Int J Adv Manuf Technol (2012) 58:1–8 DOI 10.1007/s00170-011-3388-1 ORIGINAL ARTICLE Comparison of cranioplasty implants produced by machining and by casting in a gypsum mold Dalberto Dias da Costa & Sérgio Fernando Lajarin Received: 12 August 2009 / Accepted: 12 May 2011 / Published online: 24 May 2011 # Springer-Verlag London Limited 2011 Abstract Cranioplasty is a medical technique used to correct craniofacial defects Depending on the size and location of the defect, a bone substitute to replace the deformed or missing tissue can be manufactured With the advances in computer-based systems and the invention of new biomaterials, the production of customized implants with good cosmetic and functional results has now become widespread However, little research has been undertaken into the quality of prefabricated specimens in terms of dimensional and form errors Because of the geometric complexity involved, measurement of this kind of object is a complicated process The aim of this paper is to describe two different manufacturing processes used to produce a large polymethylmethacrylate (PMMA) implant for use in cranioplastic surgery and to discuss the results of the evaluation of the dimensional errors and lead times associated with these methods In the first method, the specimen was directly machined from an acrylic block In the second, the implant was cast in a machined gypsum mold Both processes were based on a digital model of a dried human skull scanned by computer tomography Dimensional errors were evaluated with a coordinated measurement machine Despite their complexity, the PMMA specimens produced were measured and their dimensional differences established Compared with direct D D da Costa (*) Mechanical Engineering Department, Universidade Federal Paraná, Curitiba, PR, Brazil e-mail: dalberto@ufpr.br S F Lajarin Postgraduate Program in Mechanical Engineering, Universidade Federal Paraná, Paraná, Curitiba, PR, Brazil machining, casting results in a longer lead time and, because of shrinkage, a larger dimensional deviation Keywords Cranioplasty Cast implants Direct machining Introduction The use of prefabricated alloplastic implants for cranioplasty applications has grown in recent years, mainly because such implants help reduce surgical time and allow a satisfactory esthetic restoration, as has been described by several researchers [1–5] Firstly, the injured region, or in some cases the whole skull, is scanned by computer tomography (CT) The acquired image set is then processed to separate the region of interest and the edges making up the bone contours A number of commercial packages are currently available for this kind of application, and some are able to produce a 3D reconstruction of the scanned volume and export it in Initial Graphics Exchange Specification or Standard Tessellation Language (STL) format Once a computer-aided design (CAD) model has been produced, it can be adjusted digitally to facilitate attachment of the prosthesis as proposed by Weihe et al [6] Depending on the geometric complexity and biomaterial chosen, one or more manufacturing processes can be selected In most cases, more than one manufacturing process is usually required to produce the implant A number of different manufacturing alternatives have been studied and recommended for the prefabrication of cranioplasty implants Casting, machining, forming, and layer manufacturing-based processes are the most significant examples As described by Giannatsis and Dedoussis [7], Leong et al [8] and Yang et al [9], the last of these techniques allows very intricate geometric forms to be produced and is used to produce biomodels and scaffolds, which have been the object of much attention from the research community in recent years Direct machining is a very flexible process and has been used in the production of titanium [6] and acrylic implants [10] Its most important limitation is the interaction (gouging) between the cutting tool and the blind, or even small, cavities found in the surface of the implant However, as described next, the adoption of smaller cutting tools in the finishing phase can minimize this kind of geometric constraint, particularly when such cavities not represent important anatomical features In addition to the problems, they pose in terms of gouging, the free-form surfaces found in implants pose serious difficulties for setup planning insofar as determining datum and fixtures is concerned Nevertheless, if satisfactory fixture planning can be developed, machining can be considered an alternative The use of casts offers one significant advantage over other techniques, namely, the possibility of producing composite materials in the same mold, as pointed out by Schiller et al [11] The cost of making the mold, however, is one of the shortcomings of