations of cost, productivity, and recovery dri ve rolling millstowards developing the capability for processing larger ingot sizes . In contrast,the market forces are dr iving in the opposite di rection. In particu lar, becausemany of the customers are moving towards just-in -time manu facturing in theirfabrication and assembly operations, they prefer to place smal ler but morefrequent orders instead of maintaining lar ge quantities of sheet stock as rawmaterial inventories. In one instance, we observed that the average order size(in terms of pounds of each product ordered) roughly halved over the last 5 to 10years, while the faci lity concurrently upgraded its processing capabilities tohandle ingot sizes that were approximately 70% larger than before .
Con sequently, the maximum ingot size is currently about three times as large asthe average order size. The next section descri bes an order combination strategyto mediate between these two opposing trends.
Short-term Plann ing Issues
We wish to exploit the inherent flexibility of rolling Operations tosimul taneously address the rolling mills' preference for processing large ingotswhile meeting small customer orders . To accomplish this objective, we mustassign mu ltiple (say, two or three) incoming orders to a single ingot. If the ordershave similar characteristics, i .e., sam e al loy, and similar widths and gauges, wecan choose process plans that have a high degree of commonality which permitcomm on initi al rolling operations on a single, large workpiece before it is cut fororder-specific final operations . We also exploit the cold mill 's capabili ty toproduce different exit gauges within a single coil dur ing the final combined coldrolling pass . Figure 8 presents a schematic for the "combined" processing planfor two orders (see Ventola [1991 ] for more details).
Let u s fu rther explore the short -term order combinat ion problem. We aregiven a set of confirmed or anticipated orders, each specifying the alloy,dimensions (width, gauge, length of each roll, tolerances), total weight, and duedate. We ar e also given a set of standar d ingot sizes, as well as the processing andrecovery parameters (rolling speeds, gauge reduction constraints, planned scraprequ iremens , and so on ) for each operation as function of the process plan.
Consider the planning process for the avai lable orders for a particular alloy.
The order combination model seeks to combine "compatible" orders (say, 2 or 3orders per ingot) to minimize the total production cost while meetingcustomers ' quantity requirements, specifications, and due dates . A group oforders is said to be compatible if we can develop a feasible process plan satisfyingall the processing constraints to produce the selected orders using a single ingot.Thus, determining the compatibility and cost of jointly producing a combinationof orders implici tly requires ( i) selecting an appropriate ingot, (ii) developing thecommon process plan, and ( iii) verifying feasibili ty of that plan with respect toprocessing constrains such as the maximum gauge reduction per pass, andmaximum gauge differential between the orders in the group . Notice that theprocess plan requires determining the relative allocation of workloadreduction in gauge) between hot and cold rolling Operations; this allocationdepends on the efficiencies, capabilities, an d congestion in the upstream an d
downstream operations .
We refer to any group of compatible orders as a feasible order combination .
The production cost of each combination must include the cost of processing the
43
workpiece at each workstation ( including setu p times), and the cost ofreprocessing scr ap ( including gauge change scrap, an d trim loss when wecombine orders of different widths). A particular order can belong to numerousal ternative feasible combinations . Given the set of all feasible ordercombinations ( including "single combinations, that dedi cate an ingot to a singleorder) and their associated coss the order combination model must select asubset of these combinations to cover all the orders, i .e., each order mustbelong to exactly one se lected combination. The model resolves tradeoffsbetween combining orders (and hen ce in cu rring additional processing coss ) anddedi cating ingots to single orders ( thus decreasing productivity). Since thenumber of feasible combinations is exponential in the number of orders, solvingthe order combination problem manually is very tim e-con suming, and willlikely result in suboptimal solutions . Balakrishnan an d Gopalan [1992] developan integer programming approach to find near—optimal order combinations .Their approach extends to the following enhanced versions of the ordercombination problem .
Our previous description implicitly assumes that the order combinationmodel would be used , say, once a week to plan the production for order s that aredue that week. In practice, the plan t's order books might contain confirmedorders that have later due dates; accounting for the addi tional feasiblecombinations conta ining these orders might potential ly decrease unit productioncost even further . However, producing these orders before their due datesentail s additional (finished goods) inventory holding coss . This observationleads to an enhan ced order combination problem that minimizes the sum of
production an d inventory holding costs, where we now permit ear ly productionof orders in order to exploit the economies of scale in production costs due toorder combination . Another model enhancement stems from the plant's(limited) leeway in deciding the shipped weight of each order. Customersnormally specify a nominal weight, but permit a limited variance (say, iaround thi s nominal weight. The plant can exploit this flexibility during theorder combination phase. In particular, if the nom in al weighs for a particularcombination of orders does not consume the entir e ingot, the plan t can increasethe individual order weighs up to the upper limit or vice versa. Making theschoices in a princi pled way requires a profit maximizing order combinationmodel ( instead of our previous cost minimizing model) that does not specifyexactly the shipped weight but instead imposes upper and lower limis on theshipped weight for each order.
Strategic uses of the Order Combinat ion Model
We can use the short-term order combination model in an iterativeplanning-engineering fram ework similar to our proposed approachin Section
The model assum es prespecified values for the process parameters andconstraints . In particular, the model requires as input the maximum gaugereduction par ameters, and guidelines regarding the permissible gaugecombinations. Often these param eters are conservative and experience-based,but can be refined through process modeling and experimentation. By solvingthe order combination model for various values of, say, the maximum gaugereduction and combination parameters, we can determine the sensitivity of theobjective function ( total costs or net profits) to these par ameter s. This analysiscan then assist the process engineer in prior tizing various process analysis,modeling, and improvement opportunities .
The model can also be used to determine standard ingot sizes . Recal l that themodel requires prespecified ingot sizes (width, thickness, and total weight). Byiteratively varying the ingot sizes, we can select cost-effective standard sizes thatare appropriate for the projected mix of products.
