Evaluation and optimization of the design schemes of reconfigurable machine tools based on multiple-attribute decision-making

Abstract

A reconfigurable manufacturing system is one designed for rapid change in its structure, to quickly adjust its production capacity and functionality within a part family. Aiming at the diversity, cost and complexity of reconfiguration design, a method for evaluating the design scheme of a reconfigurable machine tool based on VIKOR is proposed. The module similarity between a reconfigurable machine tool and a prototype machine tool is defined, and on this basis, three quantitative evaluation indicators are established as follows: the module chain similarity determines the difficulty, effort, time and efficiency of machine tool reconstruction; the module interface complexity determines the feasibility and complexity of the disassembly and assembly of the reconfiguration module; and the reconfiguration cost determines the economic advantages of reconfigurable machines relative to fixed-structure equipment. According to three indicators, a multi-attribute decision-making method based on VIKOR is used to evaluate, calculate and sort the design scheme set of the reconfigurable machine tool, and the optimal feasible solution is obtained. An example of the reconfiguration design of a machine tool is analysed to verify the validity and feasibility of the proposed method compared with the methods of simple average weighting and technique for order preference by similarity to an ideal solution.

Keywords

Reconfigurable machine tool multi-attribute decision-making design scheme evaluation optimization VIKOR

Introduction

A reconfigurable manufacturing system (RMS) is a new type of variable manufacturing system that can rapidly adjust the processes, functions and capabilities of manufacturing according to changes in market demand and system planning by rearranging, reusing and innovating components.¹ RMS integrates the advantages of flexible manufacturing systems and dedicated manufacturing systems.² It can realize the dynamic and flexible response of manufacturing systems to the market and also achieve lower production costs when taking into account production efficiency and product quality.^3,4

The RMS consists of one or more reconfigurable machine tools (RMTs), which are an important part of the RMS.⁵ The main goal of an RMT is to handle various changes in the product or parts to be machined. The use of mechanical, control, hydraulic/pneumatic and electrical modules can achieve rapid adaptability of the RMT. Therefore, the efficiency of a machine tool can be enhanced by the development of machine modules, which can be quickly assembled and disassembled.⁶

Some research on RMS has been carried out. Kurniadi and Ryu⁷ presented the importance of the integration of Internet of things (IoT) into RMS and the development of mathematical model to solve reconfiguration planning (RP) problems in order to save reconfiguration time, cost and effort. Abdi and Labib⁸ contributed an overall approach of grouping products into families based on operational similarities, when machines are still not identified. Scholz-Reiter et al.⁹ presented a novel approach of capacity control considering the potential of RMTs and substantiate the often disregarded potential of RMTs with simulation results. Shneor¹⁰ presented the design and implementation of modular machine subsystems that enables various machining processes on the same computer numerical control (CNC) vertical milling machine. Aguilar et al.¹¹ documented the design, refinement and implementation of an RMT that provides a flexible platform for turning and milling and demonstrates satisfactorily the reconfiguration characteristics of modularity, integrability and convertibility. Padayachee and Bright¹² focused on aspects of the mechanical design and the development of a control system that supported the modularity and reconfigurability of the mechanical platform and presented a modular electronic system that is characterized by a plug-and-play approach to control scalability. Son et al.¹³ described the development of a 3-degree-of-freedom (3-DOF) desktop RMT, and presented the conceptual design of a desktop RMT, which is capable of controlling the 3-DOF orientation of a spindle. Dhupia et al.¹⁴ considered an arch-type RMT that has been built to demonstrate the basic concepts of RMT design. Adamietz et al.¹⁵ presented the concept and the prototype realization of a novel reconfigurable small-footprint manufacturing system in a transportable container.