this approach A combination of machining and casting, as proposed by Hieu et al [12] and Weihe et al [6] represents a valuable alternative, since a cheaper free-machining material could be used to build the mold cavities As well as increasing the lead time, a combination of different manufacturing techniques in the production chain of a cranioplasty implant affects the final quality of the implant, in particular its shape and dimensional deviation A further, significant problem associated with dimensional error assessment in implants arises as a result of their geometric complexity, which makes traditional linear measurements more difficult to apply [13] The aim of this paper is to describe two different manufacturing processes that were used to produce a large polymethylmethacrylate (PMMA) implant for use in cranioplastic surgery and to discuss the results of the evaluation of the dimensional errors and lead times associated with these methods The longer manufacturing chain involves mold machining and casting; and the shorter chain, direct machining of the region modeled Materials and methods The starting point for this work was a dried human skull that had been tomographed and modeled by Bazan [10] and had its calvarial region digitally extracted as shown in Fig Despite the fact that it is unique and does not correspond to a real cranial defect, the digitally extracted Int J Adv Manuf Technol (2012) 58:1–8 Fig Dried skull and the digital model of the region extracted region represents a substantial challenge both to measure and manufacture, as it contains two highly curved surfaces (the internal one and the external one) The third surface was defined by an arbitrary intersection of the digital model of the skull with a plane parallel to the scanning plane, which is roughly parallel to the occlusal plane The details of the CT and CAD modeling can be seen in reference [10] and are not repeated here PMMA was chosen in this study because it is extensively used as biomaterial, is cheap, and can be easily manufactured [3, 12, 14] The choice of autopolymerizing rather than heat-polymerizing material was influenced by the design of the mold and is explained in the next section 2.1 Direct machining A prepolymerized powder was hand mixed with the liquid monomer (Classico São Paulo, Brazil) inside an open box Based on the results reported by Jasper et al [15], the liquid-to-powder ratio adopted was 0.5 mL/g The box was then kept inside an autoclave with a positive pressure of 300 kPa, and the rectangular block formed (57×146× 175 mm) was removed from the box h later Most of the machining conditions were very similar to those used by Bazan [10], the main difference being the use of smaller cutting tools and the addition of a parallel lace milling strategy during the finishing of both the concave Int J Adv Manuf Technol (2012) 58:1–8 and convex surfaces The setup was the same as that used by Bazan [10] and involved the use of a sacrificial material for the second fixturing and localization Schematic representations of the machining strategies for both the surfaces are shown in Figs and 3, and the main cutting conditions are given in Table All the machining was planned with Edgecam software (Pathtrace Ltd., Reading, UK) and executed in a Discovery 4022 three-axis vertical machining center (Romi, São Paulo, Brazil) 2.2 Casting Fig Milling operation at the convex surface In most of the literature about acrylic castings for cranioplasty applications, the molds are produced by hand after the cranial defect has been copied using alginate or similar material [16] or by layer manufacture of an implant model [7] In both cases, the models are then used to create a gypsum-filled mold The use of mold machining is rare Hieu et al [12] proposed this technique as a way of achieving greater quality and reducing cost compared with layer manufacturing-based processes All the parts of the molds (cores and cavities) they used in their study were machined in hardwood resins and plastics In this work, we propose a different approach (see Fig 4) involving the design of a mold based on an aluminum flask that can be reused and filled up with gypsum as necessary The top of the flask can be moved along a two pin guide so that external pressure can be applied with a press The first gypsum block was cast in the flask and on the top plate After it had set, it was removed from the flask while being kept anchored to the top plate by means of machined grooves as shown in Fig After the flask had been emptied, the second block was cast and kept there until the end of the whole process The gypsum casts were made from type IV dental stone, and the water-to-powder ratio was 0.2 mL/g in accordance with the manufacturer’s instructions (Zhermack SpA, Badia Polesine, Italy) The machining