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Original Article | Open Access | Can. J. Bus. Inf. Stud., 2024; 6(5), 189-203 | doi: 10.34104/cjbis.024.01890204

Integrating Additive Manufacturing into the Supply Chain in a Fuzzy Environment

Nima Ebrahimifard* Mail Img ,
Soroush Avakh Darestani Mail Img ,
Allahyar Daghbandan Mail Img

Abstract

Additive manufacturing (AM), 3D printing, rapid prototyping, rapid development, rapid technologies, and many other similar names are terms used interchangeably for rapidly growing technologies based on adding materials, layer by layer, to build the final product, in comparison to the subtractive - conventional productions. Meanwhile, the supply chain has been greatly influenced by this phenomenon. Thus, it is necessary to provide a holistic approach to the analysis and design of the system. In this paper, a supply chain model for the integration of conventional and AM facilities in a fuzzy environment is developed. This model is focused on situations where the possibility of adding new AM facilities within the traditional plants in a broader supply chain is in question. In addition, the best production levels and transportation of the chain, along with purchasing decisions and other tactical factors, and the number of facilities at a strategic level are developed. Furthermore, 3 numerical examples are provided to examine different conceivable outcomes.

INTRODUCTION

Additive manufacturing was not widely accepted and used at the beginning of its introduction. This technology was only used as a prototype due to its lack of recognition and lack of interest. But with the introduction of processes, materials, software, and controls, the game changed. This rapid development has occupied many areas and the need for knowledge in this field seems obvious (Gebhardt & Hötter, 2016). The rapid enrichment of additive manufacturing technologies is along with an increase in the variety of materials, low-cost machines, and the possibility of application in different fields. This leads to a fundamental lack of guidelines and standards (Gao et al., 2015). Fortunately, the market has called for more advanced procedures as well as sustainable approaches, where AM can be the best solution. Additionally, if the current investments in this technology continue, we will see around 50 percent of all goods manufactured by AM by 2060 (Dzogbewu et al., 2022).

Even though there have been a lot of considerations about the costs, business models, capacities, and characteristics of additive manufacturing in the literature, the impact of location-allocation of additive manufacturing factories and their construction in the supply chain has rarely been studied. Creating additive production facilities in the existing supply chain is an important field of study (Mashhadi et al., 2015). Gress and Kalafsky, (2015) emphasized creating additive manufacturing in the value-added chain. Our research is one of the few efforts that has considered this impact on supply chain and operations. This is necessary and therefore very likely that this technology can affect many areas of life with its widespread usage. Based on this, there is a noticeable trend in the implementation of this technology in large industries such as aerospace, medicine, and automobile manufacturing. In contrast to its benefits, additive manufacturing cannot conquer conventional production. All in all, the need to enter this interesting technology seems to be a necessity (Attaran, 2017). For this reason, it is very important to plan strategically and systematically.

In general, revolutionary technologies are seen as a negative phenomenon in the opinion of existing factories. This is due to the general trend against changes in industries. To overcome this problem and also to the advantages of not only traditional production but also additive production, we have proposed a subtractive-additive production in the supply chain (Dzogbewu et al., 2022). Additive manufacturing is based on increasing materials layer by layer to build the final materials. This is necessary to strategically meet the requirements of the production comprehensively. In this paper, we look at the production holistically.