Modular design was studied as the main method for RMS reconstruction. Mpofu¹⁶ proposed a hierarchical classification mechanism for machine structures, these structures derive from module combinations where symbology is utilized to represent the machines and these symbols can be used in the configuration process. Bruzzone and D’Addona¹⁷ proposed a new modular, reconfigurable and scalable machining centre that is characterized by the possibility of modifying the machining capacity. Sibanda et al.¹⁸ presented a structured framework that will optimize the development process of a new reconfigurable guillotine shear and bending press machine to be used in sheet metal work. The framework provides a guide for designers and manufactures of sheet metal machines in developing the new machine. Xia et al.¹⁹ developed a solution framework for reconfigurable machining process planning and extend the concept of reconfigurable process planning to a concept of reconfigurable machining process planning which targets the process plan generation for a part family. Mpofu and Tlale²⁰ presented an effective method that uses multi-level fuzzy decisions to create dynamic optimal configurations of machine structures with respect to a given part geometry. Gadalla and Xue²¹ introduced an optimization approach for the design of an RMT based on evaluations to both the different machine configurations and the reconfiguration processes to change between machine configurations. Strasser et al.²² proposed an approach for an engineering support for RMS, especially for RMTs based on the holonic paradigm. Ashraf and Hasan²³ proposed a framework for configuration selection for a manufacturing flow line and demonstrated using non-dominated sorting genetic algorithm-II (NSGA-II). Huang et al.²⁴ proposed a dynamic complexity-based RMS reconfiguration point decision method to address the problem of how to identify the best time to implement reconfiguration for the RMS. Jiang et al.²⁵ introduced a Petri Net model-driven methodology for the development, validation and operation of a radio-frequency identification-enabled decentralized flexible manufacturing system.

Different methods of analysing, evaluating and optimizing RMS have also been proposed. Eguía et al.²⁶ proposed a novel data envelopment analysis approach to assess the technical efficiency of RMS by benchmarking the observed time allocation of the different system configurations and the inputs consumed and output produced in each of them. Mittal and Jain²⁷ focused on the performance measures and the way to find the best configuration for RMS among various performance measures like ramp-up time, cost, reliability, availability, lead time and reconfiguration time that affect the performance of the RMS. Liao and Lee²⁸ introduced a methodology for designing a reconfigurable prognostics platform which can be easily and effectively used to assess and predict the performance of machine tools. Lorenzer et al.²⁹ presented a software tool that allows the evaluation of the performance and conformance to requirements of machine structure variants at an early stage. Goyal et al.³⁰ presented a novel methodology to assess the responsiveness of an RMT through developing the operational capability and machine reconfigurability metrics. Youssef et al.³¹ provided a model for optimizing the capital cost of RMS configurations with multiple aspects using genetic algorithms. Yu et al.³² proposed an RMS formal model from the perspective of multi-agent systems, in order to describe, analyse and verify the reconfiguration of RMS.

The design schemes of the RMS need to be evaluated to obtain the best results. The evaluation involves the following two aspects: evaluation indicators and evaluation algorithms. Due to the criteria multiplicity and information uncertainty evaluations, the evaluation of machine tool design schemes has been examined to quantify the indicators and address the uncertainties in the evaluation process; furthermore, schemes have been evaluated, calculated, sorted and optimized. For this reason, a multi-attribute decision-making (MADM) method based on VIKOR for evaluating the reconfiguration schemes of a machine tool is proposed, and the best design proposal is obtained through the quantitative evaluation of three evaluation indicators including the module chain (MC) similarity, module interface complexity and reconfiguration cost.

Similarity between the reconfiguration module and the prototype module

According to the structural features and processing requirements of the parts to be processed, a variety of different process routes are planned to constitute a process plan set $P^{P} {p_{1}, p_{2}, \dots, p_{i}, \dots, p_{M}}, i = 1, 2, \dots, M$ . Each process plan $p_{i}$ contains different machining methods and other information, forming a processing step set $S_{i}^{P} {s_{i, 1}, s_{i 2}, \dots, s_{i, j}, \dots, s_{i, N}}, j = 1, 2, \dots, N$ . Each processing step $s_{i, j}$ corresponds to one or more modules in the prototype machine tool (PMT) and the RMT, forming a PM set $M_{i, j}^{P} {m_{i, j, 1}^{P}, m_{i, j, 2}^{P}, \dots, m_{i, j, k}^{P}, \dots, m_{i, j, U}^{P}}, k = 1, 2, \dots, U$ and an RM set $M_{i, j}^{R} {m_{i, j, 1}^{R}, m_{i, j, 2}^{R}, \dots, m_{i, j, k}^{R}, \dots, m_{i, j, U}^{R}}, l = 1, 2, \dots, V$ , respectively.