In summary, this sectionhas described the process flow and constraints inrolling operations, and identified an opportunity to improve operations byexploiting the inherent process flexibility for short-term production planning.
The flexibility permits rolling facilities to continue processing lar ge ingots inSpite of the decreasing order sizes . Although we focused on a short-termproblem, the principles that we discussed in this section are very similar to ourprevious discussion of tube manufactu ring. Indeed, we can formulate amedium-term gauge and width standardization model (to determine stan dardsheet sizes produced by thehot line) similar to the medium-term bloom sizingmodel that we described in Section 4. Likewise, we can develop Short-term ordercombination models for tube manufacturing.
6 . Conc lud ing Remarks
We believe that there are substantial opportu n ities for plan n ing and processimprovement within the metal working industry by taking advantage of theinherent process flexibility
,and by coupling engineering activities with the short,
medium, and long-term planning efforts . We have demonstrated theseopportuni ties for both tube drawing and flat rolling of metal plate and Sheet.
— 45
The improvements we propose derive from some fundamental char acteristics ofcontinuous metal forming, namely, the highly interdepen dent upstream (hotworking) and downstr eam (cold working) operati ons with wide latti tude inselecting both the upstream and the downstr eam process paths . In Spite of thisstrong interdependence, the upstream and downstr eam oper ations frequentlyfunction independently, pursuing local objecti ves without consideration foroverall efficien cy. As a resu lt the two operations develop confli cting objectivesto the detriment of the overall process . The methodology we propose couplesthe upstream an d downstream processes to exploit the process flexibili ty whiledeveloping global process plans .
We bel ieve that the strategic implications of this inherent process flexibilityhas been unappreciated and certainly unexploited . Upstream flexibility allowsprocess plans that produce dispar ate products using common process pathsthrough much of their processing hi story. We have presen ted methods toincorporate thi s process commonality within optimization models thatsimultaneously develop process plans for multiple products . The modelsincorporate the primary parameters requ ired for a global process plan:projecteddemand, processing constr aints, and processing effort an d cost. This approachcan have dramatic and far-reaching benefis including operations stream lini ng,inventory and flow time reductions, reduced setu p times, and improved quality.
The model can impose constraints on both the upstream and downstreamprocesses, including limis on the number of upstream products through directconstrains or their cost implications . The exact structure of the model dependson organization structure, cost models, capacity limits, and ease of application .
We have proposed several model varians and di scussed the implications ofeach form .
Much of our workhas also revealed the benefis of close linkage betweenenginee ring and planning models . The engineering models provide themanufactu ring constr ains that di ctate the extent of commonal ity that is possiblebetween product process plans . The feasib le area representation of tube dr awingillustr ates how engineering constraints dictate a region of process flexibility that aplann ing model can subsequently operate within . Similarly, the rollin gconstraints dictate the limits on order combination within a single ingot. Thiscombination of engineering and systems modeling is particularly powerful , forthe planning process does not have to rely upon ei ther previous processhistoryor a Single process plan . The incorporation of engineering within the planningprocess also provides feedback to the engineering process . Parametri c an alyses ofthe sensitivity to different engineering constraints indicate which constraints
46
have the gr eatest influence on process per formance. Engineers can thereforepursue improvements that provide the greatest benefit.
We believe that the interdisciplinary approaches described in this articleprovide fertile ground for significant research- new optimization models an dalgorithms, inventory management paradigms and problems, and processmodel ing Opportunities . Our workhas additionally indicated several areas ofprocess improvement, in both tube drawing and roll ing, that could have asignificant influence on performan ce. Not included in this list are otherchallenging and important research issues relating to incentive and performanceevaluation systems for decentral ized, but closely coupled, manufactu ring stages
what metr ics to use to evaluate the per formance of extrusion an d tubeOperations, what is the appropriate transfer pricing scheme), the design ofappropriate cost accounting systems, an d questions of technology choice, capacityexpansion, and cellular manufacturing .
We believe that other industries will al so benefit from the concepts presentedhere, particularly those involving large capital equipment and continuousprocessing. Prototype industri es beyond metal working include the paperindustr y, the food industry, and the structural polymer product industry. Largebenefis can be accrued by exploiting process flexibility to determine theappropriate level of commonal ity for multiple products, and integratingengineering and planning activites . The field is richwith both econom ic andtechnical opportun ities .
Acknow ledgmentsWe are very grateful to Duane Dunlap, Ricardo Kamenetzky, Brian Landis,Randy Martin, Brian Mcconville, Robert Pahl, Scott Roodvoes , and Char lesStraface for sharing their insights and providing us extensive support, access, andfeedback. Thr ee Leaders for Manufactur ing students-Timothy Loucks, DavidVentola, and Michael Dorah- played an important role by helping us betterunderstand metal forming principles, practices and performance metrics .
Finally, Ram Gopalan and Joseph Del Callar provided invaluable assistanceduring all phases of our collaborative research projects .
47
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A4
Types of Tube D raw ing Operat ions
Idrawing conditions
ink Unsuppor ted Draw
Tube Redu ct ion D iagr am
First draw
Outer Diameter OD
Figu re 5:Tu b e D r aw i n g Con str ain ts
(anneal)
Thickness
M 1:Plann ing— Eng ineer ing Iterat ions
M :Comb ined Process Plans for Two Sheet Orders
Width 48 Width 48
Gauge GaugeWeight lbs Weight lbsTemper Temper O
50 wide, 25 000 lbs ingot
50 wide, gauge,coiled sheet
50 wide, 0-063 gauge50 wide 0 05 gauge
12,000 1bs'
1 d h tcor e S eelbs coiled sheet
ORDER 2
ORDER 1
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