Attaran, (2017) tried to consider the current competition, where factories engage in innovative production and production in large numbers with the ability to meet the specific needs of customers, which additive manufacturing can easily satisfy. In addition, this production will have a major impact on the supply chain and specifically on logistics, which must be carefully studied. In short, it can be declared that this technology leads to the improvement of the chain and reduces the costs of distribution, assembly, and transportation. It can be acknowledged that this technology will gradually enter various industries and it has already indicated its potential in many industries including aerospace, automobile manufacturing, industrial goods, customer-specific goods, defense, architecture, health systems, etc. In the past, due to the high cost of the supply chain and the 5% impact on costs, manufacturing factories turned to Radio Frequency Identification (RFID) technology in 2000, and now its time to reduce supply chain costs by emphasizing additive technologies. It can be stated that the decade of 2010 is another decade of 3D printers and continues substantially. In the aforementioned research, both activities are focused on reducing supply chain costs, and it is mentioned that additive technology can reduce complexities in general. These complications range from inventory complications to assembly complications and so forth. Additive manufacturing has many advantages over traditional manufacturing, four of which include cost, quality, speed, and environmental effects. In short, we can say that additive technology has many effects on the supply chain; including accelerated product development, reducing the size of the economic package, increased production flexibility, and reduced waste. Practitioners who turn to additive manufacturing can reap other benefits, according to the stated study, from materials sourcing to logistics and distribution. The aforementioned research states that an interdependent supply chain in the global space with local production is one of the results. Additionally, as mentioned, many models will investigate additive technology in the future. These models will have the ability to reduce costs, reduce the time of sending goods, and send goods on time and efficiently. These models will be associated with simplifying and effective supply chain networks by reducing the need for storage and inventory capacities, but our model is one of the ones that studies the supply chain systematically.

New technologies such as AM should be widely researched in many developing countries to be well-applied. Although South Africa has been able to benefit from these advancements due to its cultural structure and cooperation between research and industry, what we try in this research is to introduce a very systematic approach to help all countries be better able to use this new paradigm, i.e., AM (Dzogbewu et al., 2022). Therefore, in our research, an attempt has been made to fulfill all these needs in the fuzzy space, considering the uncertainty in reality, then a model has been proposed and it has been optimized. In addition, the research has well taken into account the production requirements in the supply chain space where both production types are possible. The main question of our work is if according to the uncertainty in the chain, including demand, receiving, and sending, among others, it is possible to provide a suitable model for optimizing system costs, and if such a model is developed, how it is possible to solve and present appropriate proposals in a small and realistic environment. At the same time, by briefly dividing the research into part by parts, the necessary material has been provided for researchers and managers to better understand the model and how to use it in practice. Research objectives include general and specific objectives. The general objectives of the research are divided into two strategic and operational objectives. The strategic goals of the research include modeling and locating traditional and additive facilities. Operational goals are the optimal use of production machines in each factory, the amount of transportation in the supply chain, and the amount of stock in each facility. At the same time, other goals are considered besides these goals; such as introducing and identifying different types of additive manufacturing technologies, identifying hybrid production, characteristics of additive manufacturing supply chain, etc. The current article is organized into three remaining sections. First, we will explain the keywords along with the literature review. Followed by the research methodology provided for analysis. In the end, we will finish the discussion by providing future direction, limitations, and suggestions.

Review of Literature

Additive Manufacturing

In our research, additive manufacturing refers to manufacturing processes in which materials are deposited or melted layer by layer to reach a perfect shape or very similar (Spalt & Bauernhansl, 2016; Strong et al., 2018). Hall of the 3D Systems Group created the first 3D printer in 1984. He named the machine Stereolithography Apparatus (Attaran, 2017; Diegel, 2014). At the same time, its idea dates back more than 100 years. Its first patent for a method of producing geological maps by separating wax sheets and stacking them belongs to Blanner in 1982 (Rietzel et al., 2017). Since then, evolutionary progress has been observed in this field. Additive manufacturing includes various stages. These stages include the design stage, which is mostly with CAD data, and afterward the stage of material selection and performance analysis. The next steps are completed by sending information from a computer to the printer to increase the material based on the given coordinates and analyzing the previous steps. The first layer is printed and then the remaining layers are printed to form the final product. STL (stereo lithography or standard language) is a standard file format that is used in various additive manufacturing machines, among other formats such as Stereo Lithography Interface (SLI), Systems Layer Contour (SLC), Hewlett-Packard Graphics Language (HPGL), Common Layer Interface (CLI), Virtual Reality Modeling Language (VRML), 3D Manufacturing Format (3MF), and Initial Graphics Exchange Specification (IGES). International Standards Organization (ISO) and the American Society for Testing and Materials  (ASTM) have introduced seven different sectors for additive manufacturing technologies (Gao et al., 2015; Lee et al., 2017).