The similarity between reconfiguration module (RM) and prototype module (PM) shows the module utilization in the process of machine tool reconfiguration, including the similarities in layout, function, quantity and physics of the module. Layout similarity means that the layouts of RM and PM, such as the positional relationship, the connection mode and the arrangement mode, are similar. Functional similarity means that the functional properties of RM and PM, such as the machining speed and the acceleration, load and torque, are similar. The quantity similarity relationship refers to the similar relationship between the number of components in the RM and the PM, such as adding or deleting components in the module when modifying the module. Quantity similarity means that the number of internal parts of RM and PM is similar. Physical similarity means that the transfer mode of internal energy, information or material flows between RM and PM is similar.

The similarity features of RM and PM are denoted as a set $S^{M} {s_{1}^{M}, s_{2}^{M}, \dots, s_{i}^{M}, \dots, s_{R}^{M}}, i = 1, 2, \dots, R$ , and the weights are denoted as a set $W^{M} {w_{1}^{M}, w_{2}^{M}, \dots, w_{i}^{M}, \dots, w_{R}^{M}}, i = 1, 2, \dots, R$ , where the similar element j of the similar feature i is denoted as a set $E_{i}^{M} {e_{i, 1}^{M}, e_{i, 2}^{M}, \dots, e_{i, j}^{M}, \dots, e_{i, T}^{M}}, j = 1, 2, \dots, T$ , and the similarity coefficient of $e_{i, j}^{M}$ is denoted as $α_{i, j}^{M}$ . In similarity comparison, if the attribute values are the same, then $α_{i, j}^{M} = 1$ ; otherwise, $α_{i, j}^{M} = 0$ . The similarity $ε^{M}$ of RM and PM is calculated as equation (1)

ε^{M} = \frac{\sum_{i = 1}^{R} w_{i}^{M} \sum_{j = 1}^{T} α_{i, j}^{M}}{\sum_{i = 1}^{R} T}

(1)

where $\sum_{i = 1}^{R} w_{i}^{M} = 1$ , and $w_{i}^{M}$ can be obtained by various ways, such as the analytic hierarchy process (AHP) method,³³ an experience summary and an expert consultation.

Evaluation indicators of the RMT design scheme

The following three aspects in the reconfiguration evaluation should be considered: the degree of similarity between RMT and PMT, the complexity of the module interface and the cost of the reconfiguration.

MC similarity

The chain structure of machine tool modules to accomplish a certain function is defined as an MC. Assuming that $C^{R}$ and $C^{P}$ are the two MCs with the same function in RMT and PMT, respectively, and $M_{i}^{R}$ in $C^{R}$ and $M_{i}^{P}$ in $C^{P}$ are a pair of similar modules, while $ε_{i}^{M}$ is the similarity between $M_{i}^{R}$ and $M_{i}^{P}$ , then the similarity $ε^{C}$ between $C^{R}$ and $C^{P}$ is expressed as equation (2)

ε^{C} = \frac{\sum_{i = 1}^{N} w_{i}^{C} ε_{i}^{C}}{N}

(2)

where $\sum_{i = 1}^{N} w_{i}^{C} = 1$ , and the value of $w_{i}^{C}$ is similar to that of $w_{i}^{M}$ in equation (1).

The following three kinds of values exist for $ε^{C}$ :

When $ε^{C} = 1$ , the position and sequence of the modules in $C^{R}$ and $C^{P}$ are exactly the same.

When $0 < ε^{C} < 1$ , at least one pair of modules in $C^{R}$ and $C^{P}$ is similar.

When $ε^{C} = 0$ , no module in $C^{R}$ and $C^{P}$ is the same or similar.

