A hybrid DBH-VNS for high-end equipment production scheduling with machine failures and preventive maintenance activities
Introduction
The high-end equipment is the advanced product of high value and plays an important role in national economy. High-end equipment manufacturing represents the high-tech, high-end value chain, and the core of industrial chain [1], [2], [3]. Typical high-end equipment includes basic industrial equipment, large ship, and rail transit equipment. The manufacture of such equipment requires enormous human and energy resources, and the manufacturing process involves high temperature and pressure or other extreme conditions. The deterioration of the production system leads to major hidden dangers and threatening personal safety. Classical production scheduling addressed problems of allocating available machines to process jobs and finding the optimal job sequence [4], [5], [6], [7], where machine failures and repairs are often ignored. Hence, high-end equipment production scheduling problem under deteriorating effect and maintenance planning is challenging and significant. For example, the compressor, an important device producing high-pressure air for cooling and drying of parts in high-end equipment production, may overheat during the production, which could result in the reduction of efficiency and safety. Therefore, some preventive maintenance activities are required to constantly adjust the machine to its normal condition [8], [9]. Even so, machine failures are evitable in the production and the repair work should be operated whenever a failure happens. Manufacturing enterprises must seriously deal with the problem of machine deterioration and machine maintenance to ensure production efficiency [10].
Numerous studies have attempted to solve scheduling problems under deteriorating effect. Mor and Mosheiov [11] considered a single deteriorating maintenance activity in the deteriorating job scheduling model. Pei et al. [12] investigated a scheduling model with deteriorating jobs, multiple job types, and setup times. Wang et al. [13] proposed a novel metaheuristic to solve a flowshop scheduling problem under deteriorating effect. Yin et al. [14] took potential machine disruptions into consideration and developed effective heuristics for scheduling deteriorating jobs. The integration of deteriorating effect in these papers makes the scheduling methods more reliable and efficient. The problem of deteriorating job scheduling is an important research topic, and it will be of great benefit in real-life manufacturing industries.
Failures of machines may happen during the production, and preventive maintenance can ensure the efficiency and safety of the production. Ma et al. [15] studied a maintenance scheduling problem with past-sequence-dependent delivery times. Lu et al. [16] investigated a single-machine scheduling problem with preventive maintenance activities and uncertain failures. Liu and Wang [17] developed an effective polynomial time algorithm to minimize the total completion times on an unrelated parallel-machine manufacturing system with maintenance consideration. Rustogi and Strusevich [18] integrated the time-dependent linear deterioration into a scheduling model where machines can be restored to a better state through maintenance activities. Some researchers considered optimizing production time and costs by choosing different maintenance levels. Duan et al. [19] studied selective maintenance scheduling problem under stochastic maintenance quality, and the objective is to minimize total cost under time constraints. Pandey et al. [20] introduced selective maintenance into the Multistate System with the objective of maximizing system reliability. Considering the stochastic shift of the machine state, Lai et al. [21] formulated emergency maintenance along with preventive maintenance and proposed several models to minimize the expected average cost. Similarly, Yildirim and Nezami [22] considered preventive maintenance and repair work in their scheduling model, and the objective is to minimize the total cost. Over a long production horizon, the maintenance activity is necessary. It is important to make joint decisions on production scheduling and maintenance planning to obtain an accurate solution of the optimization problem. Table 1 provides the comparison of literature on optimization problems with maintenance and repair. From Table 1, it is seen that the existing research cannot solve the considered integrated production and maintenance scheduling problem with the objective of minimizing makespan.
The high-end equipment manufacturing involves a large number of parts orders. Many researchers have introduced the order-based production into traditional scheduling models and developed a series of new approaches. Du et al. [23] discussed and studied a robust order scheduling problem in fashion industry. Lin et al. [24] studied a two-agent multi-facility order scheduling problem and proposed a particle swarm optimization as well as an opposite-based particle swarm optimization. Considering an order scheduling problem with different product types, Framinan and Perez-Gonzalez [25] developed a greedy search algorithm as well as a heuristic and validated them by comparison experiments. Wu et al. [26] solved a multi-machine order scheduling problem using the hybrid genetic algorithm and the particle swarm optimization algorithm.
