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doi:10.1016/j.ijp
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Int. J. Production Economics 103 (2006) 17–35
www.elsevier.com/locate/ijpe
Cost estimation in mechanical production: The Cost Entityapproach applied to integrated product engineering
Fehmi H’midaa,�, Patrick Martinb, Franc-ois Vernadata
aLGIPM, University of Metz, Ile Du Saulcy, 57012 Metz Cedex 1, FrancebLGIPM, ENSAM CER Metz, France
Received 28 April 2003; accepted 21 February 2005
Available online 19 August 2005
Abstract
A new approach for product cost estimating in mechanical production is proposed within the framework of
integrated product engineering. The approach introduces the new concept of Cost Entity. It is made necessary due to
the current context of growth of indirect costs, especially in manufacturing. The objective, i.e. establishing a tight link
between technical variables (or manufacturing features) and economic variables (modeled as Cost Entities), requires to
model the reasoning procedure and associated knowledge related to cost estimating. To achieve this, two models, a
Product Model and a Costgrammes Model, are presented and used to represent and capitalize technical knowledge. The
cost estimating reasoning procedure, that takes into account alternative process plans of a product, is modeled and
solved by a constraint satisfaction problem (CSP). The solutions of the problem are ranked by economic satisfaction
order. The case of a Termoz part is used as an illustrative manufacturing example.
r 2005 Published by Elsevier B.V.
Keywords: Cost estimating; Integrated product engineering; Cost entity; Manufacturing features; Constraint satisfaction problems
(CSP)
1. Introduction
For most industrial companies, cost estimationmethods mostly determine the performances oftwo strategic functions: product design and pricing(or quotation).
e front matter r 2005 Published by Elsevier B.V.
e.2005.02.016
ng author. Tel: +333 87 34 69 47;
69 35.
ss: [email protected] (F. H’mida).
It is commonly admitted that product designcan engage up to 70–80% of the total product cost(Asiedu and Gu, 1998). The recent progressachieved in Integrated Engineering such as con-current engineering or integrated design opens anew field for cost estimating during the designstage. The objective of these approaches is to takeinto account manufacturing knowledge as early aspossible in the design stage (Parsaei et al., 1997;Roy et al., 1999).
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F. H’mida et al. / Int. J. Production Economics 103 (2006) 17–3518
In a competitive market, the inability of acompany to quickly and adequately satisfy suc-cessful requests for quotation can echo severely onits capacity to survive economically (Veeramaniand Joshi, 1996). Indeed, an underestimated costwill result in losses while an overestimated cost willprevent the company from remaining competitive.
So, there is a strong need expressed by industryto have sound cost estimating solutions, both interms of design and quotation, that can improvethe performance of these two strategic functions(Wierda, 1990).
To face this need, and to replace the analytical-based methods commonly used in manufacturingprocess planning, many companies apply para-metric and analogous cost estimation methods(Duverlie and Castelain, 1999; Layer et al., 2002;Matthews, 1983; Otswald, 1992; Stewart, 1991).These methods are really fast because they areessentially synthetic, i.e. they provide the total costof the product according to some of its character-istics. In design activities, the lack of informationabout the cost structure (e.g. composition) andabout the product production processes (i.e.process plans) does not help the designer to makethe targeted modifications for cost reduction. Inquotation activities, assigning only one cost valueto the product limits the transparent negotiation ofthe cost/delay ratio with the customer.
Another major factor justifying this researchconcerns the growth of indirect activities (i.e.costs). The product cost structure includes gradu-ally a more important part of indirect costs,materialized by the support activities, than before.In addition, the causal relationships between costobjects (products or services) and the resourceconsumptions are difficult to assess. Their trace-ability (i.e. the property that makes explicit in theform of an analysis network the links of the costsfrom accounting recording to their incorporationin products or services) is more difficult to achievewith the traditional approaches for cost estimat-ing. These are based on concepts such as main andsecondary cost centers and data (e.g. hourly rates)issued from cost accounting, the limits of whichhave been analyzed by several authors (see forinstance, Johnson and Kaplan, 1987; Lorino,1991; Bouquin, 1997; Stewart, 1991).
After a detailed study of the cost estimatingproblem in mechanical engineering, we came to theconclusion that two support models are required(H’mida, 2002): a knowledge model and a reason-ing model. Knowledge modeling is carried outusing two manufacturing-oriented models: a Pro-duct Model and a Costgrammes Model. The firstone concerns the product structure on the basis ofits manufacturing features. The CostgrammesModel is based on the Cost Entity (CE) conceptintroduced in this paper. The reasoning model firstconcerns the cost estimating procedure of amanufacturing process (i.e. the sum of the manu-facturing operation costs of its manufacturingfeatures). Then, it concerns the cost estimation ofthe alternate production processes of the product,defined as a constraint satisfaction problem (CSP).
2. Cost estimating
In traditional cost accounting methods, it iscommon to classify costs from two standpoints.First, an economical classification standpointsplits costs into:
1.