Module interface complexity

Module interface complexity is an important indicator that affects the assembly and disassembly characteristics of RMT. Non-destructive methods should be adopted as far as possible for module disassembly in the reconfiguration process to increase the module reloading efficiency and reuse probability.

Entropy, as an effective concept for expressing the amount of information, can be used to measure the interface complexity between modules. In the assembly and disassembly process, the smaller the information entropy of the module interface complexity, the less the difficulty of the assembly and disassembly.

According to the assembly and disassembly characteristics of the module, an interface number relation matrix $R^{M}$ as shown in equation (3) is constructed, where element $N^{M} (p, q)$ represents the number of interfaces between module p and module q

R^{M} = [\begin{matrix} 0 & N^{M} (1, 2) & \dots & N^{M} (1, p) & \dots & N^{M} (1, V) \\ 0 & \dots & N^{M} (2, p) & \dots & N^{M} (2, V) \\ ⋱ & ⋮ & ⋮ & ⋮ \\ 0 & \dots & N^{M} (q, V) \\ ⋱ & ⋮ \\ 0 \end{matrix}]

(3)

According to the concept of information entropy, the module interface complexity relationship is defined as shown in equation (4)

\begin{matrix} I_{i} = - \frac{1}{2 V_{i}} e \sum_{p = 1}^{V_{i}} \sum_{q = p + 1}^{V_{i}} \sum_{r = 1}^{N^{M} (p, q)} μ (p, q, c) \ln \\ \sum_{p = 1}^{V_{i}} \sum_{q = p + 1}^{V_{i}} \sum_{r = 1}^{N^{M} (p, q)} μ (p, q, c) \end{matrix}

(4)

where $V_{i}$ is the total number of modules corresponding to process plan $P_{i}$ , and $μ (p, q, c)$ is the interaction coefficient of interface c between module p and module q.

Reconfiguration cost

The reconfiguration costs of a machine tool mainly include auxiliary costs, demand costs and module reconfiguration losses. Auxiliary costs include labour costs and resource costs, of which labour costs are used to disassemble and assemble modules in the process of machine reconfiguration, and resource costs are used for the purchase, rental and energy consumption of auxiliary tools needed for reconfiguration. Demand costs are used for module purchases, leases and other expenses resulting from production changes. Module reconfiguration losses refer to the value loss caused by damage to the module structure, performance and so on during the reconfiguration process.

The cost of the reconfiguration from $M_{i, j}^{P}$ to $M_{i, j}^{R}$ is denoted as $C_{i, j}^{P, R}$ , and the reconfiguration cost of the RMT $C_{i}$ corresponding to the process plan $P_{i}$ is shown in equation (5)

C_{i} = \sum_{j = 1}^{N} C_{i, j}^{P, R} = \sum_{j = 1}^{N} (A_{i} (j) + D_{i} (j) + G_{i} (j) / 1 + r)

(5)

where $A_{i} (j)$ , $D_{i} (j)$ and $G_{i} (j)$ are the auxiliary costs, demand costs and module recovery losses corresponding to processing steps $s_{i, j}$ in reconfiguration, respectively, and r is the discount rate for free cash flow.

$G_{i} (j)$ is calculated as shown in equation (6)

G_{i} (j) = \sum_{l = 1}^{K} ρ \cdot F_{l}^{i, j}

(6)

where K is the number of modules that need to be recovered when the module is damaged in the reconfiguration process corresponding to the process $s_{i, j}$ , $ρ$ is the module recovery loss factor, which is generally derived from experience, and $c_{i, j, l}^{P, R}$ is the module cost of the recoverable module l.

$r$ is calculated based on the expected discount rate equation (7)

\begin{matrix} E (r) = r_{f} + β [E (r_{m}) - r_{f}] \end{matrix}

(7)

where $E (r)$ is the expected discount rate, $r_{f}$ is the risk-free rate, $E (r_{m})$ is the expected market rate of return and β is the risk index used to measure the volatility of capital gains risk.