The most commonly modeled processes in additive manufacturing are related to Stereo lithography (SLA), after which are Selective Laser Sintering (SLS), Selective Laser Melting (Manufacturing) (SLM), and Fused Deposition Modeling (FDM). Most authors deal with modeling of accuracy or reliability; while a few predict the mechanical properties of the final materials and the total manufacturing time (Bikas et al., 2016). SLA uses a light source to connect a pre-designed shape in liquid. On the opposite point, SLS involves heating the powder in the substrate and then melting the object (Kietzmann et al., 2015). Here, the main difference in these methods includes the method of deposit, melting, and materials used. In other words, the techniques are classified related to powder, liquid, and solid. In addition, the accuracy of each technology is different. For example, SLA ranges from less than µm10 to MicroSLA, SLM, SLS, Digital Light Projector (DLP)/Film Transfer Imaging (FTI), FDM, Direct Digital Manufacturing (DDM), MultiJet Modeling (MJM) and 3DP from µm100 to µm400. But their number in practice is much richer than what was discussed and is based on Fig. 1. Based on the methodology FDM is a common technology due to its low cost, simplicity, and high-speed process. This method was initially used to print strings of polymers, which have also been used for other materials. FDM is basically used for rapid prototyping, while the mechanical characteristics and quality of printed parts are less compared to powder-substrate methods such as SLS and SLM. Adjacent powders are fused, melted, or stuck together with the help of an auxiliary adhesive in powder-bed methods, which results in better accuracy but more cost and lower process speed. 

Direct Energy Deposition (DED) uses an energy source (laser or electron beam) to melt iron powders, unlike SLM does not use any powder bed, and the raw materials are melted similarly to FDM layer by layer with very high energy to melt iron. Contour construction, which is dependent on material (concrete) output, is used to print large structures such as buildings. Stereo lithography is one of the first 3D printing methods, which is basically used for photopolymers that have the ability to produce parts with very good quality. Finally, Laminated Object Manufacturing (LOM) is based on cutting layer by layer and aggregation of sheets or rolls on top of each other. It is very important that many materials are used for additive manufacturing: plastic, resin, rubber, ceramic, glass, concrete, and iron, each of which leads to different characteristics. In reality, there is not enough data for the actual operation of the processes and we need real and experimental information about the machines to apply one study to another. This technology has experienced many evolutionary phases. This started from prototypes for complex parts in industries, led to mass customization, which was accompanied by a development in technology, and parts were produced in small batch sizes and finally ended with the acquisition and production of parts at home. In this regard, the last steps lead to more efficient use of human resources, more reliability, nature-friendly productions, and more flexibility.

It is obvious that this technology cannot answer all the needs of the industry, and for this reason, its disadvantages are as follows:

  1. Limitations in the choice of materials, colors, and surfaces
  2. Higher costs in large productions
  3. Limited strength and durability against heat, movement, and color
  4. Limited dimensions of the product
  5. Less precision compared to other technologies
  6. Ambiguous production of risky items
  7. Problems of feasibility and intellectual property
  8. Software support
  9. Continuity and reliability
  10. Quality assurance (Chua et al., 2017).

In addition, financial services, professional business services, telecommunications, internet-based industries, retail, hospitals, entertainment, media, music, and other service industries cannot be produced and therefore are not related to this technology. Additive manufacturing has a small application in energy production, for example, electric and nuclear, as well as industries involved in the development of organic materials (Hannibal & Knight, 2018). To a large extent, the limitations of traditional production, such as the limitations of dimensions and costs of production in small dimensions, when talking about additive manufacturing, are related to past technologies. This is due to the fact that additive manufacturing has many advantages over traditional manufacturing, which can be used in complex dimensions, and in this matter, we can add other pros such as fewer costs, customizing users at no additional cost, the ability to recover materials and the cost efficiency of parts in small dimensions.