Direct costs: may be directly allocated to a costobject, such as a piece of product.2.
Indirect costs: costs that cannot be directlyallocated to a cost object.Second, a morphological classification stand-point brakes down costs as
1.
Material costs: occur by consuming materials 2. Labor costs: occur by utilizing human laborforce
3. Overhead costs: occur by consuming costelements other than the above two.
In manufacturing, cost estimating is the art ofpredicting what it will cost to make a givenproduct or batch of products (Matthews, 1983;Otswald, 1992). Various techniques exist for costestimating (Stewart, 1991). The manufacturingcost of a part can be estimated using one or moreof four basic methods: intuitive, analogous, para-metric, and analytical (Duverlie and Castelain,
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Cost Entity
Input Object Resources
Driver
Activity
Output Object
Cost
Fig. 1. The Cost Entity representation.
F. H’mida et al. / Int. J. Production Economics 103 (2006) 17–35 19
1999; Layer et al., 2002; Cavalieria and Maccar-rone, 2004). The intuitive method relies on theexperience of the estimator to predict the cost. Theanalogous methods are based on cost extrapola-tion from previous estimates made for similar oranalogous parts, often retrieved using a grouptechnology code. Parametric estimating methodsclassically entails the linking of cost to technicalparameters bound in mathematical relations tobuild cost-estimating models. Finally, the analy-tical methods rely on a cost summation related tothe steps in the product production process; and assuch can only occur late in the engineering process.
Based on these methods, different softwaresystems have been developed to assess manufac-turing costs. A detailed analysis of existingcommercial software tools and major proprietarysystems has been published by DoD (1999). Fromthe academic community, noticeable contributionscan be mentioned such as TIMCES, a manufac-turing cost estimation system that integrates CADand process planning aspects in a unified system,but that only considers predefined process se-quences (Wong et al., 1992), neural network-basedapproaches (Shtub and Zimerman, 1993), a frame-work for estimating manufacturing cost fromgeometric design data (Wei and Egbelu, 2000)and, more recently, FIPER developed at NIST asa hierarchical cost estimation tool in all phases ofthe design stage (Koonce et al., 2003).
Another recent trend, related to the analyticalcost relation methods, concerns the Activity-BasedCosting (ABC) approach (Brimson, 1991; Cooperand Kaplan, 1992). In this approach, products orservices consume activities, and activities consumeresources that generate costs. The problem is toidentify cost drivers for each activity. Elements ofthese methods are more or less applicable atvarious stages of the product life cycle. The ABCmethod has been investigated for cost estimatingand management in design and manufacturing(Ben-Arieh and Qian, 2003; Ozbayrak et al., 2004).
Due to the generalized use of integrated productengineering methods and tools, the use of moresophisticated and integrated production facilities(e.g. machining centers, transfer lines, etc.) and theoperations in networked organizations (such assupply chains or virtual enterprises), the manu-
facturing industry is currently characterized by asignificant growth of indirect costs. Therefore,traditional costing methods per se cannot applyanymore. This is why we propose a novel costestimating technique, based on the CE concept.
3. The Cost Entity concept
Still adhering to the principles of the ABCmethod but augmented by the principles of themethod of Analysis Centers of cost accounting(Stewart, 1991; Garrison and Noreen, 1997), wepropose the concept of ‘‘Cost Entity’’ to profitfrom both methods. In the Analysis Centermethod, the costs of auxiliary sections (e.g.logistics) are assigned to the main sections whichdirectly benefit to the products (e.g. machiningoperations). Then the section costs are added andthe total cost is distributed between the products.To be correctly applied, both methods assumehomogeneity of resources generating costs.A CE can be graphically represented as shown
by Fig. 1. A definition follows and the funda-mental homogeneity validity condition of theconcept is explained.
Definition. A Cost Entity (CE) is a cost aggrega-tion associated with resources consumed by anactivity. The fundamental condition on a CEconcerns the homogeneity of the resources, whichpermits to associate a driver with the CE.
Homogeneous resources are stable and inter-dependent. Stable means that the imputation rateh/X (e.g. h/min, h/L) of each resource does notchange according to the product. Interdependentmeans that the resources are consumed in the sameproportion for one or the other, whatever theproduct that uses them.
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Let Ri ¼ fk : k 2 Kg represent the set of theconsumed resources for the CE (CEi) for therealization of ith activity ðAiÞ. If ½y
ikðxiÞ ¼ xiak� is
equivalent to the quantity of resource k consumedfor the realization of activity Ai of driver xi (whereak is the consumption coefficient of the resource k)and if [Ck ¼ yi
kðxiÞ. Imputation rate] correspondsto the cost of y units of k, the basic equation of themodel will be:
CostCE ¼Xk2Ri
CkðyikðX iÞÞ (1)
Example : resource cost
¼ Driver ðnbÞakðh=nbÞimputation rateðh=hÞ
¼ xiak|{z} imputation rate
¼ yikðxiÞimputation rate|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
¼ CkðyikðxiÞÞ,
where ak is the consumption coefficient of theresource k and nb the identifier of the cost driver.
