Examining additive manufacturing in supply chain context through an optimization model

https://doi.org/10.1016/j.cie.2020.106335Get rights and content

Highlights

  • Additive manufacturing in supply chain context is examined.

  • An optimization model is developed to formulate the problem.

  • Several structural properties and a lower bound are presented for the problem.

  • Best-fit heuristic based algorithms are employed.

  • BFCUBS algorithm is suggested for solving the problem.

Abstract

This study explores the problem of integrated jobs and vehicles scheduling in a two-stage supply chain, where parts are processed on additive manufacturing (AM) machines and then distributed to customers. In this study, we develop an optimization model for the problem with the objective of makespan minimization. Besides, several structural properties and lower bound formulation are provided to explain the main characteristics of the problem. In this regard, this study also contributes to the existing academic literature by investigating the two-stage supply chain scheduling problem with the additive manufacturing technology. Because the addressed problem belongs to non-deterministic polynomial-time hardness (NP-hard) problem class, a best-fit heuristic-based approach and several selection rules are developed to solve the problem. Each selection rule is designed by considering a distinct structural property of the problem and, thus, each of which is considered to be a different algorithm. A comprehensive experimental study is conducted through random instances, which are generated for small- and large-sized problems by considering real-production data. According to the computational results, the best-fit capacity utilization based selection (BFCUBS) algorithm is superior to others and yields a substantial improvement in the makespan. The reason behind this fact is that the high utilization of capacity enables a large number of jobs to be completed in a short time. Besides, as the number of jobs decreases and the capacity utilization rates increases all algorithms provide better results.

Introduction

Supply chain management becomes one of the most important topics in manufacturing research with high customization of products and small volumes of job orders. Ayyıldız, Özçelik, and Demirci (2018) state that, in the current turbulent environment, manufacturing companies realized that the coordination among the customers, manufacturers, and distributors play a vital role in the supply chain management to provide sustainable service to their customers. With the increasing demand for customized products, emerging technologies have taken places in manufacturing and, thereby, new problems have arisen in different areas (Pei et al., 2014). One such an emerging technology is Additive Manufacturing (AM), which has been adapted to the production process as a response to rapidly changing customer demands. Therefore, further research on the application of AM technology in the multi-stage supply chain framework is necessary to make the management more customer-oriented (Özçelik & Gencer, 2018).

Because the impact of coordinated solutions on the performance of supply chain is important, the integrated scheduling problems considering all actors (e.g., customers and manufacturers) should be investigated in detail (Cevikcan et al., 2011, Pei et al., 2015).

In this study, we focus on an integrated job and vehicle scheduling problem in a two-stage supply chain. First, the parts are assigned to the jobs and processed together on the AM/3DP machines in a single manufacturer and, then, transported by the vehicles to multiple customers. In the production stage, the main aim is to increase the utilization rate of AM machine capacity that directly affects the total time spent to produce the parts. As the filling rate of AM machine increases, the total time for producing the parts is affected and, thereby, the time spent to produce a part shows a decrease. In order to reduce the total time spent for production, the assignment decisions of jobs to AM machines are made in the first stage followed by that the finished parts are distributed to the customers using a vehicle fleet in the transportation stage. While the production of a job is important in terms of “the value of place, presentation, and time”, the distribution of the same job is important regarding “the value of time” (Baudin, 2005, Durmusoglu et al., 2017).

