Assessing cloud manufacturing applications using an optimally rectified FAHP approach

Cloud manufacturing (CMfg) is a manufacturing model for enabling ubiquitous, convenient, and real-time access to a shared pool of configurable manufacturing resources through the Internet [1]. CMfg aims to provision and release manufacturing resources rapidly with minimal management efforts or service provider interaction [2]. In the view of Fisher et al. [3], CMfg is able to show the most sustainable and robust manufacturing route, which highlights the importance of cross-organizational collaboration to CMfg. According to Chen [4], the benefits of CMfg reside in the following respects: cost savings, efficiency, additional data analysis capabilities, flexibility, and closer partner relationships.

Tao et al. [5] classified CMfg technologies into eight categories: underlying support, resource access, resource perception and processing, resource virtualization, resource servitization, service management, demand management, transaction management, user business management, and platform support. Various CMfg models have been proposed and applied to different stages of the manufacturing life cycle [6]. For example, a CMfg model was proposed by Laili et al. [7] for the product design stage, so that product designs and design knowledge could be easily shared online. In the production planning stage, Chen and Lin [8] established a CMfg system for distributing production simulation tasks among several cloud-based simulation services. To facilitate the mass production of a product, sensors and adapters were adopted to convert manufacturing resources into cloud resources [5], so that manufacturing resources could be shared to support factories without enough capacities. Among manufacturing resources, three-dimensional (3D) printers are especially easy to be put on clouds. Chen and Lin [9] used this feature to establish an agile and ubiquitous additive manufacturing system that distributed an order among several 3D printing facilities and arranged the transportation plan to pick up the printed pieces, which was the application of CMfg to both mass production and logistics. The scheduling of jobs in a CMfg system is a challenging task, because jobs are usually distributed in multiple facilities [7]. Laili et al. [7] proposed an energy-adaptive immune genetic algorithm to schedule jobs in a CMfg system for facilitating collaborative product design. Liu et al. [10] considered a multi-task scheduling problem under a CMfg environment, which was a very challenging topic since multiple tasks were to be sequenced across multiple factories. The computational complexity was doubled. To address this topic, they applied production simulation to create promising schedules instead of formulating an optimization model to find out the best schedule. Chen and Wang [11] proposed a branch-and-bound algorithm to minimize the cycle time for delivering a job in a 3D-printing-based CMfg system. A recent literature review on CMfg refers to Ghomi et al. [12].

Although CMfg has been a hot research topic since its emergence, it still faces the following difficulties before being widely applied in practice:

For these reasons, a systematic procedure for evaluating a CMfg application is needed so that factory managers can choose from several alternatives for investment. However, this issue has not been fully explored in the past. In contrast, only a few references considered the selection of machines or resources for specific CMfg applications [13, 14]. The motivation of this research is to fill this gap.

An optimally rectified fuzzy analytical hierarchy process (FAHP) (OR-FAHP) approach is proposed in this study. In the proposed methodology, FAHP [15, 16] is applied to rank the priorities of criteria for assessing the performance of a CMfg application. However, to address the inconsistency of the pairwise comparisons made by a decision maker (DM), the proposed methodology rectifies the fuzzy judgment matrix of the DM, thereby enhancing the reliability of the assessment results.

The OR-FAHP approach has been applied to assess 10 CMfg applications to illustrate its applicability. An existing method was also applied to assess these CMfg applications to make a comparison. The differences between the proposed methodology and some existing methods are summarized in Table 1.

The contribution of this study lies in the following aspects:

The remainder of this paper is organized as follows. Section Proposed methodology introduces the OR-FAHP approach. Ten CMfg applications were assessed using the proposed methodology to illustrate its applicability, as detailed in Sect. Assessing ten CMfg applications. Finally, Sect. Conclusions concludes this paper and provides some directions for future research.

The proposed methodology was applied to assess 10 CMfg applications. According to the survey by Oliveira et al. [29], the relative advantage (CF1), technology readiness (CF2), firm size (CF3), and cost savings (CF4) are factors critical to the adoption of CMfg technologies. For this reason, the priorities of the four critical factors were to be determined. After a series of pairwise comparisons, the following fuzzy judgment matrix was constructed:

The consistency of the pairwise comparisons was evaluated aswhich showed some inconsistency. As a result, the judgment matrix needed to be rectified. Lingo was adopted to build and optimize the Model PP of this problem on a PC with i7-7700 CPU 3.6 GHz and 8 GB RAM, as shown Fig. 2. ξ and σ were set to 0.2 and 1/3, respectively. A branch-and-bound algorithm was applied to solve the PP problem. The execution time was less than 1 s. The optimal solution wasorgiving \(Z^{*} = CR({\mathbf{A}}^{{\prime}} ) = 0.{053}\). The consistency of the fuzzy judgment matrix has been significantly enhanced after rectification. In addition, the pairwise comparison results were inconsistent before rectification, but became consistent after rectification. The cores of the fuzzy priorities of criteria determined using the proposed methodology were 0.080, 0.165, 0.127, and 0.628, respectively.