3.1. Parent Cost Entity (PCE)
In the absence of the homogeneity resourcecondition, the CE will be considered as a PCE (ormacro-entity). Its decomposition into elementaryCost Entities, in order to respect the homogeneitycondition, is mandatory. The parameters (re-sources, activity, input–output objects) and thecost of the PCE are, respectively, the union of theparameters and the sum of the costs of theelementary CE’s that make it.
CostPCE ¼Xi2N
Xk2Ri
CkðyikðX iÞÞ, (2)
where N is the number of Cost Entities making thePCE.
4. Modeling cost estimating knowledge
The necessary knowledge for the cost estimatingis represented in the form of a Product Model anda so-called Costgrammes Model. The ProductModel is built on the basis of the manufacturing
features. For design, manufacturing and costestimating, this notion presents a federative aspect(Feng et al., 1996; Wei and Egbelu, 2000; Wierda,1991). The Costgrammes Model will be based onthe CE concept.
4.1. The product model
The proposed Product Model uses three no-tions: product, manufacturing feature and opera-tion. Two levels are used (Fig. 2). The first one isabout the geometrical and specific description ofthe product in terms of manufacturing features.The second level expresses the manufacturing andthe cost estimating point of view.Fig. 2 describes the structural links between the
different components of the Product Model. Theselinks are mandatory or optional. Solid linesindicate mandatory links (Product/ManufacturingFeatures/Operations relationships) and dottedlines indicate optional ones. The last ones repre-sent all the machines able to realize a determinedoperation. Each manufacturing feature is de-scribed by internal parameters (dimensions, toler-ances, surface texture, etc.), geometrical inter-feature tolerances (perpendicularity, parallelism,etc.), and finally by topological inter-featurerelations (starts on, opens on, etc.).CostAdvantage, an expert system tool, has been
utilized to structure these data (Cognition, 2000).The representation used in CostAdvantage isbased on the notion of object classes, calledcontexts.
4.2. The costgrammes model
To each activity corresponds a CE that capita-lizes the cost estimating expertise linked to thiselement. The proposed Costgrammes Model al-lows to have a global view of all the Cost Entitiespresent in the company and concerned by theproducts being processed (Fig. 3).The first level of the Costgrammes Model
represents all the necessary operations for therealization of the manufacturing features involvedin the product. This corresponds to the directcosts. The second level presents the hierarchicalrelationship in a CE. It contains a direct/indirect
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Operation (i,j,k): Option k (machine M) of operation j generated by the manufacturing feature i
Product
Manufacturing feature N˚1
Manufacturing feature N˚i
Manufacturing feature N˚n
Operation (1,1,3)
Operation (1,3) Operation (n,1)Operation (1,2) Operation (1,1)
Operation (1,1,2)Operation (1,1,1)
Conceptual viewpoint
Operations
Alternate Machines
Manufacturing and cost
estimation viewpoint
Operation (1,2,1)
Fig. 2. The Product Model.
Tool Change
Cost Entity
Qualityplan
Cost Entity
NC-programing
Cost Entity
Scheduling Cost Entity
Logistics Cost Entity
Release Cost Entity
HandlingCost Entity
Setup Cost Entity
Process planning
Cost Entity
MachiningCost Entity
QualityControle
Cost Entity
HandlingCost Entity
Operation Cost Entity
(1,1)
Operation Cost Entity
(1,2)
Manufacturing preparation Production
Machine M1 Machine M2
Level 2
Level 1
…
…
Operation Cost Entity
(1,3)
Operation Cost Entity
(2,1)
Operation Cost Entity
(2,2)
Fig. 3. The Costgrammes Model.
F. H’mida et al. / Int. J. Production Economics 103 (2006) 17–35 21
and elementary/PCE relation. So, the distinctionbetween direct/indirect costs looses its usefulnesssince all the costs are directly connected to the
product. The computer tool, used to structurethese data, is again the CostAdvantage expertsystem.
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The ‘‘Operation’’ CE makes the link betweenthe Product Model and the Costgrammes Model(Figs. 2 and 3). The driver, issued from the productcharacteristics and then from the level 1 (Fig. 3),insures, respectively, the causality of thecosts engaged in level 1 (Fig. 3) and in level 2(Fig. 3).
5. Modeling the cost estimating reasoning process
The cost estimating reasoning procedure iscarried out in two subsequent phases. The firstone is relative to the generation of the costs ofthe manufacturing process associated with eachmanufacturing feature of the part or product.The second one is relative to the generation of thecosts of an alternate production process of theproduct.
5.1. Cost estimating of a manufacturing feature
For each type of manufacturing features, thereis a set t of operations potentially necessary for itsrealization. T corresponds to all the operationsthat could be used for the most varied instance ofevery manufacturing feature. The technologicalcriteria (e.g. the quality to be obtained) conditionthe decisions that lead to associate a given processas the effective manufacturing process, so formingthe subset t 2 T .