Hybrid processes

We start by mentioning this sentence from Silva et al. (2013):

"Additive manufacturing is not going to replace traditional processes. However, it will work seemingly, at least in the near future." Due to the benefits of additive production and traditional production, we have estimated that the transportation of parts from traditional production factories to additive production and vice versa will take place in the supply chain, thanks to which we increase the advantages of both factories and was used similarly to Flynns work in 2016. Each additive manufacturing and traditional manufacturing have disadvantages when considered separately. Hybrid production provides both advantages and new possibilities. Lee et al. (2017) were able to achieve this goal in their efforts by introducing step-by-step hybrid production, energy, resources, and environment. AM is considered to be advantageous in the supply chain, since it improves the supply chain costs and enhances sustainability, yet, we need to evaluate the costs associated and current lack of knowledge in this field (Calignano et al., 2023). Here, it is of critical significance to clarify what we mean by a hybrid process. As mentioned briefly, hybrid productions use both subtractive and additive processes simultaneously. This provides the benefits of both processes in production; that is, the complexity of additive production and the appropriate quality of the level of traditional production (Du et al., 2016; Gebhardt et al., 2016; Gibson et al., 2015; Newman et al., 2015).

More precisely, based on each aspect of the technologies, we are given the opportunity to choose the most appropriate choice. If, for example, the process has a large volume to cut and/or the material is very expensive, additive manufacturing is very useful as long as the lifespan is considered. In this case, traditional production can help to form a suitable product with the combination of additive production. The cell interaction in a hybrid system should be very strong to be able to control the various processes in the machines and to be able to manage the related data in the system. The control system must have the ability to manage the sequence and improve the processes in the whole chain so that the operation is in an efficient and agile mode. In our model, a hybrid production is proposed due to its rich advantages. It should be mentioned once again that hybrid production is a combination of additive and traditional production that is used sequentially or in an integrated mode, including a fixed base and a direction controller to shape the parts. This method has been used to increase the accuracy of dimensions and improve the entire production process. In addition, the problem of producing complex areas, i.e., where one process (reductive or additive) is not enough, is solved with hybrid technologies. Li et al. (2017) considered the integration of additive and subtractive manufacturing, especially for end-of-life products, to strategically and systematically produce new parts without any recycling. Their attempt led to the reduction of energy consumption, resources, and environmental benefits. In 2018, it was studied by Bandyopadhyay et al. that hybrid production with the possibility of using Wi-Fi and prefabricated components improves production by reducing waste. In addition, in the same year, Kaspar et al. (2018) benefited from a comprehensive and integrated view of hybrid production and materials, processes, and goods, and all of them were considered at the same time by means of a chart. In their study, more systematic considerations were also requested for further research. A structural comparison between traditional and additive processes allows us to have a suitable application. The first thing is that every technology has its own advantages that need to be applied carefully. For example, complex components must be manufactured by additive manufacturing. The second, states that some processes cannot be compared equally; for example, some cases require about twenty processes that can be combined with an additive process. In the end, innovation is a suitable result of additive production, which is very limited in traditional production. In the literature, there are various methods for the hybrid processes. In this research, the possibility of production planning has been given to the designer. In a nutshell, we can assert that all the possibilities of designing traditional production at the beginning and adding materials with additive production, using robots to combine processes at the same time, or using reduced production as the only post-processing of the process has been left as free decisions. A good hybrid method is characterized by its ability to combine additive and subtractive sequential processes. This topic is an important research area for machine designers to improve hybrid production. The flow of materials and information is among other important decisions. The main challenge for the integration of additive and subtractive manufacturing in current hybrid methods is the need for a hybrid process planning protocol for the post-processing of additive manufacturing, which represents the different nature of the additive manufacturing process (material erosion, layer thickness, direction, etc.), machining (tool design, the amount of machining, etc.) and the specific features of the part (main features and tolerance requirements). As part of the model, post-processing is recommended to be done whenever possible by a traditional factory. Similarly, parts produced in traditional factories can also be produced in additive manufacturing factories.