MADM evaluation of the RMT design scheme based on VIKOR

The evaluation of the RMT design scheme is a typical MADM problem. For the benefit of group evaluation, the VIKOR is used for evaluation, which provides the optimal ranking of alternatives with the characteristics of maximizing ‘group benefits’ and minimizing ‘individual regrets’ and performs evaluation optimization to obtain the optimal feasible solutions.^34,35

The decision-making algorithm of the RMT design scheme based on VIKOR is as follows:

Step 1. For decision alternatives $A_{1}, A_{2}, \dots, A_{m}$ , build a standardized decision matrix D based on evaluation attributes $X_{1}, X_{2}, \dots, X_{n}$ (such as MC similarity, interface complexity and reconfiguration cost) as in equation (8)

D = {[f_{ij}]}_{m \times 3} = {[\frac{x_{ij}}{\sqrt{\sum_{j = 1}^{n} x_{ij}^{2}}}]}_{m \times n}, i = 1, 2, \dots, m

(8)

where $x_{ij}$ is the evaluation value of the attribute j of scheme $A_{i}$ .

Step 2. Determine positive ideal solution $A^{+}$ and negative ideal solution $A^{-}$

\begin{matrix} A^{+} = {(max_{i} f_{ij} | j \in J), (min_{i} f_{ij} | j \in J') | i \in M} \\ = {f_{1}^{+}, f_{2}^{+}, \dots, f_{i}^{+}, \dots, f_{n}^{+}} \end{matrix}

(9)

\begin{matrix} A^{-} = {(min_{i} f_{ij} | j \in J), (max_{i} f_{ij} | j \in J') | i \in M} \\ = {f_{1}^{-}, f_{2}^{-}, \dots, f_{i}^{-}, \dots, f_{n}^{-}} \end{matrix}

(10)

where J is a profitable attribute set, and $J'$ is a cost attribute set. The indicators of plan $A^{+}$ are all the upper limit of the profitable indicator or the lower limit of the cost indicator, which is the most preferred plan; the indicator of plan $A^{-}$ is the lower limit of the benefit indicator or the upper limit of the cost indicator, which is the least preferred plan.

Profitable attributes are the MC similarity, and cost attributes are the interface complexity and reconfiguration cost.

Step 3. Calculate group benefit $S_{i}$ and individual regret $Q_{i}$

S_{i} = L_{i}^{p = 1} = \sum_{j = 1}^{n} [\frac{w_{j} (f_{j}^{+} - f_{ij})}{(f_{j}^{+} - f_{j}^{-})}]

(11)

Q_{i} = L_{i}^{p = \infty} = max_{j} w_{j} (f_{j}^{+} - f_{ij}) / (f_{j}^{+} - f_{j}^{-})

(12)

Equation (11) shows that when p is small (e.g. $p = 1$ ), emphasis is placed on maximizing group efficiency. As p increases, individual regrets gradually gain more attention; thus, $min_{i} S_{i}$ is used to maximize group interests. Equation (12) represents individual regret, and $min_{i} Q_{i}$ focuses on minimizing individual regrets.

Step 4. Calculate the comprehensive index $R_{i}$ generated by each scheme

R_{i} = v (S_{i} - S^{*}) / (S^{-} - S^{*}) + (1 - v) (Q_{i} - Q^{*}) / (Q^{-} - Q^{*})

(13)

where $S^{*} = min_{i} S_{i}$ , $S^{-} = max_{i} S_{i}$ , $Q^{*} = min_{i} Q_{i}$ and $Q^{-} = max_{i} Q_{i}$ . v is the coefficient of decision-making mechanism as follows: $v > 0.5$ indicates that the scheme is selected based on majority preferences, $v \approx 0.5$ indicates that the scheme is selected based on the equilibrium compromise and $v < 0.5$ indicates that the scheme is selected based on the decline. This article sets $v = 0.5$ in order to take into account the maximization of group benefits and the minimization of individual regrets.

Step 5. Sort the alternatives in ascending order of $R_{i}$ , $S_{i}$ and $Q_{i}$ and determine the compromise solution, where the solution that satisfies both C1 and C2 and in which $R_{i}$ is the minimum is the optimal solution.