Fig. 4 shows an example of a potential opera-tion set T relative to the manufacturing feature:Threaded Hole. According to the intrinsic data of
Threaded Hole Center drilling Drilling
Manufacturingfeature Draft operations
Fig. 4. The set T of the potential operations relative
the feature (Quality, Angle b of the chamfer), thesubset t of the effective manufacturing processcannot contain the Boring and/or Counter sinking
operations.So, the expertise linked to the manufacturing of
each type of features has to be transcribed in theform of ‘‘If–Then’’ rules in the knowledge base ofthe expert system. Each operation type includesthe expertise of the associated cost estimatingprocedure. The implementation of these principles,by the means of an expert system such asCostAdvantage, allows to generate, for a definedmanufacturing feature, the estimated costs of themanufacturing process corresponding to the effec-tive manufacturing operations of the feature(H’mida, 2002).
5.2. Production cost estimating: A constraint
satisfaction problem
The cost estimation model that seems the mostsuited for explicit representation of the multiplicityof technical solutions, and to consider the varioustrue dependencies between the design, manufac-turing and production functions, appears to be aCSP. The approach consists in building thereasoning procedure from an identification of therelevant variables, knowledge and constraints.Solving a CSP consists in finding a set of eligiblevalues for all the variables such that all theconstraints are simultaneously verified (Tsang,1993). In our model, a solution takes the formof a production process with an estimated cost,noted CPP.
Boring Counter sinking Tapping
Finishing operations
to the ‘‘Threaded Hole’’ manufacturing feature.
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5.2.1. Variables
The expert system, mentioned in Section 5.1, isused to associate all possible manufacturingoperations with the product brake-down intofeatures. For each operation, the capable alter-native machines are also capitalized. This allows toparameterize every operation by the Xijk notation,i.e. machine option k realizing the operation j
generated by the manufacturing feature i.Two types of variables for the production
process can be established on the basis of thisknowledge. Using similar notations as thoseprovided by Wei and Egbelu (2000), these are:
�
Boolean variables relative to the possible pre-cedence cases between two manufacturingoperations.X ijki0j0k0 :
1 If the option k0 of the operation j0
generated by the manufacturing feature i0
follows the option k of the operation j
generated by the manufacturing feature i
ðor X i0j0k0 follows X ijkÞ;
0 Otherwise
8>>>>>>>><>>>>>>>>:
�
Integer variables relative to the rank of eachmanufacturing operation.Uijk :
m If the option k of the operation j
generated by the manufacturing
feature i is executed as the mth
operation in the production process:
8>>><>>>:
A third declared variable is relative to the costof a production process solution. It is
� A real variable defined over a fuzzy domain andnoted CPP.
5.2.2. Knowledge cores
The expertise on cost estimating capitalized atthe level of each operation is used to determine themanufacturing cost (ECf) corresponding to eachassociation of the operation/machine type. Theknowledge on the production system machinesand their arrangement in the workshop with thematerial handling system used allows to identifythe machine preparation cost (ECpr) and the
handling cost (ECm) relative to each variableXijki0j0k0. They are defined as follows:
� ECfijk: M
anufacturing cost of the option k ofthe operation j generated by the
manufacturing feature i.
� ECpr
ijki0j0k0:P
reparation cost of the option k0 of theoperation j0 generated by the manu-
facturing feature i0 if it follows the
option k of the operation j generated
by the manufacturing feature i.
0
I f Xijk et Xi0j0k0 areperformed on
the same machine,
C
onstant [f(k)] I f they are notperformed on the
same machine.
I
nterviews with the machineoperator who knows well the existing
relations between the product and the
machine preparation time can bring
to the determination of the adequate
driver. In our case, the hypothesis is
made of assigning a constant
preparation cost according to each
machine k.
� ECmijki0j0k0 :H
andling cost of the option k0 of theoperation j0 generated by the
manufacturing feature i0 if it follows
the option k of the operation
j generated by the manufacturing
feature i.
0
I f Xijk and Xi0j0k0 areperformed on the same
machine,
E
Cmijki0j0k0 I f they are not performedon the same machine.
5.2.3. Constraints
The cost estimating reasoning procedure of aproduct is build around four types of constraints:appropriate constraints for the model, cost con-straint, manufacturing constraints and productionconstraints. All these constraints contribute to thecost estimation of a product production processsolution (H’mida, 2002).
5.2.3.1. Inherent constraints of the model. Theseconstraints are completely independent of the
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product and of the production context. Theymainly concern the model definition.
Let us consider:
n: number of manufacturing features,ni: number of manufacturing operations of a
feature i,nij: number of options for an operation j of a
feature i,N: total number of possible manufacturing
operations.