Role in the supply chain

Additive manufacturing has the ability to change the entire supply chain and can eliminate many unnecessary processes. The supply chain has become known as "global-local". In other words, parts are produced with high interaction between customers and producers, while information can be exchanged between them and a smaller inventory can be stored with higher responsiveness. This is called the reshoring shift in the view of Calignano et al. (2023). In fact, the supply chain has changed dramatically with the introduction of additive manufacturing. In 2013, Liu et al. used a supply chain operations reference model to analyze the impact of aircraft spare parts supply chain integration and achieved savings, especially in terms of costs and inventories. In their study, it is also mentioned that the number of steps can be reduced in comparison with traditional productions. In addition, additive technology provides the ability to redesign products with fewer parts and closer to customers. In order to fully understand the integration of additive and subtractive processes, a holistic view of the requirements of these processes is essential. A similar study was conducted by Ford et al. (2016) and they noted that investigating additive production is very necessary and every study is associated with a gap in knowledge and practice. Here, we need to respond to questions such as the structure and network of the supply chain and intermediate parts in the chain network. Additive manufacturing should be seen as a transitional technology. This causes multiple transitions of production items. This causes the transition of traditional business models. This will change existing supply chains. It also causes the transition of economy of place, manner, and time of production of objects. Gao and Attaran, (2013, 2017) noted considerable impacts in industrial, assembly, and supply chain industries, respectively. Kitzman et al. (2015) claimed that 3D printing enables just-in-time manufacturing and Kanban systems for factories by eliminating unnecessary inventory. From the point of view of an industrial supply chain, many effects were observed in the warranty of service components, repairs, and return of goods. In 2017, reductions in cost, carbon dioxide emissions, and transportation were observed by Chuva et al. This issue was also investigated by Ayers et al. in the same year that a systematic view is required for the integration of all systems involved in the production of final parts. Thus, this issue should be noted that the production is performed in a holistic perspective, and internal systems and the environment should be considered as a supply chain network. In this respect, the only difference is that the post-processing responsibility is assigned to the traditional factory to improve the value chain. These facts were emphasized by Hannibal and Knight, (2018) who state that even on a global scale, the need for local and widespread additive production does not change, yet the use of this technology, especially in developing countries is different, with regard to the economical limitations. This importance was also added by Hannibal and Knight that the entire logistics network can be changed with shorter connections and simplicity.

Furthermore, this is essential to consider sustainability factors so that competitive, economic, social, and more importantly environmental aspects can be achieved simultaneously. In the literature by Al Muslimi in 2018, several methods to achieve these strategies were proposed, based on the reduction of materials, energy, and waste. This subject was taken into account by more independent energy-consuming products and better information flow. In addition, key attributes are very important for all companies. These items are considered separately by the companies, but they all lead to quality and sustainability. A supply chain is a combination of supply components from suppliers to final consumers and all members under consideration when we talk about additive supply chains. To be more precise, the benefits of this change are countless, some of which are gathered in Table 1.

