# A modified variable neighborhood search algorithm for manufacturer selection and order acceptance in distributed virtual manufacturing network

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## Abstract

In this paper, we investigate a manufacturer selection and composition problem for Distributed Virtual Manufacturing Network (DVMN) with order acceptance and scheduling of deteriorating jobs, where potential manufacturers include proprietary plants and outsourced co-manufacturers. In such a problem, at the beginning of planning horizon, a manufacturing company (MC) receives a series of order requests from its customers. Due to the limited production capacity, the MC is not able to fulfill all the orders requested by the customers on time. To satisfy the order demand as much as possible, one of the MC’s choices is to establish a collaborative manufacturing platform (i.e., DVMN) that leverages the advantages of a social manufacturing network to expand their production capabilities. However, the increase in production capacity does not mean that all orders from the customers are able to be accepted and produced. In fact, standing at the profit-maximizing point of view, the order requests that do not bring profits to the company need to be rejected at the beginning of planning horizon. For the accepted orders, the MC will produce a part of them by its plants in the DVMN, and the remaining orders will be outsourced to other co-manufacturers in the DVMN. Based on some structural properties, we develop a novel Reduced Variable Neighborhood Search (RVNS) algorithm incorporated multiple random mutations neighborhood structures (NSs-MRM) to determine the composition of the DVMN, and further determine which orders should be rejected, which accepted orders should be processed by the company-owned plants in the DVMN, and which accepted orders should be outsourced to the co-manufacturers in the DVMN. In particular, the processing sequence of the orders produced in the company-owned plants are also determined. Finally, a reasonable composition of the DVMN and corresponding order acceptance as well as order scheduling on each member of the DVMN are given. To evaluate the proposed algorithm, a series of computational experiments are conducted, and the experimental results show that the proposed algorithm outperforms other existing baseline algorithms in solving both small-scale and large-scale problem instances.

## Keywords

Variable neighborhood search algorithm Order acceptance Outsourcing selection Production scheduling Dynamic programming algorithm## Notes

### Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 71871080, 71601065, 71690235, 71501058, 71601060), and Innovative Research Groups of the National Natural Science Foundation of China (71521001), Anhui Province Natural Science Foundation (No. 1908085MG223), Base of Introducing Talents of Discipline to Universities for Optimization and Decision-making in the Manufacturing Process of Complex Product (111 project), the Project of Key Research Institute of Humanities and Social Science in University of Anhui Province, Open Research Fund Program of Key Laboratory of Process Optimization and Intelligent Decision-making (Hefei University of Technology), Ministry of Education.

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