Then the two states X 011 and X nþ1;11 are used torespectively represent the state of the product inthe raw material stock and in the finished productstock. An extract of the main inherent constraintsof the model is presented as follows:
Conjunctive mutually exclusive constraintsOnly one operation can follow a given operation:
Xnþ1i0¼1
Xni0
j0¼1
Xni0 j0
k0¼1
X ijki0j0k0 ¼ 1 for i ¼ 0; . . . ; n;
j ¼ 1; . . . ; ni; k ¼ 1; . . . ; nij. ð3Þ
Only one operation can precede a given opera-tion:
Xn
i¼0
Xni
j¼1
Xnij
k¼1
X ijki0j0k0 ¼ 1 for i0 ¼ 1; . . . ; nþ 1;
j0 ¼ 1; . . . ; ni; k0¼ 1; . . . ; ni0j0 ð4Þ
The finished part state ðX nþ111Þ is preceded byonly one operation except ðX 011Þ:
Xn
i¼1
Xni
j¼1
Xnij
k¼1
X ijk nþ1;1;1 ¼ 1 (5)
Disjunctive mutual dependence constraints:An operation can only follow or precede a given
operation:
Xn
i¼1
Xnij
k¼1
Xnþ1i0¼1
Xni0 j0
k0¼1
X ijki0j0k0
aXn
i¼1
Xnij
k¼1
Xnþ1i0¼1
Xni0 j0
k0¼1
X i0j0k0ijk
for j ¼ 1; . . . ; ni;j0 ¼ 1 or 2 or . . . ni0 . ð6Þ
Constraints relative to the enumeration ofoperation order:Operation order in the operation sequence:
Uijk �Ui0j0k0 þ X ijki0j0k0 ¼ 0 (7)
Constraints on the first and last position in theprocess (initialization):
U0;1;0 ¼ 0 Raw material stock; (8)
Unþ1;0;0 ¼ N þ 1 Finished product stock: (9)
5.2.3.2. Cost constraint. The second type ofconstraints concerns the cost constraint. Theproduct design should respect an acceptablemaximal cost, a priori fixed at the beginning ofthe estimating exercise. If this limit is not ex-ceeded, this guarantees the company’s profita-bility and assures competitiveness on the market.This constraint sanctions any production pro-cess solution far-off the economic objectivesand expresses a satisfaction degree for anysolution. An example of such constraint can takethe form given by inequality (10), if we assumethat in this example the cost is only a function ofthe set-up, manufacturing and handling costs andthat only the manufacturing cost depends on thebatch size.
Xnþ1i¼1
Xni
j¼1
Xnij
k¼1
Xn
i0¼1
Xni0
j0¼1
Xni0 j0
k0¼1
ðECpr
ijki0j0k0
þQECfi0j0k0 þ ECm
ijki0j0k0 ÞX ijki0j0k0
hAcceptable maxiCost ð10Þ
(in this case, Q corresponds to the size of themanufacturing batch and is assumed to be a prioriknown to the estimator. The determination of Q isout of the scope of this paper).The first term of constraint (10) corresponds to
the variable CPP previously defined, that is, thecost of a product production process solution.This real variable belonging to a fuzzy domainformalizes the relation existing between the knowl-edge of ECf
ijki0j0k0 , ECpr
ijkij0k0, ECm
ijki0j0k0 and theoperations Xijk. Every production process solutionhas associated with it a cost value CPP with a
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F. H’mida et al. / Int. J. Production Economics 103 (2006) 17–35 25
satisfaction degree.
Cpp ¼Xnþ1i¼1
Xni
j¼1
Xnij
k¼1
Xn
i0¼1
Xni0
j0¼1
Xni0 j0
k0¼1
ðECpr
ijki0j0k0
þQECfi0j0k0 þ ECm
ijki0j0k0 ÞX ijki0j0k0 . ð11Þ
Expressions (10) and (11) depend on theproblem at hand and may contain additionalterms to take into account other resourceconsumptions as categorized for instance byLakhal et al. (1999).
In Fig. 5, the function Sestimated cost (CPP)represents the satisfaction degrees associated withthe various values of the Cost CPP.
The expression type of this cost constraintallows to classify all the solutions in decreasingorder of the satisfaction degree. So, all thesolutions are included between a minimal cost(miniCost) and a maximal cost (maxiCost).
5.2.3.3. Manufacturing constraints. The manu-facturing constraints concern the geometrical
Fig. 5. A fuzzy domain associat
Fig. 6. Rules of pose constraints associa
and topological relationships between the manu-facturing features. They describe the precedenceorder to be respect between the operations of thefeatures. They have a direct influence on themachine preparation costs and on the handlingcosts.The analysis of the geometrical and topological
relationships between features is made in our casewith the CostAdvantage system. We define a rulebase that decides the possible precedence relationsto be respected between the manufacturing opera-tions. It sets the constraints to be satisfied in theprocess plan.The rules presented in Fig. 6, associated with the
‘‘parallelism’’ relationship expressed between twofeatures i and i0, impose, according to the capacityof a feature to be a support in the set-up of thepart, a precedence constraint (Sabourin andVilleneuve, 1996). According to Rule 1, theprecedence order to be respected is between thetwo finishing operations ni and ni0 belonging,respectively, to the features i and i0. Rule 2, a
ed with a cost constraint.
ted with the relation ‘‘Parallelism’’.