The parallel-batch scheduling problem exists in many typical manufacturing procedures such as rolling [27] and burn-in operations [28]. Table 2 gives a review of papers related to this topic. From the above review, the parallel-batching scheduling problems have been investigated by many researchers. However, most of these studies discussed idealized production situation, specifically neglecting the deteriorating effect, order-based production, preventive maintenance, and repair work. The neglecting of important practical issues will make the obtained solution far from its real optimal point. Hence, multiple manufacturers parallel-batching scheduling, order-based production, and maintenance planning should be considered together with deteriorating effect in order to obtain the accurate schedule. The main contributions of this paper are as follows.
- (1)
Faced with the challenge in high-end equipment production, we propose an integrated order scheduling and maintenance planning model with position-based processing time, parallel-batching processing, and multiple manufacturers.
- (2)
For each order during the manufacturing, several useful lemmas and an optimal algorithm for scheduling jobs within the order are proposed.
- (3)
Under the case where orders have been assigned to manufacturers and sequenced, a dynamic programing algorithm is developed to schedule the preventive maintenance activities.
- (4)
Since the investigated problem is NP-hard, we propose a DBH-VNS to solve the problem. The performance of the DBH-VNS is validated by computational experiments.
The remainder of this paper is organized as follows. Section 2 gives a description of the problem and some important notations. In Section 3, we derive some useful lemmas and develop two heuristics to solve the problem under certain cases. A brief introduction of two metaheuristics is provided in Section 4. In Section 5, we propose the DBH-VNS metaheuristic. Section 6 presents the results of our computational experiments. Finally, Section 7 gives a conclusion to this paper and suggests some future research directions.
Section snippets
Notations and problems statement
The used notations throughout this paper and their definitions are presented in Table 3.
The high-end equipment manufacturing is usually order-oriented and includes various products in small numbers. To help manufacturing companies improve production efficiency and ensure a stable and orderly production process, we formulate an integrated maintenance planning and order-based production scheduling model. Fig. 1 shows the structure of the considered problem. There are orders to be processed by
Structural properties and schedule rules
In this section, we focus on the decisions (3), (4), and (5). The problems of job batching, batch sequencing, and maintenance planning are solved with the heuristic algorithm and the dynamic programming algorithm. We first study the problems of job batching and batch sequencing within each order. Some useful lemmas are derived and a schedule rule is proposed. Then, based on the optimal schedule results within each order, a dynamic programing algorithm is developed to make decisions on the
Brief introduction of black hole algorithm and variable neighborhood search
Black hole (BH) algorithm and variable neighborhood search (VNS) are two very effective metaheuristics. They are both easy to be implemented with little amount of computation. In recent years, they have been widely used in various optimization problem. For example, Nemati et al. [40] solved a discrete optimization problem in the power system with using BH. Azizipanah-Abarghooee et al. [41] investigated a scheduling problem in thermal power systems and developed a hybrid BH algorithm, which is
The DBH- VNS metaheuristic
For the proposed scheduling problem, we design a discrete encoding scheme. Also, the new solution updated scheme is developed. In the following of this section, the details of the proposed discrete black hole (DBH)-variable neighborhood search (VNS) algorithm are presented with the context of application to the investigated scheduling problem.
Computational experiments
In this section, we conduct computational experiments to validate the performance of the proposed DBH-VNS metaheuristic. We select a set of effective metaheuristics for comparisons, including BH [56], VNS [57], and VNS-TS [58]. The VNS and VNS-TS can be directly used to solve optimization problems under discrete coding. Though, the BH is proposed for solving optimization problems under continuous encoding. Thus, the BH [56] is modified based on the encoding strategy and population updated
Conclusions
We investigate an integrated problem of order scheduling and maintenance planning. In this problem, there are several orders to be processed by manufacturers, and each manufacturer has a single parallel-batching machine. Jobs within each order are processed on the machines and the job processing time is a general non-decreasing function of its position. The preventive maintenance can be performed between two orders to reset deterioration effect and reduce the number of failures. If a failure
Acknowledgments
This work was supported by the National Key Research and Development Program of China (2019YFB1705300), the Fundamental Research Funds for the Central Universities (Nos. JZ2020HGTB0035), the National Natural Science Foundation of China (Nos. 71871080, 71801071, 71922009, 71601065, 71690235, 71501058, 71601060), Innovative Research Groups of the National Natural Science Foundation of China (71521001), Anhui Province Natural Science Foundation (No. 1908085MG223), the Fundamental Research Funds
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