ترکیب برنامه ریزی تولید و زمان بندی نگهداری پیشگیرانه غیر چرخه ای برای سیستم های چند حالتی
Integrating noncyclical preventive maintenance scheduling and production planning for a single machine
چکیده : این مقاله نگهداری و تعمیرات پیشگیرانه غیر دوره ای را با برنامه ریزی تولید تاکتیکی در سیستم های چند حالته ترکیب می کند. سیاست نگهداری و تعمیرات ، جایگزینی پیشگیرانه غیردوره ای را برای اجزای تجهیز و حداقل تعمیر (minimal repair) را در اجزای خراب شده ی تجهیز پیشنهاد می کند. این مدل موارد مناسبی را برای نگهداری و تعمیرات پیشگیرانه و تصمیمات مربوط به برنامه ریزی تولیدبه طور همزمان فراهم می کند. این مدل یک استراتژی اندازه انباشته و نگهداری و تعمیرات یکپارچه را تعیین می کند به گونه ای که مجموع هزینه های نگهداری و تعمیرات اصلاحی و پیشگیرانه، هزینه های راه اندازی، هزینه های نگهداری (Holding Cost)، هزینه های سفارش تحویل نشده و هزینه های تولید را کاهش می دهد و در عین حال تقاضا برای تمام محصولات را فراهم می کند. این مدل ابتدا با مقایسه نتایج تعدادی مسئله چند-محصولی که در بر گیرنده مسائل اندازه انباشته تولید است حل می شود. سپس، الگوریتم شبیه سازی تبرید (simulated annealing algorithm ) از طریق آزمایش های عددی برای مسائل عمده توسعه می یابد و نشان داده می شود.
کلمات کلیدی : نگهداری و تعمیرات پیشگیرانه – حداقل تعمیر – برنامه ریزی تولید – بهینه سازی
- چکیده انگلیسی
- مقدمه انگلیسی
- نتیجه گیری انگلیسی
This paper integrates noncyclical preventive maintenance with tactical production planning in multi-state systems. The maintenance policy suggests noncyclical preventive replacements of components, and minimal repair on failed components. The model gives simultaneously the appropriate instants for preventive maintenance, and production planning decisions. It determines an integrated lot-sizing and preventive maintenance strategy of the system that will minimize the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs, and production costs, while satisfying the demand for all products over the entire horizon. The model is first solved by comparing the results of several multi-products capacitated lot-sizing problems. Then, for large-size problems, a simulated annealing algorithm is developed and illustrated through numerical experiments.
Maintenance scheduling and production planning are two important activities which can significantly contribute to better business management in industry. These activities directly operate on the same resources and equipment. Due to the difference between maintenance and production purposes, their relationship has been considered as mutually in conflict, especially if the production and maintenance planning are done separately. According to Berrichi et al. , the conflicts may result in an unsatisfied demand in production, due to equipment unavailability if the production service does not respect the time needed for maintenance activities. Integration of maintenance and planning activities can avoid conflicts. In Aghezzaf et al.  and Chung et al. , the authors have shown the benefits of integrating maintenance and production planning. Communication and collaboration between the two departments are the main keys to doing successful planning in production systems. Much research related to integrated production and maintenance planning can be found in the literature, especially during the last few years. In these integrated models, it is considered that the beginning times of preventive maintenance (PM) tasks are decision variables, as well as production jobs, and both (maintenance and production) are jointly scheduled . Budai et al.  classified these problems into four categories: high level models, the economic manufacturing quantity models, models of production systems with buffers, and production/maintenance optimization models. In the last category, where our work is situated, many problems have been presented in the literature. Most of these models aim to optimize a combination of maintenance and/or production costs, production makespan or system availability (or unavailability). Berrichi et al.  suggested a model minimizing, simultaneously, the makespan for production and the system unavailability for systems with parallel machines. The model was solved by genetic algorithms. Berrichi et al.  improved the obtained results by using an ant colony algorithm. Ben Ali et al.  studied a job-shop scheduling problem under periodic unavailability periods for maintenance tasks. The problem was solved by developing an elitist multi-objective genetic algorithm minimizing makespan and total maintenance cost. Chung et al.  presented a model also optimizing the production makespan, with a reliability option based on the acceptability function for multi-factory networks. The maintenance strategy is suggested for both perfect and imperfect maintenance policies. A bi-objective optimization model minimizing simultaneously the production makespan and the system unavailability is considered by Moradi et al. , where production decisions assign the appropriate n jobs to m machines and maintenance decisions determine the instants of PM activities. Pan et al.  suggested an integrated scheduling model incorporating both production scheduling and preventive maintenance planning for a single machine in order to minimize the maximum weighted tardiness. Cassady and Kutangolu  and Sortrakul et al.  proposed an integrated maintenance planning and production scheduling model for a single machine minimizing the total weighted expected completion time to find the optimal PM actions and job sequence. Yu-Lan et al.  extended these researches where PM actions can be performed under flexible intervals (instead of equal intervals) which leads to more efficient solutions. Jin et al.  presented a model determining the optimal number of preventive maintenance activities in order to maximize the average profit under uncertain demand by using the financial “option” approach. A mathematical model for a single unit determining simultaneously the optimal value of lot size and the optimal preventive replacement interval with non-conformity constraints is suggested by Chelbi et al. . Hajej et al.  investigated stochastic production planning and the maintenance scheduling problem for a single product and a single machine production system with subcontracting constraints. Ashayeri et al.  proposed a model optimizing total maintenance and production costs in discrete multi-machine environment with deterministic demand. Weinstein and Chung  worked on an integrated production and maintenance planning model in a hierarchical environment, where decisions about maintenance and production planning are made in aggregate and disaggregate levels. Coudert et al.  used a multi-agent paradigm and fuzzy logic for a cooperative production/maintenance scheduling to avoid conflict. A simulation-based approach is presented by Benmansour et al.  for joint production and preventive maintenance planning for a failure-prone machine in just-in-time context. Aghezzaf et al.  proposed a mixed non-linear periodic maintenance and production planning model, and a mixed linear model for a general preventive maintenance and production planning problem. Both models are solved with an approximate algorithm based on Lagrangian decomposition. Najid et al.  extended these researches and suggested an integrated model where