planning and conditions were the same as those used for the PMMA milling, which are shown in Figs and and Table A circular groove was milled along the upper surface of the gypsum and a rubber O-ring was inserted in the groove to provide a mechanical seal during the pressing phase A sufficient volume of PMMA mixture was prepared to provide the 150 mL required for the casting itself and the excess portion that flows out of the mold, thus guaranteeing that the mold would be completely filled Five minutes after the PMMA was prepared, the mold was closed and secured to the table of a hydraulic press An axial load of kN was applied for h to guarantee complete polymerization The setup and run times for each task were recorded to enable the process times for both manufacturing processes to be compared Fig Milling operation at the concave surface 2.3 Dimensional error assessment After the manufacturing phases had been completed, the skull, gypsum mold (core and die) and directly machined and molded acrylic implants were all measured against the digital STL model Because the skull was a complete piece, its inner surface was not inspected All measurements were carried out with a coordinated measuring machine (CMM) (Discovery II from Sheffield, WI, USA) equipped with a 2-mm spherical touch tip and an accuracy of 5+L/200 μm PC-DMIS™ CAD++ software (Wilcox, UT, USA) was used for the localization procedure and measurement analysis This package has a special “best-fit” resource based on the least-squares method that allows the automatic localization of complex parts The Design Coordinate System (DCS) was based on the STL model and used to determine the Measurement Coordinate System (MCS) for all the inspected parts The procedure to localize the MCS consisted of three steps, which were applied to the seven surfaces Firstly, based on the “3-2-1 principle”, six points were manually defined to achieve rough localization In the second stage, a grid composed of 160 points was created in the DCS and used by the PC-DMIS localization algorithm This second stage was applied iteratively until the system reported Int J Adv Manuf Technol (2012) 58:1–8 Table Machining conditions Cutting conditions Surface Operation Strategy Cutting speed (m/min) Concave End milling the sacrificial material Roughing First finishing pass at Z=32 mm Second finishing pass at the end Roughing Z constant Z constant Z constant Parallel lace Z constant 157 157 44 44 157 0.3 0.3 0.22 0.22 0.3 20 mm end mill 20 mm end mill mm ball nose mm ball nose 20 mm end mill First finishing pass at Z=6 mm Second finishing pass at Z=40 mm End milling to cut off the sacrificial material Parallel lace Z constant Z constant 44 44 44 0.22 0.22 0.22 mm ball nose mm ball nose mm end mill Convex convergence In the last stage, a regular grid with 5,000 points was defined to cover the visible surfaces For every digitized point, the difference (T) between the point in the MCS and the corresponding point on the digital surface in the DCS was computed according to the following equation: T ẳ i x m x d ị ỵ j y m y d ị ỵ k ð z m À z d Þ ð1Þ where the unit vector “i, j, k” defines the direction in which the touch trigger approaches the surface, xm, ym, and zm are the Cartesian coordinates of the point measured in the MCS, and Xd, yd, and zd are the Cartesian coordinates of the digital model in the DCS The root mean square (RMS) of the measurements was used to estimate the dimensional deviation for the inspected surfaces In addition, to improve the RMS-based analysis, the bounding boxes were calculated for the manufactured specimens using the digitized points Their dimensions were defined by the differences between the largest and smallest values in the X, Y, and Z directions Fig Mold design Feed per tooth (mm/rev) Cutting tool Results The machined surfaces resemble the surfaces in the digital model very closely As shown in Fig 5, even small anatomical marks, such as those in the calcified sutures, were reproduced As aluminum alloys have good mechanical strength, the reusable mold case could be easily referenced and fixed to the machine table The case also increased the stiffness of the gypsum, thus helping reproduce the small details found in the STL model The machined core and cavity can be seen in Fig As the core moves into the cavity, the excess PMMA flows out of the mold; once the core is fully inserted into the cavity, the rubber O-ring forms a seal between the two parts of the mold allowing a positive pressure to be maintained during polymerization After the setting time, the casting was easily removed without damaging the machined gypsum As shown in Fig 7, minor flash formation alternating with small unfilled regions occurred at the mold parting line The flashes were manually cut off before any measurements were taken