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Multi-factor integrated configuration model and three-layer hybrid optimization algorithm framework: turnkey project-oriented rapid manufacturing system configuration

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Abstract

In the context of increasingly prominent product personalization and customization trends, intelligent manufacturing-oriented turnkey projects can provide manufacturers with fast and convenient turnkey services for manufacturing systems. Their key characteristic is the transformation of the traditional design process into a configuration process. However, the scope of configuration resources in existing research is limited; the cost and time required for manufacturing system construction are overlooked; and the integration of the system layout configuration is rarely considered, making it difficult to meet the manufacturing system configuration requirements of turnkey projects. In response, this study establishes a multi-factor integrated rapid configuration model and proposes a solution method for manufacturing systems based on the requirements of turnkey projects. The configuration model considers the system construction cost and duration and the product manufacturing cost and duration, as optimization objectives. The differences in product feature-dividing schemes and configuration of processes, equipment, tools, fixtures, and layouts were considered simultaneously. The proposed model-solving method is a three-layer hybrid optimization algorithm framework with two optimization algorithm modules and an intermediate algorithm module. Four hybrid configuration algorithms are established based on non-dominated sorting genetic algorithm-III (NSGAIII), non-dominated sorting genetic algorithm-II (NSGAII), multi-objective simulated annealing (MOSA), multi-objective neighborhood search (MONS), and tabu search (TS). These algorithms are compared and validated through a hydraulic valve block production case, and the TS and NSGAIII (TS-NSGAIII) hybrid algorithm exhibits the best performance. This case demonstrates the effectiveness of the proposed model and solution method.

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Abbreviations

\(i\), \(j\), \(p\), \(m\), \(t\), \(f\) :

Indexes of the five-element combination, product machining feature, process type, equipment type, tool type, and fixture type

n :

Index of the selected equipment’s different type categories

\(w_{n}\) :

Index of the selected equipment of the n-th type category

\(l_{j}\), \(o_{j}\), \(e_{j}\) :

Indexes of the selected equipment, tool, and fixture for the j-th machining feature

\(b_{nks}\) :

Index of the s-th machining feature processed by the n-th type category of equipment using the k-th type category of tool

\(c_{nuv}\) :

Index of the v-th machining feature processed by the n-th type category of equipment using the u-th type category of fixture

\(a_{nr}\) :

Index of the r-th machining feature processed by the n-th type category of equipment

\(C_{{\text{B}}}\), \(T_{{\text{B}}}\), \(C_{{{\text{TP}}}}\), \(T_{{{\text{TP}}}}\) :

System construction cost, system construction duration, product manufacturing cost, and product manufacturing duration

\(C_{{{\text{TM}}}}\), \(C_{{{\text{TT}}}}\), \(C_{{{\text{TF}}}}\), \(C_{{{\text{TV}}}}\) :

Purchasing costs for equipment, tools, fixtures, and material transportation systems

\(C_{{{\text{MC}}}}\), \(C_{{{\text{TC}}}}\), \(C_{{{\text{FC}}}}\), \(C_{{{\text{VC}}}}\) :

Installation and commissioning costs of equipment, tools, fixtures, and material transportation systems

\(N_{{\text{J}}}\), \(N_{{\text{P}}}\), \(N_{{\text{M}}}\), \(N_{{\text{T}}}\), \(N_{{\text{N}}}\) :

Numbers of product processing features, process types, equipment types, tool types, and selected equipment’s different type categories

\(N_{{{\text{PR}}}}\), \(N_{{\text{L}}}\) :

Numbers of products to be processed and equipment stations in the workshop

\(R_{n}\) :

Number of the machining features processed by the n-th type category of equipment

\(H_{m}\), \(G_{m}\), \(g_{m}\), \(I_{m}\) :

The price, installation and commissioning cost, installation and commissioning time required, and available quantity of the m-th type of equipment

\(\varPhi_{t}\), \(\varphi_{t}\), \(\phi_{t}\) :

The price of the t-th type of tool, and the price and average service life of its consumable accessories

\(T_{{{\text{SH}}}}\), \(T_{{{\text{SI}}}}\), \(C_{{{\text{PM}}}}\), \(C_{{{\text{MH}}}}\) :

The time required for tool installation and accessory replacement, the per-unit time cost of tool installation or accessory replacement, and the total cost of tool accessory replacement

\(V_{f}\), \(W_{f}\), \(C_{{{\text{AZ}}}}\) :

The price and installation time required of the f-th type fixture, and the per-unit time fixture installation cost

\(C_{{{\text{SV}}}}\), \(C_{{{\text{SW}}}}\), \(T_{{{\text{VR}}}}\), \(T_{{{\text{VC}}}}\) :

The scale coefficient between the purchase price, installation and commissioning cost, and installation and commissioning time required of the material transportation system and the number of the processing equipment. The installation and commissioning duration of the material transportation system

\(K_{n}\), \(U_{n}\) :

Numbers of different tool and fixture type categories used by the n-th type category of equipment

\(\alpha_{nk}\), \(S_{nk}\) :

The purchase quantity of consumable accessories for the k-th type category of tool used by the n-th type category of equipment, and the number of machining features processed by the n-th type category of equipment using the k-th type category of tool

Z n :