From the table and from the point of view of a production system, it can be concluded that the supply chain will be significantly lean and agile and at the same time lean and agile. Material performance, parts flexibility, fast ordering, and less waste make additive production capable of being lean and agile at the same time. In addition, it is predicted that the whiplash effect in the supply chain will decrease with additive production. In general, additive manufacturing affects the supply chain from product design, machine design, production line design, and facility design to the design of the entire supply chain. By using AM in the chain network, it is necessary to consider all the advantages, which are sometimes very difficult to measure and count. This is because AM eliminates many unnecessary steps and therefore it is necessary that the models show all the advantages and uncertainties in the supply network. In fact, it is easily noticeable that AM can affect every step of the chain. In addition to integrating the entire chain network, additive manufacturing can remarkably integrate assembly activities into one step. For example, a robotic system that requires many parts to be assembled to make the final product can be produced in one stage. Logistics is another issue that can be shaped differently by incremental production. In general, closer communication is observed along with customized mass production at a lower cost. Indeed, the market will be closer to the customers and many of the current and unnecessary processes will be removed. Logistics are affected as below

  1. Mass ordering results in reducing inventory levels and warehouse requirements.
  2. Goods that are produced in other countries can be produced locally, leading to a reduction in transportation.
  3. The production process is amazingly done by only one facility. Therefore, logistics providers will be less involved in upstream supply chains.
  4. There will be a change in procedure from push supply chains to pull supply chains. Long productions for mass production (economic order point) are replaced by limited mass order productions and customized products (economy of scope).
  5. Manufacturers will have a better ability to respond quickly to customer demands.
  6. There will be less work-in-process inventory and fewer finished goods in the warehouse and in transit, which will reduce the overall costs of the supply chain system.
  7. 7) One of the first sectors that is affected by additive manufacturing technologies is the logistics sector of parts services. Additive manufacturing can order the design of parts services in a short period of time and can eliminate the huge amount of rework that is wasted in opening parts in supply chains (Attaran, 2017; Rahman KS., 2021).

All of the mentioned literature clearly emphasizes a holistic view of the supply chain for facility integration. This issue was mentioned by Hannibal and Knight (2018), who emphasized reconsidering value chains and traditional productions and a need to replace local and customized productions. Based on this, an AM supply chain model has been introduced by the authors to be a strategic and operational guide for decision-making.

Fuzzy Logic

According to the systems perspective, expressed by Ayers et al. (2017), it is implied fluctuations in the chain should be considered. Although there have been many views to deal with these uncertainties; For example, stochastic models, gray method, robust optimization, etc., the fuzzy method is a very effective method that helps managers to control these uncertainties; therefore, it is used in our model to achieve aforementioned desired goals. Another reason for using fuzzy logic is that it takes linguistic variables into consideration, which is a very important advantage in modeling. It should be noted that fuzzy logic deals with these problems easily with the membership degree of each variable between 0 and 1.

Related literature

Until now, most of the literature has emphasized the cost analysis of the application of Additive Manufacturing. But in 2014, Mellor et al. emphasized the analysis of location. In addition, Mashhadi, Esmaeilian, and Behdad, (2015) broadly stated which literature is available in this field and then provided two case studies in supply chain analysis with simulation methods and dynamic systems. In their research, order time reduction was the result of an agent-oriented simulation and reduction of the whiplash effect of the results of dynamic systems. Scott et al. (2015) presented a holistic model for analyzing the whole chain in a stochastic space. These examples are great improvements for practitioners to decide which production technology to use. In addition, it was observed which factors had an essential role in acceptance; which are demand, and cost of materials, among many others. In the following year, 2016, a deterministic model was developed by Barez et al. This model included a two-stage supply chain network node and tried to minimize the costs of the whole chain. Afterward, an analysis of the US iron supply chain was conducted by Strong et al. In this research, the optimal number of AM hubs in the chain with the help of locating facilities without capacity and mean-location analysis was observed. The processes here were considered hybrid; which is because, for example, the parts were processed in the traditional factory.

METHODOLOGY

In this research, random numerical examples have been used to test the accuracy of the model. First, we will introduce the sets and parameters of the model and then present the model with a description of the de-fuzzification method. In the end, we use GAMS 25 software to solve the examples and we will analyze the results.