Subsequently, the value of σ was changed to 1/6. In this way, the rectified judgment matrix would be closer to the original one. The optimization result wasgiving \(Z^{*} = CR({\mathbf{A}}^{{\prime}} ) = 0.109\). The consistency was still considerably better than that of the original fuzzy judgment matrix, which revealed that even a very minor adjustment was helpful to the improvement of consistency.

A parametric analysis was also conducted to analyze the effect of ξ on the consistency that could be achieved. When the value of ξ increased, the rectifying flexibility became higher. Five values of ξ, from 0.1 to 0.5, have been tried. The results are summarized in Fig. 3. As expected, the CR that could be achieved improved with the increase in the value of ξ, and converged to about 0.048, which implied the limit of the proposed methodology.

The optimally rectified fuzzy judgment matrix was constructed according to Eqs. (59) and (60) as

The fuzzy maximal eigenvalue and the fuzzy priorities of the critical factors were derived using alpha-cut operations, and then were approximated with TFNs as.

\(\tilde{\lambda }_{\max }^{*}\) = (4.010, 4.143, 5.150).

\(\tilde{w}_{1}^{*}\) = (0.043, 0.080, 0.151).

\(\tilde{w}_{2}^{*}\) = (0.095, 0.165, 0.288).

\(\tilde{w}_{3}^{*}\) = (0.066, 0.127, 0.257).

\(\tilde{w}_{4}^{*}\) = (0.461, 0.628, 0.708).

Ten CMfg applications were evaluated. The contents of the CMfg applications are shown in Table 3. The most recent (after 2017) and most widely cited (according to Google Scholar) references are provided to support each CMfg application. The performances of the CMfg applications by considering the critical factors have been evaluated according to the rules depicted in Table 4 [29, 30].

The evaluation results are summarized in Table 5.

FWA was applied to derive the overall performance of each CMfg application by considering all the critical factors. The results are shown in Table 6.

The overall performance of each CMfg application was defuzzified using the center-of-gravity (COG) method. The results are summarized in Table 7.

The most preferable CMfg was “migrating management information systems to cloud-based services”, followed by “3D-printing-based ubiquitous manufacturing” and “capacity sharing via business-to-business electronic commerce system”. In contrast, the least preferable CMfg application was “cloud-based environment for customer-oriented product design”. It was noted that such results were dependent on the DM’s subjective judgment.

For comparison, the existing rectifying fuzzy geometric mean (FGM)-FWA method was also applied to the collected data, which rectified the fuzzy judgment matrix by adjusting the most influential element [53, 54]. As a result, the fuzzy judgment matrix changed togiving \(CR({\tilde{\mathbf{A}}}^{{\prime}} ) = (0,\;0.119,\;6.108)\), which was less consistent than that rectified using the proposed methodology. The fuzzy priorities of critical factors were derived as.

\(\tilde{w}_{1}^{*}\) = (0.040, 0.080, 0.201).

\(\tilde{w}_{2}^{*}\) = (0.082, 0.163, 0.329).

\(\tilde{w}_{3}^{*}\) = (0.070, 0.158, 0.345).

\(\tilde{w}_{4}^{*}\) = (0.354, 0.600, 0.759).

The overall performance of each CMfg application was evaluated using FWA, and then defuzzified using COG. The results are summasrized in Table 8. The most suitable CMfg application, “migrating management information systems to cloud-based services”, did not change. However, the ranking result was different from that generated using the proposed methodology [55‐88].

As a new paradigm of manufacturing, CMfg is expected to bring several benefits to a manufacturer. However, most existing CMfg studies were of experimental natures or only the illustration of conceptual ideas. In addition, the cost effectiveness of a CMfg system has rarely been evaluated. As a result, a manufacturer is not sure whether or how to adopt a CMfg application. To address this issue, the OR-FAHP approach was proposed in this study to assess and compare CMfg applications. The OR-FAHP approach was an extension of the conventional FAHP method by resolving the inconsistency problem. In the proposed methodology, a FNLP model was first formulated to optimize the consistency by rectifying the fuzzy judgment matrix. Compared with existing methods for the same purpose, the OR-FAHP approach was able to ensure the optimality of the solution, which guaranteed the correctness of the decision.

The OR-FAHP approach has been applied to assess and compare 10 CMfg applications. According to the experimental results,

Obviously, the objective of this study, comparing CMfg applications systematically, has been achieved. In addition, the OR-FAHP approach proposed in this study also successfully improved the consistency of the fuzzy judgment matrix by 39% without drastically changing the fuzzy judgment matrix.

Subsequently, the proposed methodology can be extended to deal with cases involving multiple DMs. In addition, the participants of a supply, design, or demand chain should choose CMfg applications that are compatible with those chosen by others. Further, a tailored algorithm can be designed to help solve the PP problem to improve the computational efficiency. These constitute some directions for future research.