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constraint on the variable Xij(M)i0j0(M0), means thatthe two finishing operations ni and ni0 are realizedon the same machine (machine M or machine M0).
Fundamentally, the precedence relationshipsbetween operations are conditioned by the preci-sion of the existing geometrical and topologicalrelationships between the features. They aredecided during the detailed design stage.
5.2.3.4. Production constraints. The productionconstraints arise from the consideration of themachine availability during cost estimating (Fig. 7).The following formalization is made in theCostAdvantage expert system. First, the user selectsthe cost estimation context: Planned or Not
Planned. Under the Planned context, each machinecan take two logical textual values: Available,Unavailable. A rule base is associated with eachof these contexts. For each ‘‘Unavailable’’ valuetaken by a machine, the corresponding ruleactivates one or several production constraints inorder to satisfy any process solution.
Fig. 8. An activation rule of the production constraint r
UnavailaMachin
ExXijk112 =Xijk312 =
Production planning ormachine maintenance
Causes Constra
Fig. 7. Examples of prod
In the example of Fig. 8, the rule tests theavailability of the Cu4x machine. If the machine isunavailable, then the production constraint isapplied, any variable Xijki0j0k0 having for optionmachine k or k0 on Cu4x is forced to 0. This avoidsto have in the process plan solution this unavail-able machine and prevents an invalid product costestimation.In the case of a Not Planned context, we
consider the hypothesis of the availability ofmachines without any production constraint.
5.2.4. Problem resolution
The problem resolution consists of two phases.First, comes a filtering phase that consists ineliminating the values of the variables which haveno chance to intervene in a solution. This preventsdoing afterward useless calculations. Then, comesthe solution search phase, that is the combinationsof coherent values.To support the reasoning of cost estimating for
the product production process, we have chosen
elative to the unavailability of the machine Cu4x.
ble es
: 0 0
Alternate machines at different costs
EC112 canceled EC312 canceled
ints Effect
uction constraints.
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the Con’flex environment (Rellier, 1996). This CSPsoftware provides a language for problem expres-sion in terms of variables and constraints, and itsupplies a set of resolution algorithms. Thesealgorithms aim, on one hand, at reducing the sizeof the search space (this operation is calledfiltering) and, on the other hand, at scanning thisspace (in a treelike way) to find the solutions.Resolution refers to the procedure that implementsat the same time the filtering and the solution
search phases.
The interest of this modeling approach (con-straints modeling) is that it is able to deal withvariables of totally different natures: Boolean,numerical or fuzzy variables. The establishedconstraints can make reference to discrete domains(discrete constraints), continuous domains (con-tinuous constraints), discrete and continuousdomains altogether (mixed or hybrid constraints)as well as to fuzzy domains (flexible constraints).Constraint-based modeling accepts a tremendousheterogeneity in the expression of the constraintsand the variables.
6. Illustrative case study
First, the role of the two software packagesused is reminded: CostAdvantage and Con’flex
(Fig. 9).
Reasoning model based on CSP : • Alternative solution search,• Solution ranking by economic satisfaction o• Determination of the [maxiCost, miniCost] in
Knowledge capitalization:• Product Model,• Costgrammes Model.
Reasoning model based on «If-Then» rules: • Manufacturing operation cost generation,• Manufacturing and production constraint ac
Variables
Fig. 9. Role of the two
6.1. Specification of the problem to be solved
6.1.1. ‘‘Termoz’’ part
The part for which the cost is to be estimated iscalled the ‘‘Termoz’’ part. A layout drawing of aninstance of this part is presented in Fig. 10.From the analysis of the ‘‘Termoz’’ part
drawing, the list of its constituting manufacturingfeatures can be established (Table 1, Fig. 11).On the other hand, the analysis of the Termoz
part drawing makes it possible to establish the listof the geometrical relationships between themanufacturing features (Table 2).
6.1.2. Manufacturing workshop
It is assumed that four potential machines canbe used in the available manufacturing facility: a 4-axis milling machining center (Cu4x), a 3-axismilling machining center (Cu3x), a 3-axis turningcenter (Ct3x), and a 2-axis turning center (Ct).Each manufacturing operation realized on onecenter becomes an elementary CE ECf.The machine preparation cost corresponds to
the time interval necessary for the operator to setup the environment (assembly of the fixing devices,setting the machining parameters, etc.) for a newtype of part. The associated CE is denoted ECpr
and we assume that it is constant for everymachine type (Table 3).
rder,terval.
tivation.
CostAdvantage
(expert systemgenerator)
Con'flex
(constraints satisfaction
environment)
Constraints
software systems.
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Table 1
Example of manufacturing features information
Name Type Nominal geometrical
information
Micro-geometrical
information
Topological information
F1 Circular_Surface Ø 104 (X�Y) Flatness 0.05 A2 and R support
Ra 1.6
F2 Rectangular_Surface 52 (X)� 42 (Z) Ra 1.6 TT support
Fig. 11. The manufacturing features of the Termoz part.