Symbols and signs
Sets
a A Set of AM factories
c c Set of customers
i I Set of products
p P Set of traditional factories
s S Set of suppliers
t T Set of time intervals
w W Set of warehouses
Parameters
Demand
Demand by customers for each product (fuzzy)
Production
Traditional factory capacity
mfg_var_costpit Variable cost of traditional factory production (fuzzy)
mfg_oper_costpit The operational cost of traditional factory production workshop (fuzzy)
mfg_open_costp The cost of opening a traditional factory
Distribution
wh_var_costwit Variable storage cost (fuzzy)
wh_oper_costwit Warehousing operational cost (fuzzy)
wh_open_costw The cost of opening the warehouse
supplier_capacityspit Capacity of suppliers (fuzzy)
supplier_costspit Supplier unit cost (fuzzy)
Additive manufacturing factory
am_mach_hoursat The set of production hours of the product unit
am_cap_usageit AM machine capacity
am_mach_oper_costait Operating cost of AM machine
am_mach_purch_costait The cost of purchasing an AM machine
am_mat_costt Cost of raw materials per kilogram of AM factory (fuzzy)
am_mat_usageit The amount of consumption per product of AM
am_open_costa The cost of opening AM
am_var_costait Variable cost of AM (fuzzy)
Transportation
am_trans_costacit Transportation cost from AM to customers (fuzzy)
asm_trans_costapit Transportation cost from AM to traditional production (fuzzy)
ib_trans_costpwit Transportation cost from traditional factory to warehouse (fuzzy)
ibs_trans_costpait Transportation cost from traditional factory to AM (fuzzy)
  Binary variable transition from AM to traditional factory
  Binary variable transition from traditional factory to AM
ob_trans_costwcit Transportation cost from warehouse to customer (fuzzy)
supply_trans_costspit Transportation cost from supplier to traditional factory (fuzzy)
Inventory
am_start_invait Initial inventory of AM
inventory_hold_costi Inventory holding cost (fuzzy)
mfg_start_invpit Traditional factory initial inventory
wh_start_invwit The initial warehouse inventory
inf A large number
Decision variables
am_opena Binary variable for an additive manufacturing location
am_oper_machinesait Integer variable for the number of additive manufacturing machines running
am_purch_machinesait Integer variable for the number of AM machines
mfg_openp Binary variable for traditional factory location
mfg_operatingpit Binary variable for traditional factory running machines
wh_openw Binary variable for warehouse location
wh_operatingwit Binary variable for warehouse operations
am_flowacit Flow rate from AM to customers
ib_flowpwit Flow rate from traditional factory to warehouse
ibs_flowpait Flow rate from traditional factory to additive manufacturing
ob_flowwcit Flow rate from warehouse to customers
asm_flowapit Flow rate from AM to traditional factory
supplier_flowsait Flow rate from supplier to AM
am_ending_invait Ending inventory of AM
am_productionait AM production rate
mfg_ending_invpit Traditional factory-ending inventory
wh_ending_invwit End stock of the warehouse

Model
min z =  + + + + + + + + + + + + + 
Equation (1)
st:
 - -  ≤  
Equation (2)
 +  ≥  
Equation (3)  
 + - +  =  
Equation (4)
  ≤  
Equation (5)
  ≤  *inf
Equation (6)
  ≤  
Equation (7)
  ≤  
Equation (8)
 + + +  ≥  
Equation (9)
 * + + -  =  
Equation (10)
  ≤  
Equation (11)
 -  =  
Equation (12)
  ≤  
Equation (13)
 ≤  *inf
Equation (14)
  ≤  *inf
Equation (15)
 
De-fuzzification
Due to the triangular fuzziness of some parameters in the objective function, we de-fuzzified them using the following formula.
cj =    j (Shondi 2016)
Equation (16)
By defining the following variables:
pi = The amount of tolerance for  
bi = 
To de-fuzzify the demand that is in one of the constraints the following algorithm has been used.
max  
st:
 zu-zl) – cx ≤ -zl
 i +  ijxj ≤ bi + pi   i
other non-phase constraints
Equation (17)
Equation (1) seeks the minimum possible costs regarding the model, the sum of all possible costs. Equations (2) to (15) are all constraints of the model, guaranteeing the logic of the model. Finally, equations (16) and (17) are the algorithms we used to de-fuzzify our fuzzy equations.

