A three-level particle swarm optimization with variable neighbourhood search algorithm for the production scheduling problem with mould maintenance
Introduction
Because of the special merits of plastics such as high strength, low price, light weight, and user-friendliness, plastics materials find extensive utilization in many industries and daily life [1]. Moreover, the plastics industry greatly contributes to the economy of many countries, such as the United States, through providing employment to a large number of people, and is regarded as the third largest manufacturing industry in the country [2]. The main process of converting plastics into products is by injection moulding, which needs both an injection machine and an injection mould. Since consumer demand for plastic products is reflected by the overall growth of plastics sales [2], more methods are being explored to improve the resource efficiency of the production process under new visions for the future, for example, the “smart factory” [3]. Furthermore, to realize production objectives and avoid production bottlenecks, production scheduling is planned in advance. A good production scheduling can ensure the efficient use of labour resources and guarantee a high machine utilization rate [4]. Many good algorithms are proposed for the scheduling problem [[5], [6], [7], [8]]. In most research studies on production scheduling, it is postulated that machines are always available throughout the whole production planning stage. However, in actual situations, this assumption may not be reasonable, because failure may occur at any time, making some machines unavailable for job processing [9]. So, machine maintenance planning is essential, and can enhance the reliability of the system. To maximize the system productivity, maintenance planning and production scheduling must be considered together, and be given the same importance level [10]. More and more scholars are paying attention to production scheduling with the machine maintenance problem, and different models which integrate production scheduling with machine maintenance planning have been built to optimize productivity by harmonizing both activities. However, only the machine maintenance is considered in traditional production scheduling with the resource maintenance problem and research on production scheduling with the mould maintenance problem is very limited. The injection mould is also a significant component in the plastics industry and the breakdowns caused by factors related to mould are even more than breakdowns caused by factors related to machine [11]. The plastics manufacturer needs to consider the condition of the mould to guarantee a good production efficiency. So the integrated problem with mould maintenance consideration should be given more attention.
Recently, a model [11] was built to integrate production scheduling with mould maintenance. Time-dependent deteriorating maintenance schemes for the machine and mould were used, and a joint scheduling strategy was proposed. This strategy decided production scheduling, machine maintenance, and mould maintenance simultaneously to minimize the overall makespan. The genetic algorithm (GA) approach was used to solve this problem. However, the maintenance planning found may not be the most appropriate one for the production scheduling, when production scheduling and resource maintenance planning are decided concurrently, since the local search ability of the genetic algorithm (GA) is limited. The mismatch between production scheduling and resource maintenance is underestimated, which may result in the low production efficiency. In addition, more efficient algorithms need to be found to improve the quality of the solutions.
To overcome the shortcomings of previous research and improve the overall production efficiency, this study proposes a problem decomposition mechanism to deal with the production scheduling with the mould maintenance (PS-MM) problem, and presents an effective and efficient hybrid metaheuristic algorithm: the TLPSO-VNS algorithm, which innovatively combines three-level particle swarm optimization (TLPSO) and variable neighbourhood search (VNS). Firstly, this integrated problem is divided into a basic production scheduling problem, a machine maintenance problem and a mould maintenance problem. To minimize the overall makespan, the production scheduling problem is considered first. The corresponding machine maintenance planning is decided after the production scheduling is determined. Once the production scheduling and machine maintenance are confirmed, the corresponding mould maintenance is determined. Every sub-problem is solved by one single particle swarm optimization (PSO) algorithm and these three PSOs are interrelated. Once good solutions are obtained by the three-level PSO (TLPSO), variable neighbourhood search (VNS) is applied to these solutions to conduct the local search. Seven types of neighbourhoods are designed, and they are changed systematically. The best solution is chosen as the final solution when all the processes finish. The proposed TLPSO-VNS algorithm is robust and can find high-quality solutions by effectively exchanging search intensification and diversification. To our knowledge, this algorithm is the first algorithm to hybridize TLPSO with VNS to solve the integrated problem, building on the advantages of these two individual metaheuristic components and overcoming the inherent limitations.
The reminder of this paper is organized as follows: Section 2 is a review of the literature on this topic, which provides an understanding of the previous research in this area, as well as providing a rationale for the choice of the topic in the present study. Section 3 restates the production scheduling with mould maintenance (PS-MM) problem. Section 4 proposes the TLPSO-VNS algorithm. Section 5 presents the computational results acquired and shows the superiority of the TLPSO-VNS algorithm. Section 6 provides the conclusions and suggestions for further research.
Section snippets
Literature review
Manufacturers are forced to improve their efficiency because of the growing expectation of customers and the fierce competition in the market. As one of the most vital elements in many industries, maintenance planning has an explicit effect on the improvement of the overall production performance [12]. Traditionally, production scheduling and preventive maintenance planning decisions are made independently although they are interdependent. Nowadays, more and more researchers are trying to
Problem description
The production scheduling with mould maintenance (PS-MM) problem was firstly proposed by Wong, Chan, and Chung [11]. It is a single-operation scheduling problem with identical parallel machines. In the practical plastics injection production system, each job has only one operation and workshop of the system contains more than one machine. The processing time for different machines is the same if the injection mould for the job could be installed properly on these machines. The details of the
Optimization methodology
The optimization algorithm, named the TLPSO-VNS algorithm, is introduced in this part. The overall algorithm structure is introduced firstly and includes two stages: the stage of swarm initialization and swarm improvement by TLPSO and the stage of swarm intensification via VNS. Since encoding and decoding of the particles are critical for the successful application of TLPSO, encoding and decoding of the particles are introduced before the details of the algorithm.
Numerical experiments
The main objective of the numerical experiments is to test the optimization performance of the proposed TLPSO-VNS algorithm. For a fair comparison, the maintenance scheme of the resources and three datasets generated by Wong, Chan, and Chung [11] are adopted. The sizes of these three problems are (3035), (40610) and (60915). The quality of the solutions produced by the proposed TLPSO-VNS algorithm will be verified by comparing the results obtained by GADG (Strategy 4) [11] and results
Conclusions
This paper proposes a new hybrid algorithm named the TLPSO-VNS algorithm for the production scheduling with the mould maintenance (PS-MM) problem, which combines the three-level particle swarm optimization (TLPSO) algorithm and variable neighbourhood search (VNS). Differing from the joint scheduling approach, this integrated problem is divided into three sub-problems: production scheduling problem, machine maintenance problem and mould maintenance problem. Three interrelated PSOs are used in
Conflicts of interest
None.
Acknowledgements
The work described in this paper was supported by The Natural Science Foundation of China (Grant No. 71971143, 71471158, 71571120); a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 15201414); a grant from the Research Committee of The Hong Kong Polytechnic University under student account code RUKH; Project of Guangdong Province Higher Vocational Colleges & Schools Pearl River Scholar Funded Scheme 2016.
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