Fig. 10. The Termoz part.
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F. H’mida et al. / Int. J. Production Economics 103 (2006) 17–35 29
In terms of material handling, it is assumed thatan electric cart with a driver and stocking contain-ers are used. The set (cart, driver) represents ahomogeneous CE, named Handling Cost Entityand denoted ECm. The handling costs, issued fromthe machine arrangement in the workshop, aregiven by Table 4.
Table 2
Example of geometrical relations between the manufacturing
features
Type Feature 1 Feature 2 Name Value
Perpendicular F1 F2 reference R? (F2,F1) 0.05
Coaxial A1 A2 reference RY(A1, A2) 0.05
Table 3
Preparation machine costs
Machine Preparation cost in Euro (indicative values)
Cu4x 7
Cu3x 6.3
Ct3x 5.5
Ct 3.8
Fig. 12. The Product Model
The choice of these types of machines andhandling systems allows to discard a large numberof scenarios frequently used in manufacturingworkshops.
6.2. Product Design—Costgrammes Models
6.2.1. Product Model
The Product Model is elaborated from all themanufacturing features in use in the company.Fig. 12 illustrates a Product Model specification inthe French version of CostAdvantage (in whichfeatures are declared as functions). With eachfeature context are associated all the potentialoperations as sub-contexts as well as a rule base
Table 4
Handling costs between two machines
Cu4x Cu3x Ct3x Ct
Cu4x 0 1.2 0.4 0.2
Cu3x 1.2 0 0.6 0.4
Ct3x 0.4 0.6 0 0.6
Ct 0.2 0.4 0.6 0
(with CostAdvantage).
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F. H’mida et al. / Int. J. Production Economics 103 (2006) 17–3530
used to generate the effective manufacturingprocess according to the geometrical characteris-tics. A given manufacturing feature for a parti-cular product is an instance of the context.
The exploitation of this Product Model makes itpossible to identify and to automatically generateall the Cost Entities ECf
ijk present in a particularpart.
Reminder. ECfijk: cost of the manufacturing opera-
tion j performed on the machine k and generatedby the manufacturing feature i chosen by the user.
6.2.2. Costgrammes Model
The Costgrammes Model (Fig. 13) contains allthe Cost Entities dealing with establishing the costof the problem at hand. There are two types ofCE’s: elementary and parent Cost Entities. Theparent CE’s contain sub-contexts relative to theCE’s that make them, and which can be elemen-tary or not.
At the level of each context of a CE, thefollowing knowledge is associated:
Fig. 13. The Costgrammes Mod
�
el (
the attributes (type, resources, etc.),
� the formula of the cost estimation.In the case of a PCE, the cost estimationformula is recorded in the form of rules that addthe cost of the elementary Cost Entities afterchecking their instantiation.
6.2.3. Generation of the manufacturing operation
cost
In Fig. 14, in addition to the specification of themanufacturing feature example (entitled ‘‘Threa-
ded_Hole’’) by the estimator operator using thefirst window, the system automatically generates,in the second window, the corresponding manu-facturing process plan and the processing cost ofeach operation by default (The values given areindicative). By double-clicking on each operation,another window pops up to indicate the operationcost for an alternative machine and the values ‘‘i, j,k’’ corresponding to the ECf
ijk.
with CostAdvantage).
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Fig. 14. Generation of the manufacturing process for a ‘‘Threaded_Hole’’.
F. H’mida et al. / Int. J. Production Economics 103 (2006) 17–35 31
6.2.4. Activation of the manufacturing constraints
According to the specification of some manu-facturing features, the system alerts the user of aprecedence condition among some of the opera-tions. In Fig. 15, the topological relationship‘‘Starts_on’’ among, for instance, the ‘‘Threaded_
Hole’’ and ‘‘Rectangular_Surface’’, implies theprecedence condition between the finishing surfaceoperation (X22k) and the boring and tappingoperations ðX 14k;X 14kÞ independently of their rea-lization machine k. This is translated into con-straints of the form: U22koU14k and U22koU15k
(Fig. 15).
6.2.5. Activation of the production constraints
If an Unavailable machine is selected, the systemalerts the user for impossible operation. In Fig. 16,the unavailability of the machine Cu3x cancels theoperations X 111 and X 121 concerning the manu-facturing feature ‘‘Rectangular_Surface’’; thismeans cancellation of all the variables: X111i0j0k0
and X121i0j0k0.The Costgrammes Model design provides all the
Cost Entities ECfijk of the Termoz part, as well as
the manufacturing and production constraints tobe respected. The term Xijk allows to determine all
the variables Xijki0j0k0 of the problem with theCon’flex CSP solver.
6.3. Generation of the cost of alternate production
processes
The production process of the Termoz part takesinto account the material handling costs (ECm
ijki0j0k0 ),
the machine preparation costs (ECpr
ijki0j0k0), in addi-
tion to the manufacturing operation costs (ECfijk).