RESULTS

Numerical examples in GAMS 25 optimizer software have been developed to address the functionality and accuracy of the model. Tables 2 - 4 and Fig. 2 briefly show the results. In this research, first, these examples are presented in a non-fuzzy environment. Then, the objective function of formula number 1 in the last chapter has been de-fuzzified. At the same time, upper and lower bounds are defined for the demand constraint, which are shown as zu and zl respectively. In the next step and at the end, relations number 2 has been used to determine the minimum operational and strategic costs of the objective function, taking into account all the predefined restrictions.

DISCUSSION

From the resulting tables in the previous chapter, it can be predicted that, with the decrease in demand, a greater number of AM factories will be used in comparison with traditional production. This is because AM has the ability to respond to low-volume demands at a lower cost and faster. However, it should always be considered that by improving the supply of raw materials and lowering its costs, better benefits can be achieved; Among them, lack of dependence on traditional production and cheaper production on high scales; is a vast research area for future directions. Additionally, the developed model showed that it is possible to analyze the data precisely and simply with linguistic variables. This model shows us that it is not difficult to reach an optimal solution in the supply chain according to the amount of variable demand, among other variables. The functionality of the model was shown with examples in different dimensions. Yet, it is obvious that considering the existing limitations, it is recommended that this effort be evaluated in reality and with more extensive data.

CONCLUSION AND RECOMMENDATIONS

The presented model has the ability to calculate in different dimensions. The model can also evaluate data in different time periods. This is especially useful for situations where we have to analyze the data in multiple steps and in different time periods. This problem can be considered as further research due to its breadth and complexity. Limitations of the research included, to a large extent, data limitations. In the conducted research, there was no standard available data. In addition, this field needs a huge amount of investment to find a real case study. All in all, this model is a practical solution for all the enthusiasts of various industries to design their supply chains and take advantage of AM production. All models are completely practical and open the way for new technologies. As stated, it is suggested that people related to supply chain design and analysis, or any other title, can benefit from this research

  1. In the first case, it is suggested to use random fuzzy numbers to get a more accurate result.
  2. Second, according to the practical nature of the research, standard or real data should be used.
  3. A green supply chain is one of the new research areas. Therefore, for proper productivity and nature-friendly production, it is suggested to build green AM production.
  4. Lateness and earliness are important and vital issues in many supply chains. Based on the costs of lateness and earliness, the presented model can be developed so that the costs of this field can be optimized.

AUTHOR CONTRIBUTIONS

N.E. conceptualization, methodology, writing the manuscript, N.E.; and S.A.D. contributed in analysis, investigation, visualization. A.D. finally checked the manuscript and editing, and Formal Analysis. All authors who are involved in this research read and approved the manuscript for publication.

ACKNOWLEDGEMENT

We are grateful to all the dear professors for providing their information regarding this research study.

CONFLICTS OF INTEREST

The authors declared obviously in the manuscript and have no conflict of interest.

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Article Info:

Academic Editor

Dr. Doaa Wafik Nada, Associate Professor, School of Business and Economics, Badr University in Cairo (BUC), Cairo, Egypt

Received

September 8, 2024

Accepted

October 10, 2024

Published

October 18, 2024

Article DOI: 10.34104/cjbis.024.01890204

Coresponding author

Nima Ebrahimifard*

Master Graduate, Industrial Engineering Department, Kooshyar Higher Education Institute, Rasht, Iran.

Cite this article

Ebrahimifard N, Darestani SA, and Daghbandan A. (2024). Integrating additive manufacturing into the supply chain in a fuzzy environment, Can. J. Bus. Inf. Stud., 6(5), 189-203. https://doi.org/10.34104/cjbis.024.01890204

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