The time required for the n-th type category of equipment from the beginning of system setup to the completion of equipment, tools, and fixtures’ installation and commissioning

\(D_{m}\), \(\varUpsilon_{t}\), \(O_{f}\), \(T_{{{\text{VD}}}}\) :

The delivery time required for the m-th type of equipment, the t-th type of tool, the f-th type of fixture, and the material transportation system

\(C_{{{\text{WJ}}}}\), \(C_{i}\), \(\rho_{i}\) :

Process operation cost. Processing cost and duration of the i-th five-element combination

\(C_{{{\text{MW}}}}\), \(C_{{{\text{JH}}}}\) :

Cost of equipment standby and tool change

\(\varOmega_{m}\), \(\psi_{m}\), \(\psi_{m}\) :

Per-unit time standby cost and average tool change cost and time required of the m-th type of equipment

\(C_{{{\text{WF}}}}\), \(C_{{{\text{ZJ}}}}\), \(\varTheta_{f}\) :

Total cost and per-unit time cost of workpiece clamping. Workpiece clamping time required for the f-th type of fixture

\(C_{{{\text{WT}}}}\), \(C_{{\text{D}}}\), \(T_{{\text{V}}}\), \(D_{{\text{S}}}\) :

Total cost, per-unit distance transportation cost, and average transportation speed of the material transportation system. Average material transportation distance for each product

\(C_{{{\text{RM}}}}\), \(C_{{{\text{PR}}}}\), \(C_{{{\text{PR1}}}}\), \(C_{{{\text{PR2}}}}\) :

Total cost and average per-piece cost of raw materials. Average per-piece cost of raw materials when using machining and 3D printing, respectively

\(\beta_{nr}\), \(\theta_{nr}\) :

Whether the tool needs to be changed before the r-th machining feature processed by the n-th type category of equipment, if yes, it is 1, otherwise it is 0 (when each equipment processes the first product and subsequent products, respectively)

λ j :

Whether it is necessary to clamp the workpiece before processing the j-th machining feature, if yes, it is 1, otherwise it is 0

µ m :

Whether the m-th type of equipment has multi-axis processing capability, if yes, it is 1, otherwise it is 0

d jqh :

The transportation distance between the q-th equipment selected for the j-th machining feature and the h-th equipment selected for the \((j + 1)\)-th machining feature. When the two equipment types are the same, \(d_{jqh} = 0\)

ω j :

The number of selected equipment for the j-th machining feature

\(T_{{\text{A}}}\), \(T_{{{\text{SP}}}}\) :

Production rhythm and manufacturing duration of a single product

Λ n :

Average processing time spent on the n-th type category of equipment (except for processing the first product)

\(J_{j}\), \(P_{p}\), \(M_{m}\), \(T_{t}\), \(F_{f}\) :

The j-th machining feature, the p-th type of process, the m-th type of equipment, the t-th type of tool, and the f-th type of fixture

\({\varvec{D}}_{i}\), \({\varvec{W}}\), \({\varvec{E}}\) :

Optional tool axis direction set for the i-th five-element combination, feasible solution space for the five-element combination, and reasonable solution space for equipment quantity configuration

\(N_{{{\text{IT}}1}}\), \(N_{{{\text{IT2}}}}\) :

The configuration algorithm’s overall maximum number of iterations, and the maximum number of iterations for the historically optimal population/solution set/solution that remains unchanged

\(T_{{{\text{SA}}}}\), \(L_{{{\text{SA}}}}\), \(K_{{{\text{SA}}}}\) :

The temperature, the number of perturbations at each temperature level, and the Boltzmann constant in the MOSA algorithm

\({Q}\), \({{Q}}_{{\text{R}}}\) :

The manufacturing system configuration solution set obtained from configuration algorithm, and the real Pareto solution set

\(I_{{{\text{PSN}}}}\), \(I_{{{\text{CT}}}}\), \(I_{{{\text{IGD}}}}\), \(I_{{{\text{DPO}}}}\), \(I_{{{\text{HV}}}}\) :

The number of Pareto front solutions, the program calculation duration, the average distance between the global Pareto solutions and each algorithm’s Pareto front, the proportion of each algorithm’s Pareto solutions that are not dominated by other algorithms’ solutions, and the hypervolume of the Pareto front

\(\delta\), \(\xi_{\eta }\) :

The Lebesgue measure, and the hypervolume consisting of the η-th Pareto solution

z j :

Index of the selected five-element combination for the j-th machining feature

N n :

Number of the selected the n-th type category of equipment

L jq :

Location of the q-th equipment selected for the j-th machining feature

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Acknowledgements

This work was supported by the National Key Research & Development Program of China (Grant No. 2017YFE0101400 , 2022YFE0114100).

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  1. School of Mechanical Engineering, Tongji University, Shanghai, 201804, People’s Republic of China

    Shu-Lian Xie, Feng Xue, Wei-Min Zhang, Jia-Wei Zhu & Zi-Wei Jia

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Xie, SL., Xue, F., Zhang, WM. et al. Multi-factor integrated configuration model and three-layer hybrid optimization algorithm framework: turnkey project-oriented rapid manufacturing system configuration. Adv. Manuf. (2024). https://doi.org/10.1007/s40436-023-00476-8

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