Int J Adv Manuf Technol (2012) 58:1–8 Fig Comparison of the digital STL model and the machined specimen Figure shows a histogram of the T values and a graphical representation of the distribution of these values over the skull surface generated with the PC-DMIS software The darker areas (red and dark blue) indicate the values outside a range of ±0.3 mm The maximum values for T+ and T− are also identified A similar analysis was conducted for all the surfaces inspected The results are summarized in Table 2, which gives the RMS values and the amplitude of the points measured Table gives the results of the bounding box calculations for the external surfaces of both the cast and the machined specimen The values for the STL model were used for comparative purposes The elapsed times for each task in both processes are shown in Tables and The setup time includes planning, machine preparation, and material handling The process times are the sum of the setup or run times for each task in the sequence in which they are carried out to produce a single PMMA specimen Discussion and conclusion Starting from a digital STL model produced by Bazan [10] of a large hypothetical cranioplasty implant, two specimens Fig Visual comparison of the digital model (convex surface) with the machined (concave) gypsum cavity were produced using two different manufacturing processes The specimens, which were made of PMMA, were evaluated with a CMM Dimensional error assessment was based on a comparison of the surfaces of the specimens with the surfaces of the STL model Because of the high degree of geometric complexity imposed by this kind of surface, PC-DMIS software was used to run an automatic localization procedure As a real clinical case was not available for study, a large region of the skull corresponding to the top of the calvarium was analyzed It is reasonable to suppose that such a specimen is representative, from the point of view of the geometry, of a great number of the skull defects reported in the specialized literature [17–19] Of course, in the case of smaller implants, especially those with small cavities, more effort is needed to design and machine the gypsum molds However, as pointed out by Hue et al [12], correct planning of the parting line and selection of small cutting tools can minimize the problem, allowing the molds to be satisfactorily milled in a three-axis machine tool The largest RMS value (0.169 mm), which coincided with the second largest amplitude (T+ =0.816 mm and T− =−0.669 mm), was observed when the digital model (STL) was compared with the original dried skull This difference can be attributed to three sources of error The Int J Adv Manuf Technol (2012) 58:1–8 Fig Cast implant with minor flash formation at the mold parting line first, which is known as the partial-volume effect, is a consequence of the use of computed tomography As pointed out by Mazzoli et al [13] and Bouyssié et al [20], this kind of deviation depends on the scanning parameters adopted, such as section thickness, pitch, tube current, and voltage The second source is related to the 3D reconstruction and factors such as the bone segmentation, contour vectorization, tessellation, and interpolation methods The millimeter-to-pixel ratio adopted in the model evaluated was 250/512, as reported by Bazan [10] Despite the facilities available in the software for image segmentation, contour interpolation and tessellation, a certain amount of error, albeit small, can be expected from this kind of processing Mazzoli et al [13] and Choi et al [21] Fig Histogram of T values and a graphical representation of these on the digital STL model after measurements of the skull were taken highlighted the importance of the threshold value adopted during image segmentation as a factor that has a significant effect on the quality of the digital model The third source of error can be attributed to the localization procedure Despite the large point set adopted here, a certain amount of error should be expected, which, as pointed out by Lai and Chen [22], depends mainly on the quality of the points measured The analysis in Fig helps to corroborate the last error source discussed above The histogram indicates a wellcentered distribution of the T values, i.e., roughly 50% of the points are positive However, their spatial distribution over the skull surface reveals two patterns The first, corresponding to the dark blue area, is mainly composed Int J Adv Manuf Technol (2012) 58:1–8 Table Results of the dimensional error assessment of the different surfaces inspected Surface inspected T (amplitude) (mm) T+ Skull External (cast) Internal (cast) Gypsum mold (cavity) Gypsum mold (core) External (machined) Internal (machined) 0.816 0.516 0.517 0.314 0.462 0.986 0.637 T− 0.161 0.121 0.117 0.022 0.028 0.043 