preventive maintenance actions are planned in time windows and demand shortage is allowed when capacity is not sufficient to meet all demand. A hierarchical general (non-cyclic) model is developed by Sitompul and Aghezzaf . The authors integrated preventive maintenance activities into the aggregate planning, while corrective maintenance and uncertainty due to machine breakdowns are tackled in the detailed level planning. All the above mentioned papers assume that the production system may experience only two performance levels (perfect functioning or complete failure). In a recent contribution , we presented an integrated production and cyclical PM planning model for multi-state systems. Unlike the existing papers, this contribution assumes that the production system may experience a range of performance levels from perfect functioning to complete failure, which is more realistic. In Fitouhi and Nourelfath , we have extended our previous work (i.e. Nourelfath et al. ) to noncyclical PM for a single machine. In Nourelfath and Châtelet , the authors have dealt with the integration of production, inventory and maintenance planning for a parallel system with dependent components. The present paper proposes an integrated model for noncyclical PM and tactical production planning for multi-state systems. The model suggests a maintenance policy for each component where maintenance actions can be carried out at the beginning or inside any production planning period. There are others existing papers dealing with joint optimization. In Levitin and Lisnianski , the authors formulated the joint redundancy and replacement schedule optimization problem generalized to multi-state system. In Levitin and Lisnianski , the authors considered a preventive maintenance optimization problem for multi-state systems, for which the reliability is defined as the ability to satisfy given production demand. The authors of Rosqvist et al.  presented a value-driven maintenance planning approach and applied it to approach to a production plant. In Vatn and Aven , the authors have shown the importance of linking maintenance and safety risks, and presented an approach to maintenance optimization where safety issues are important. The authors of Cowing et al.  presented a dynamic modeling of the trade-off between productivity and safety in critical engineering systems. In Vatn et al. , the authors presented an overall model for maintenance optimization. They developed an approach for identifying the optimal maintenance schedule for the components of a production system. Safety, health and environment objectives, maintenance costs and costs of lost production are all taken into account, and maintenance is thus optimized with respect to several objectives. Finally, in Nourelfath et al. , the authors have formulated a joint redundancy and imperfect preventive maintenance planning optimization model for seriesparallel multi-state degraded systems. A heuristic approach was also proposed to solve the formulated problem. This heuristic is based on a combination of space partitioning, genetic algorithms (GA) and tabu search (TS). After dividing the search space into a set of disjoint subsets, this approach uses GA to select the subspaces, and applies TS to each selected sub-space. Although the above cited papers deal with joint optimization, to the best of our knowledge, the present paper is the first to develop an integrated model for noncyclical PM and tactical production planning for multi-state systems. This new model will be first solved by comparing the results of several multi-product capacitated lot-sizing problems. Then, for large-size problems, a simulated annealing algorithm will be developed. Simulated Annealing (SA) has been applied to many production and maintenance planning problems. The SA performs in combinational optimization due to the use of analogous cooling operation for transforming a poor, unordered solution into an ordered and desirable solution, which can optimize the objective function . SA can contribute to solve large scale problems with good quality in a reasonable computing time . For the production planning research area, Teghem et al.  used SA algorithm in order to solve a mixed linear integer production planning for a book cover printing process. An adaptation of SA algorithms in project scheduling with limited resource was presented in Bouleimen and Lecocq . Loukil et al.  proposed a SA algorithm to solve a production scheduling problem for flexible job-shop with batch production and process constraints. Shan et al.  improved the efficiency of solution research for a production assembly sequence by combining GA and SA approaches. Tang  applied the SA approach for a lot sizing problem to determine the optimal binary lot-sizing matrix decision. In maintenance planning, Leou  used the SA combined with GA for solving a maintenance scheduling problem optimizing reliability and operation cost. In Raza and Al-Turki , the authors have shown, through a large scale comparative study, the efficiency and the performance of SA approach for a maintenance scheduling problem minimizing total makespan. These successful implementations of SA algorithms for production and maintenance planning problems have motivated the proposed SA approach to solve the formulated optimization problem when the studied examples are large. This paper is organized as follows. The next section presents the mathematical model, and its characteristics. Section 3 explains the maintenance policy, and methodology used to estimate the model parameters. An exhaustive search method and a simulated annealing approach are presented in Section 4 to solve the proposed integrated production and maintenance planning model. Numerical examples are presented in Section 5, which is solved with both solution methods. The proposed model is extended in Section 6. Finally, conclusions are given in Section 7.
In this paper, we presented an integrated model for production and general preventive maintenance planning for multi-state systems. For the production side, the model generates, for each product and each production planning period, the quantity of inventory, backorder, items to produce and also the instant of set-up. For the maintenance side, for each component, we proposed the instant of each preventive maintenance action which can be carried out during the production planning period. A Matrix based methodology was used in order to estimate model parameters such as system availability and the general capacity. The proposed model was solved by the ES method and SA. The exhaustive search method gives the optimal solution however, due to computing time and the high number of combinations, it can only be used for small production systems. The SA method reduces the solution time. It was also shown that the integration of acyclical maintenance and production planning improves the total production and maintenance costs. The paper discussed the merit of allowing preventive maintenance actions only at the beginning or inside the production planning period through a modified model and a numerical example. Future work will extend the model presented in this paper to deal with the case of systems containing dependent components.