Additive Manufacturing (AM), also known as 3D printing or rapid manufacturing, has attracted researchers from both academia and industry over the last few decades. It is described as the process of adding raw materials to produce physical objects from 3D modeling, typically layer upon layer. Because the AM is accepted as a complementary technology to the conventional subtractive manufacturing, it is considered the future of manufacturing with its distinctive features yielding resource efficiency, production flexibility, design optimization, direct kitting, waste elimination, competitiveness, and customized parts (Qiang et al., 2017; Mellor et al., 2014, Lyly-Yrjänäinen et al., 2016, Oh et al., 2018, Cooper et al., 2012). Because the AM/3DP brings aforementioned benefits to the industry, many large-sized enterprises are already implemented AM technology to their production process. Moreover, the number of small- and medium-sized enterprises seeking to benefit from AM technology is increasing day by day. An important aspect of AM technology is that it has the potential to positively affect the traditional supply chain by simplifying management (Khajavi, Partanen, & Holmström, 2014). With the distributed deployment of AM, the makespan decrease whilst the response rate increase thanks to high service quality and low inventory levels (Holmström et al., 2010, Pérès and Noyes, 2006). However, as indicated earlier, high capital investment and processing cost of AM machines make the centralized deployment, i.e., centralized production, more practical for today’s companies. (Khajavi et al., 2014). Therefore, when AM machines become cost-effective over time, the distributed deployment rate would increase (Thomas, 2016).

There are several types of AM methods used for prototyping of materials, namely fused deposition modeling, laminated object manufacturing, stereolithography, and selective laser sintering. In addition to these methods, laser engineered net shaping, electron beam melting and selective laser melting/direct metal laser sintering (SLM/DMLS) techniques are used for the direct part production (Qiang et al., 2017; Hopkinson, Hague, & Dickens, 2006). There are many examples of the use of AM methods; however, the main focus of this study is not to provide examples but to develop a comprehensive optimization model for the supply chain where SLM/DMLS technique is used in the production stage. The SLM/DMLS method is the most widely used one to produce metallic parts to meet the specific needs of customers. The aerospace and defense industry, which is one of the important application areas for the SLM/DMLS technique, has currently a 10% worldwide market share tending to increase dramatically over the next decade. On the other hand, the metal AM industry has been growing by 80% during the last 20 years (Li, Kucukkoc, & Zhang, 2017). The SLM/DMLS process is employed to produce lightweight parts for the aerospace industry where traditional manufacturing methods cannot be used efficiently due to lack of flexibility. For instance, NASA (National Aeronautics and Space Administration) has been trying to use AM technology in the International Space Station for quick response to the needs of astronauts during their mission.

The AM technology has been using for direct part manufacturing, i.e., rapid manufacturing, with the recent development in applications for customized products. An AM machine allows producing parts without inhibitions encountered in traditional manufacturing, such as design inflexibility, large batches, high inventory levels, longer lead times, complex supply chain (Cevikcan and Durmusoglu, 2011, Holmström et al., 2010, Romero and Vieira, 2015). In addition to the benefits provided by AM technology, it leads to a paradigm shift in enterprises towards to lean manufacturing principles by reducing the wastes in terms of resources, e.g., materials and movements. The ability to produce customized parts makes the AM an indispensable technology for the manufacturing companies. From the production planning perspective, AM technology is investigated by Li et al., 2017, Chergui et al., 2018. They provided a comprehensive study for the production processes of SLM/DMLS technique which is also investigated in this paper from the supply chain perspective. In this context, a supply chain scheduling problem is studied by focusing on the production and transportation stages to make the supply chain more responsive thanks to the AM technology. The addressed problem is described in detail in Section 3.

One of the most challenging issues in supply chain management is the need to provide a valuable service to the customers, while simultaneously reducing the completion time. The introduction of a new supply chain design with the AM technology offers a solution approach to overcome the dominant limitations that prevent makespan reduction. To this end, we focus on the centralized deployment approach for the two-stage supply chain by taking necessary actions to reduce the completion time. A new optimization model is developed with the makespan minimization objective. The SLM/DMLS technique is considered for the addressed problem, which arises from a startup in the aviation industry. Because the problem is proved to be strongly NP-hard, a heuristic procedure with five different selection rules is proposed by investigating the structural properties of the problem. Furthermore, computational experiments are performed to compare the selection rules employed in the heuristic procedure.

The noteworthy contributions of this study are outlined from different perspectives as follows.