0.045 of negative values less than −0.30 mm The second, which follows the calcified sutures, contains positive values greater than 0.30 mm (red area) and is a result of a discontinuity in the modeled surface The dimensional error found in the cast implant was less for both surfaces (RMS=0.121 and 0.117 mm for the external and internal surfaces, respectively) than that observed for the skull, but with a larger amplitude (T+ = 0.517 and T− =−1.373 mm for the internal surface) As with the skull, a similar pattern for the more negative T values was observed, but this is largely explained by the shrinkage that occurs after the setting and curing time for the PMMA This shrinkage can be confirmed by analysis of the bounding box values given in Table The mean value of the difference between the cast and the digital model was estimated to be −0.63% However, this cannot be entirely attributed to shrinkage alone as other sources of error are present, such as the localization procedure, the machined gypsum mold, and the distortion caused by demolding The value observed lies in the linear shrinkage range reported by Keenan et al [23] during injection molding of PMMA dentures While according to Silikas et al [24], the estimated theoretical value for the proportion of monomer used could be expected to be larger, the smaller shrinkage observed in the present study can be explained by the fact that positive pressure was maintained throughout the polymerization phase and, as reported by Gilbert el al [25], by the mixing Table The bounding box dimensions for the manufactured specimens and the STL model External surface Digital model Cast Machined Task Setup time (min) Run time (min) Preparing the gypsum Machining the mold cavity Machining the core Machining the circular groove Casting the PMMA Process time 15 40 35 10 30 130 200 100 95 135 535 T (RMS) (mm) −0.669 −0.706 −1.373 −0.141 −0.090 −0.373 −0.175 Table Setup and run times for the main casting tasks procedure adopted here, i.e., hand mixing instead of vacuum mixing As the PMMA specimen was cooled inside the mold, the expansion and contraction caused by the exothermic reaction during polymerization were constrained by the mold walls suggesting that residual stress may be present in the cast specimen Both the machined surfaces were found to have low RMS values, with more than 98% of all the points measured lying within a range of ±0.1 mm Larger values were considered to be outliers, particularly those occurring at the calcified sutures This close visual and dimensional resemblance to the digital model agrees with the results reported by Da Costa [26] The RMS T value measured for the gypsum mold (core and cavity) was slightly lower than that observed for the machined PMMA surfaces The small difference can be attributed to the greater stiffness afforded by the gypsum and the aluminum flask As milling was done after the setting time had elapsed, no significant expansion of the gypsum was expected, contrary to what is observed when an implant is molded in gypsum slurry [27] The casting time was longer than that recorded for direct machining, as it includes the time required for tasks related to the production of the mold as well as the molding phase itself The process times shown in Tables and are the sum of the setup or run times for each task in the sequence in which they are carried out However, as preparation of the gypsum and casting of the PMMA block can be carried out beforehand, both the cast and direct-machining process times can be shortened to 7.5 and 4.7 h, respectively Layer-manufactured patterns are extensively used to produce molds for cast PMMA implants [1, 7] D´Urso et Table Setup and run times for the main direct-machining tasks Directions X (mm) Y (mm) Z (mm) 133.077 131.704 132.688 163.588 161.885 163.297 44.680 44.756 44.446 Task Setup time (min) Run time (min) Casting the PMMA block Machining the sacrificial material Machining the concave surface Machining the convex surface Process time 15 30 15 70 130 120 25 65 80 290 al [1] reported an average time of 10 h to produce casting patterns and h to cast the PMMA implant However, despite the time saving afforded by the processes investigated here, these cannot compete with layer-based technology when the implant geometry is highly complex, particularly when the implants contains hollow regions and small cavities The main goal of this work was achieved Despite their complexity, the PMMA specimens produced were measured and the dimensional differences for each specimen were determined Compared with direct machining, casting implies a longer lead time and larger dimensional deviation However, if a proper offset value is adopted in the molddesign phase, shrinkage can be minimized Accordingly, the inherent advantages of casting, such as the