We differentiate the modeling steps on threelevels:
�
The declaration of the Boolean variablesXijki0j0k0, the integer variables Uijk and the fuzzyvariable CPP, � The declaration of the model constraints, themanufacturing constraints, the production con-straints and the cost constraint,
� The declaration of the CE (ECfijk, ECmiji0j0k0 and
ECpr
ijki0j0k0) knowledge.
The modeling of production cost estimating inthe form of a CSP allows to answer the followingquestions: Are there any production processes for
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Fig. 15. Example of manufacturing constraint activation.
Fig. 16. Example of production constraint activation.
F. H’mida et al. / Int. J. Production Economics 103 (2006) 17–3532
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F. H’mida et al. / Int. J. Production Economics 103 (2006) 17–35 33
the Termoz part and the workshop at disposalwhose cost is lower than a given value and whosegeometrical specifications can be respected? Whatis the cost of each solution?
The answer to these questions provides thedesigner with an economic evaluation of his/hertechnical choices. We propose the following designscenario for the Termoz part:
The initial part design involves the F1, F2, A1 andTT1 manufacturing features. The part is produced inbatches of 100 units at a 4.9 Euros per unit cost. Anadditional function of the part requires the creationof two new manufacturing features: The Bored_Hole
A2 and the Slot R with the symmetry geometricalspecification RCðR;A2Þ ¼ 0:05 and topological spe-cification R Opens on A2. The acceptable maximalproduction cost of the part is 7.3 Euro/unit.
The calculations realized with Con’flex for thecost estimation of the production process solutionfor the manufacturing workshop at disposal showsthat:
�
For a satisfaction degree equal to at least 0.09(equivalent to the production process for whichthe part unit cost is lower than 7.084 Euro): 49solutions exist. � For a satisfaction degree equal to at least 0.190(equivalent to the production process for whichthe part unit cost is lower than 6.844 Euros): 49solutions exist.
� For a satisfaction degree equal to at least 0.290(equivalent to the production process for whichthe part unit cost is lower than 6.604 Euros): 35solutions exist.
� For a satisfaction degree equal to at least 0.390(equivalent to the production process for whichthe part unit cost is lower than 6.364 Euros): 3solutions exist.
� For a satisfaction degree equal to at least 0.490(equivalent to the production process for whichthe part unit cost is lower than 6.124 Euros): 0solution exists.
For the three solutions of Fig. 17, the value‘‘CoutTotal’’ represents the total batch cost (100parts) corresponding to the production processsolution. The mention ‘‘�2.500’’ means, in Con’-flex, that the solution value is an interval centered
on the shown value and the width of which is therange declared for the variable. The value‘‘Sat ¼ ’’ is the satisfaction degree of the solution.Indication ‘‘Nbr of instantiations’’ and ‘‘Nbr ofconstraints tests’’ are a measure of the path (in thetreelike search) that it was necessary to scan to findthe solutions.The solutions corresponding to the minimal
satisfaction degree (0.09) allow to determine theinterval of the part unit cost [CPP min, Cpp max] inthe fuzzy interval [4.9, 7.3] (Fig. 18). The indicativevalues of the costs put in application (machining,machine set-up and handling costs) provide theinterval [6.3, 6.7].
7. Conclusion
The objective of this research work was topropose a cost estimating method fitted to recentindustrial context evolution. It is our belief that allthe concepts and the techniques presented in thispaper sustain this objective. The CE conceptallows to unify the estimation of direct andindirect costs. Establishing the causality relationsexisting between the specification of the manufac-turing features and the engaged costs of themanufacturing operations provides support tothe economic decision at the detailed designstage. The consideration of constraints comingfrom the market, from the manufacturing shopand from production shows the integration capa-city of the cost estimation function. For a givenproduct, the generation of different cost setsrelative to the alternate production processes givesthe quotation function a tool to negotiate the cost/
delay ratio, and provides the designer with a[miniCost, maxiCost] interval to control thetechnical choices.For the future work, it seems very interesting to
investigate the possibilities offered by cost estimat-ing modeling in the form of a flexible CSP
problem. Under this formalism, the variables canhave domains with imprecise borders, the con-straints to be satisfied are more or less importantand, they can be more or less satisfied by thevarious combinations of values of variables.Finally, one could accept a solution that satisfies
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1
0.1 7.3
Cost
Satis
fact
ion
degr
ee
0.5
4.9
Fig. 18. The fuzzy subset [4.9, 7.3] of the total cost.
Fig. 17. Costs of the production process solutions for a satisfaction degree at least equal to 0.390.
F. H’mida et al. / Int. J. Production Economics 103 (2006) 17–3534
only partially all the constraints. Another researchdirection could consist in searching the set ofvariables, domains and constraints that allow toevaluate the design solution by a Quality/Cost
satisfaction degree.An interesting valorization of the work that
could be investigated concerns the incorporationof the CE approach with its Product Model andCostgrammes Model in CAD or CAE work-stations. Depending on form features and partmaterial used the system could estimate a roughcost interval and warn the part designer if he
exceeds the cost limit or provide a decisionguidance in the choice of features of the part.
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