C1 is an acceptable advantage

R ″ - R' \geq 1 / (m - 1)

(14)

where $R'$ and $R ″$ represent the values of R of the first and second schemes sorted by R, respectively, and m is the number of schemes. Equation (14) is a necessary condition for the first scheme to be significantly better than the second scheme, and the schemes are compared in turn when there are multiple schemes.

C2 is acceptable reliability.

After sorting according to R values, the value of S or Q of the first scheme must be better than that of the second scheme, and the schemes are compared in turn when there are multiple schemes.

If C1 and C2 cannot be satisfied at the same time, a compromise set is obtained. If the relationship between the first scheme and the second scheme only satisfies C2, both schemes are considered to be optimal schemes. If C1 is not satisfied between the first scheme and other schemes, and only C2 is satisfied, then these schemes are considered to be the optimal schemes close to the ideal scheme.

Case analysis

The PMT model is shown in Figure 1, and the part model is shown in Figure 2.

Figure 1.

PMT model.

Figure 2.

Part model.

Based on the module composition of the PMT and the machining feature of the part to be machined, five process plans are obtained for the part. The RM of each programme is shown in Table 1.

Table 1.

Modules for process plan.

Process plan	A1	A2	A3	A4	A5
Modules	Motor	Motor	Motor	Motor	Motor
	Rotary spindle head	Rotary spindle head	Turntable table	Turntable table	Turntable table
	Flat end mill	Flat end mill	Flat end mill	End mill	End mill
	Ball end mill	Ball end mill	Ball end mill	Cone cutter	Cone cutter
	Rib slide	Rib slide	Reversing mechanism	Turbine shaft	Gear mechanism
	Drill	Thread mechanism	Hydraulic support	Drill	Drill
	Boring cutter	Reamer	Boring cutter	Reamer	Boring cutter
	Reamer	Drill	Reamer	Boring cutter	Reamer

The MC similarity and interface complexity of the RMT are determined by the structure position and the connection mode of the modules. The risk-free interest rate of the reconfiguration cost is calculated using the 1-year fixed deposit interest rate of 3.5%, the risk factor is set to 1.5 according to the market prospect and the market return rate is expected to be 10%. The expected discount rate is

E [r (t)] = r {(t)}_{f} + β [E (r {(t)}_{m}) - r {(t)}_{f}] = 3.5 % + 1.5 \times [10 % - 3.5 %] = 13.25 %

The above five process schemes are evaluated according to the three evaluation criteria including the MC similarity, interface complexity and reconfiguration cost, and the obtained values are standardized as shown in Table 2.

Table 2.

Decision indicator attribute value after normalization.

Process plan	A1	A2	A3	A4	A5
Module chain similarity	0.601	0.392	0.383	0.482	0.326
Module interface complexity	0.438	0.564	0.483	0.436	0.259
Reconfiguration cost	0.446	0.531	0.319	0.406	0.502

The MC similarity is an efficiency index, and the interface complexity and the reconfiguration cost are cost indicators, which can be obtained according to Table 2.

The positive ideal solution $A^{+} = {0.601, 0.259, 0.319}$ , the negative ideal solution $A^{-} = {0.326, 0.564, 0.531}$ and the index weight vector given by the expert using the AHP is $W = {0.43, 0.25, 0.32}$ . The values of R, S and Q for each alternative are calculated according to equation (16), and the results are shown in Table 3.

Table 3.

Sorting algorithm-based VIKOR, $v = 0.5$ .

	R		S		Q
	Value	Order	Value	Order	Value	Order
A1	0.014	1	0.339	1	0.192	2
A2	0.788	4	0.896	5	0.326	3
A3	0.484	3	0.525	3	0.341	4
A4	0.110	2	0.462	2	0.186	1
A5	0.830	5	0.707	4	0.430	5

According to Table 3, $R_{1} < R_{4} < R_{3} < R_{2} < R_{5}$ , that is, the overall performance of scheme $A_{1}$ is the best. However, $(R_{4} - R_{1} = 0.096) < [1 / (5 - 1) = 0.25]$ means that $A_{1}$ cannot satisfy the acceptable advantage condition C1, and $S_{1} < S_{4}$ satisfies the reliability condition C2. Therefore, a compromise solution set ${A_{1}, A_{4}}$ is obtained according to the VIKOR evaluation criterion. The group benefit of $A_{1}$ is the greatest, but the individual regret is slightly insufficient; the individual regret of $A_{4}$ is the smallest, and the group benefit is second only to $A_{1}$ . Comprehensively comparing the two solutions, the gap between the advantages and of the two solutions is not obvious, so both are selected as the optimal solution.