possibility of producing implants made of composite materials, as proposed by Schiller et al [11], can compensate for the longer lead time associated with this technique Acknowledgments The authors would like to express their gratitude to CAPES, the Brazilian Agency for Postgraduate Education References D’Urso PS, Earwaker WJ, Barker TM, Redmond MJ, Thompson RG, Effeney DJ, Tomlinson FH (2000) Custom cranioplasty using stereolithography and acrylic Br J Plast Surg 53(3):200–4 Barker TM, Earwaker WJS, Lisle DA (1994) Acccuracy of stereolithographic models of human anatomy Australas Raiol 38:106–111 Eppley BL (2005) Biomechanical testing of alloplastic PMMA cranioplasty materials J Craniofac Surg 16(1):140–143 Eufinger H, Wehmöller M, Harders A, Heuser L (1995) Prefabricated prostheses for the 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Bouyssié JF, Bouyssié S, Sharrock P, Duran D (1997) Stereolithographic models derived from X-ray computed tomography— reproduction accuracy Surg Radiol Anat 19:193–199 21 Choi J-Y, Choi J-H, Kim N-K, Kim Y, Lee J-K, Kim M-K, Lee J-H, Kim M-J (2002) Analysis of errors in medical rapid prototyping models Int J Oral Maxillofac Surg 31:23–32 22 Lai JY, Chen KJ (2007) Localization of parts with irregular shape for CMM inspection Int J Adv Manuf Technol 32:1188– 1200 23 Keenan PLJ, Radford RD, Clark RKF (2003) Dimensional change in complete dentures fabricated by injection moulding and microwave processing J Prosthet Dent 89(1):37–44 24 Silikas N, Al-Kheraif A, Watts DC (2005) Influence of P/L ratio and peroxide/amine concentrations on shrinkage-strain kinetics during setting of PMMA/MMAbiomaterial formulations Biomaterials 26:197–204 25 Gilbert JL, Hasenwinkel JM, Wixson RL, Lautenschlager EP (2000) Theoretical and experimental analysis of polymerization shrinkage of bone cement: a potential major source of porosity J Biomed Mater Res A 52(1):210–18 26 Da Costa D, Pedrini H, Bazan O (2009) Direct milling of polymethylmethacrylate for cranioplasty applications Int J Adv Manuf Technol doi:10.1007/s00170-009-1978-y 27 Heshmati RH, Nagy WW, Wirth CG, Carl GW, Dhuru VB (2002) Delayed linear expansion of improved dental stone J Prosthet Dent 88(1):26–31 Int J Adv Manuf Technol (2012) 58:9–17 DOI 10.1007/s00170-011-3365-8 ORIGINAL ARTICLE Multi-objective optimization of green sand mould system using evolutionary algorithms B Surekha & Lalith K Kaushik & Abhishek K Panduy & Pandu R Vundavilli & Mahesh B Parappagoudar Received: May 2010 / Accepted: 25 April 2011 / Published online: May 2011 # Springer-Verlag London Limited 2011 Abstract The quality of cast products in green sand moulds is largely influenced by the mould properties, such as green compression strength, permeability, hardness and others, which depend on the input (process) parameters (that is, grain fineness number, percentage of clay, percentage of water and number of strokes) This paper presents multi-objective optimization of green sand mould system using evolutionary algorithms, such as genetic algorithm (GA) and particle swarm optimization (PSO) In this study, non-linear regression equations developed between the control factors (process parameters) and responses like green compression strength, permeability, hardness and bulk density have been considered for optimization utilizing GA and PSO As the green sand mould system contains four objectives, an attempt is being B Surekha : P R Vundavilli (*) Department of Mechanical Engineering, DVR & Dr HS MIC College of Technology, Kanchikacherla, Andhra Pradesh 521180, India e-mail: panduvundavilli@gmail.com B Surekha e-mail: surekha_vundavilli@yahoo.co.in L K Kaushik : A K Panduy Department of Mechanical Engineering, Rungta College of Engineering & Technology, Bhilai, Chattisgarh 490024, India L K Kaushik e-mail: lalithkumar.kaushik@gmail.com A K Panduy e-mail: abhishek.pandey2321@gmail.com M B Parappagoudar Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Durg, Chattisgarh 491001, India e-mail: maheshpg@gmail.com made to form a single objective, after considering all the four individual objectives, to obtain a compromise solution, which satisfies all the four objectives The results of this study show a good agreement with the experimental results Keywords Green sand mould system Optimization Genetic algorithm Particle swarm optimization Introduction During moulding process, the quality of the parts produced depends on the properties (that is, green compression strength, permeability, hardness and bulk density) of moulding sand It is important to note that improper levels of these properties leads to common casting defects, such as blow holes, pinhole porosity, poor surface finish, dimensional variation, scabs and rat tails, misruns, etc It is also important to note that the mould properties are