  • From the theoretical perspective, the novel contribution of this study is to develop an optimization model that integrates the problems of two-stage supply chain scheduling and the production planning of AM machines. Several studies investigate the production planning problem in literature, see for example, Li et al., 2017, Chergui et al., 2018, Wang et al., 2019, Kucukkoc, 2019. These studies solely focused on the planning aspects of AM technology without considering the supply chain concept. In this environment, this study aims to define the addressed problem through the optimization model. Besides, several structural properties are presented to further explain the problem.

  • When the method is considered, a best-fit heuristic is proposed for the addressed problem. Five different selection rules, each of which corresponds to a distinct property of the problem, are also developed and used as an algorithm with the proposed heuristic procedure.

  • As for the managerial point of view, this study provides several managerial insights related to additive manufacturing within the context of the supply chain based on the research data. In this manner, it intends to be a stepping stone for the researchers and practitioners in the industry.

The rest of this paper is organized as follows. A comprehensive literature review on the two-stage supply chain scheduling and the AM technology is presented in Section 2. The problem statement and optimization model along with the main characteristics of the problem are provided in Section 3. The structural properties and the lower bound for the problem are presented in Section 4. The main heuristic procedure and selection rules employed for solving the problem are given systematically in Section 5. A computational study is designed and conducted in Section 6. Conclusions and future research directions are given in Section 7.

Section snippets

Literature review

The supply chain is affected by the implementation of AM from several aspects, such as personalization, transportation, design, capital investment, flexibility, relationship with the consumer, and collaborative relationships (De la Torre et al., 2016, Masood, 2014, Nuñez et al., 2019, Wagner and Walton, 2016). Because the main aim of this paper is to analyze the implementation of AM in the context of supply chain scheduling, the review explores both the two-stage supply chain scheduling and

Problem statement

This study explores the AM/3DP technology in the context of two-stage supply chain and aims to shorten makespan including the time spent on production and transportation stages. In this regard, a supply chain scheduling problem is analyzed by considering the production and transportation stages so that the demand can be fulfilled in less time and the supply chain can be more responsive.

The detailed description of the investigated problem is provided as follows:

  • (1)

    At the production stage, a set {P1

Structural properties and lower bound for the problem

In this section, the structural properties of the problem are investigated, which are used to develop the selection rules employed in the steps of the heuristic procedure thereafter. The lower bound equation is also presented to be used in the comparison analysis.

Lemma 1

There exist a schedule П = (j1, j2, j3,.., jf,.., jg,…,jJ) for the investigated problem, in which the solutions remain unchanged when: (1) positions of any two parts in the same job are exchanged, (2) positions of any two jobs (except

Heuristic procedure and selection rules

In this section, first a heuristic procedure and then five different selection rules are developed for solving the investigated problem. The structural properties of the problem are taken into consideration while developing the rules.

Each selection rule with the heuristic procedure is accepted to be a separate algorithm to compare them among each other.

Computational study and results

In this section, experiments are conducted to evaluate the performance of each selection rule employed in the BF heuristic procedure. The test results are obtained from (i) the developed optimization model solved in GAMS® 23.5/CPLEX 12.2 software for small-sized problem instances and (ii) the BF heuristic with selection rules coded in Matlab 2015a for large-sized problem instances. A personal computer with hardware of Intel® CoreTM i7-3630QM CPU and 16 GB memory is used to conduct experiments.

Conclusions and future research

Additive manufacturing is an emerging technology and being increasingly implemented in manufacturing systems. Because the AM technology has a considerable impact on the supply chain performance, solving tactical level problems play a vital role to improve system performance. However, we found that little research attention is paid to investigate such problems so far. The importance of these types of problems motivates us to fill this research gap in the literature. In this study, we investigate

Acknowledgement

I would like to express my sincere gratitude to Professor Panos M. Pardalos for sharing his guidance and wisdom on this study.

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