To compare the effectiveness of the proposed method, simple average weighting (SAW) and technique for order preference by similarity to an ideal solution (TOPSIS) are used to evaluate the alternatives. SAW is a weighted linear combination or scoring technique, which is based on the weighted average and an evaluation score is measured by multiplying the normalized value of each criteria for the objectives with the importance of the criteria. The objectives could be ranked and objective with the highest score is selected as the preferred one.³⁶ TOPSIS is a method of compensatory aggregation that compares a set of alternatives by identifying weights for each criterion, normalizing scores for each criterion and calculating the geometric distance between each alternative and the ideal alternative, which is the best score in each criterion.³⁷ The details of the two methods mentioned above are not listed due to space limitations.

MC similarity, module interface complexity and reconfiguration cost are used as evaluation indicators in SAW, TOPSIS and the proposed method, and the same index weight vector $W = {0.43, 0.25, 0.32}$ given by the experts is used in the proposed method and TOPSIS. The comparison results of the three methods are shown in Table 4.

Table 4.

Comparison results of the proposed method, SAW and TOPSIS.

Process plan	Proposed method		SAW		TOPSIS
Process plan	Value	Rank	Value	Rank	Value	Rank
A1	0.014	1	0.375	1	0.368	1
A2	0.788	4	0.671	4	0.575	3
A3	0.484	3	0.523	3	0.579	4
A4	0.110	2	0.451	2	0.477	2
A5	0.830	5	0.712	5	0.846	5

SAW: simple average weighting; TOPSIS: technique for order preference by similarity to an ideal solution.

From Table 4, it can be seen that the ranking results obtained by the three methods are basically the same. Therefore, the proposed method is reasonable and feasible for evaluating the performance of the RMT reconstruction scheme. In addition, the decision value obtained by the proposed method is more distinct than the value obtained by SAW and TOPSIS, which can provide more accurate evaluation information for decision makers. This result is also consistent with the research conclusions of Opricovic and Tzeng.^38,39

However, it is also noteworthy that the coefficient of decision-making mechanism v in the proposed method plays an important role in the alternative ranking. Different values of v have a big impact on the results. There are other shortcomings in the article: (1) the main research object in this article is a serial machine tool, and the case of parallel and hybrid machine tools is not considered; (2) only a few key indicators are used for evaluation in this article, but in practice, a comprehensive and complete evaluation indicator system and a complete weight determination and evaluation algorithm are needed.

Conclusion

Aiming at the diversity of RMT design schemes, this article proposes a new method for the evaluation and optimization of reconfiguration schemes based on MADM. The method has the following characteristics:

The module similarity is defined and calculated according to the similarities in layout, function, quantity and physics of the module, to describe the module utilization in the process of machine tool reconfiguration.

The following three indicators are constructed for the reconfiguration evaluation of RMT design scheme: the MC similarity, the module interface complexity and the reconfiguration cost, and the quantitative calculation methods are also proposed.

The reconfiguration design schemes are evaluated using the multiple-attribute decision-making algorithm based on VIKOR that maximizes ‘group benefits’ and minimizes ‘individual regrets’ to obtain the best design scheme for RMT.

An example of the reconfiguration design of a machine tool is analysed to verify the validity and feasibility of the proposed method compared with the methods of SAW and TOPSIS.

Footnotes

Handling Editor: Michal Kuciej

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: The authors would like to thank the National Natural Science Foundation of China (Grant No. 51875515) for the support given to this research.

ORCID iD

Guodong Yi

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