influenced by a large number of controllable parameters (that is, grain fineness number, percentage of clay, percentage of water and number of strokes) Hence, it is important to identify the levels of the input variables that provide required mould properties, which improves the quality of the parts produced by this mould Most of the research work on moulding sand during 1960s and 1970s was based on experimental and theoretical approaches The relationship between permeability and transformation zones, mould pressure, void space control, etc., was developed by Marek [1] through substantial mathematical equations In addition to this, Frost and Hiller [2] established the pressure and hardness distributions in sand moulds Later on, Wenninger [3] utilized the rigid water theory to explain sand–clay–water relationships This approach was completely theoretical and not supported by a Int J Adv Manuf Technol (2012) 58:397–409 401 Table Information sharing in supply chains Reference Cachon and Fisher [5] Gaonkar and Viswanadham [20] Gavirneni et al [22] Huang et al [31] Lau et al [35] Lee et al [37] Lin et al [39] Raghunathan [52] Tu et al [60] Zhao et al [71] Reddy and Rajendran [55] This study Level of information sharing No information or only order information Inventory information √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ Production schedule Forecast demand √ √ √ √ √ √ √ occurrence of various failures and equipment breakdowns) The major contribution of this study is the introduction of reliability information sharing in a supply chain The supplier reliability information is fed forward to alter the transportation lead time in an attempt to meet the customer delivery due date or to revise the order in real-time with an alternative supplier, when the current supplier is unable to fulfill the order in time Real-time order revision is an attempt to secure supply for an alternative source, when an irregular failure occurs Transportation lead time alteration is interpreted as altering the transportation mode, which is implemented to deter due date lateness when an alternative supplier’s safety stock is not adequate Order revision and change in transportation mode both have cost components, which are balanced in lieu of the need to fulfill customer orders on time Model development In this study, a hypothetical supply chain model, as shown in Fig 1, is developed in order to investigate via simulation the impact of information sharing mode (i.e., inventory information, customer demand information, and reliability information), capacity tightness, and reliability on on-time deliveries and total cost in a supply chain The hypothetical supply chain model maintains a policy of dual sourcing for supply, which allows the use of alternative suppliers Two suppliers provide inputs for the subsequent tier The model has two shipment modes: regular and expedited Regular shipment mode uses a longer lead time at a lower cost than expedited, which is much faster at a higher cost Finished goods inventory Reliability information √ √ √ √ Customer demand √ √ √ √ √ √ √ √ √ √ and safety stock are kept at tier and tier suppliers However, due to delayed differentiation based on a customer order at the Manufacturing and Assembly facility, only finished goods due for shipment are kept in inventory Similarly, at the Distributor facility, only goods undergoing shipment act as temporary inventory The goal is to reduce cost while maintaining the highest on-time delivery rate possible The three information sharing modes affect decision making in the supply chain Sharing of inventory information affects production and shipment schedules, while customer demand information is used in conjunction with inventory safety stock level, production, and shipment schedules Sharing of reliability information affects order revision and shipment mode selection related decisions Inventory information sharing (INV) It consists solely of sharing the order-up-to inventory level and the current inventory level on a daily basis Inventory information is shared by the immediate downstream business partner in the supply chain with the immediate upstream suppliers Suppliers then can plan production for the new day based upon the previous day’s inventory status The inventory order-up-to quantity is based on the base stock model The base stock model (R, s, S) uses periodic review, order-up-to-level with nonstationary demand where R is the period of time (performed daily in this study) to check inventory position, s is the reorder point, and S is the stock level The reorder point (s) is equal to the mean of customer demand (μcd) of the Poisson arrivals multiplied by the lead time (L) plus safety stock: s ¼ ðmcd  Lị ỵ S 2ị 402 Int J Adv Manuf Technol (2012) 58:397–409 Fig Hypothetical supply chain model Tier Supplier A Tier Supplier A Tier Supplier B Manufacturing and Assembly Distributor Customer Tier Supplier C Tier Supplier B Tier Supplier D This replenishment policy uses customer demand from the current period along with historical data to forecast a future inventory level given a safety stock level Customer demand information sharing (CD) It incorporates the use of real-time customer demand information to determine production and inventory levels Instead of waiting for orders to perturbate through the various echelons, immediate real-time customer demand is used as a production signal The reorder point (s) is equal to the forecasted daily usage (FDU) multiplied by the lead time (L) plus safety stock (S): s ẳ FDU Lị þ S ð3Þ The forecasted daily usage is calculated at the end of each day using a simple moving average of the customer demand Safety stock is based on three sample standard deviations (3σ) away from the mean This safety stock level covers 99.865% of the possible inventory positions Lead time is fixed at days The stock level is the present inventory level Hence, if at any time S>s, production stops until S i¼1 > rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > m m > P P > > ðxij Àxj Þ2 ðxik Àxk Þ2 If objectives of criteria j and k are same < i¼1 i¼1 Rjk ¼ j and k ¼ 1; 2; 3; ; n n P > ðxij Àxj Þðxik Àxk Þ > If objectives of criteria j and k are different > > i¼1 > À rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > m m P P > > : ðxij Àxj Þ2 ðxik Àxk Þ2 i¼1 ð16Þ i¼1 In Eq (16), m is the number of materials, n is the number of criteria, xj and xk are the average values of criteria j and k and Rjk is the correlation between criteria j and k A value of R near indicates little correlation between criteria, while a value near or −1 indicates a high level of correlation The advantage of suggested formula in Eq (16) over the existing one in Eq (8) is that it does not need normalization of criteria (Eqs (6 and 7)), while the final results are the same An excessive set of criteria leads to more analytical effort and can make communication with the results of the analysis more difficult Yurdakul and Tansel [51] suggested limiting the number of the criteria around seven, because models with lower number of criteria are usually more sensitive to changes in weights of criteria Decision making to remove a criterion from the decision matrix should be carried out carefully based on the idea of DM Moreover, according to Fig 1, high correlation with a criterion or other criteria needs to be considered as well as less objective weights Step (3): Calculate weight of correlation's effect according to Eq (17) n P wcj ẳ Rjk ị kẳ1 n P n P Rjk ịị j ẳ 1; 2; 3; :::; n 17ị jẳ1 kẳ1 Step (4): According to Fig in the situation with the low number of criteria, direct weighting techniques are suggested for subjective weighting and, either MDL or AHP is proposed for the high number of criteria Weighted least-square technique is also suggested when there is inconsistency in DM judgments because it is easier than eigenvector approach [30] In material selection, scholars always look for logical and simple 416 Int J Adv Manuf Technol (2012) 58:411–420 Fig The suggested flowchart for objective, subjective, and dependency weight in material selection Start No Are quantitative values available for all criteria? Yes Calculate objective weights using entropy method Remove unnecessary criteria Calculate intercriteria correlation Is there any unnecessary criteria? Yes No Calculate weight of correlation effect using proposed formula No Is the number of criteria high? Yes Using direct weighting procedures Using AHP or MDL to calculate subjective weights Is there inconsistency in DM judgment? Yes Using weighted least square method No Subjective weights methods to help designers and decision makers in engineering design applications Step (5): Combine the weights according to the suggested formula in Eq (18), wherewoj , wsj , and wcj are the objective, subjective, and correlation effect's weights, respectively MCDM This improvement is attributed to a systematic process presented for both objective and subjective approaches, less amount of computation for correlation effect's weight compared to CRITIC technique and a novel formula for combining the three types of weight ðwoj »wsj ằwcj ị Wj ẳ P n woj ằwsj ằwcj ị j ẳ 1; 2; 3; :::; n 18ị jẳ1 To sum up, this paper provides a framework for designers in subjective and objective weighting of material selection's criteria, which has slightly improved the weighting procedure of Case study This example is about material selection of mass produced non-heat-treatable cylindrical cover sheet [10, 24, 35] which is in the group of highly sensitive components In this wellknown material selection problem, the sheet should operate