برنامه زمانی برای نگهداری پیشگیرانه و جابه جایی درسیستم‌های قابل تعمیر و نگهداری با استفاده از برنامه نویسی دینامیک

This paper presents mathematical models and a solution approach to determine the optimal preventive maintenance schedules for a repairable and maintainable series system of components with an increasing rate of occurrence of failure (ROCOF). The maintenance planning horizon has been divided into discrete and equally-sized periods and in each period, three possible actions for each component (maintain it, replace it, or do nothing) have been considered. The optimal decisions for each component in each period are investigated such that the objectives and the requirements of the system can be achieved. In particular, the cases of minimizing total cost subject to a constraint on system reliability, and maximizing system reliability subject to a budgetary constraint on overall cost have been modeled. As the optimization methodology, dynamic programming combined with branch-and-bound method is utilized and the effectiveness of the approach is presented through the use of a numerical example. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.

Preventive maintenance is a broad term that includes a set of activities to improve the overall reliability and availability of a system. All types of systems, from conveyors to cars to overhead cranes, have prescribed maintenance schedules set forth by the manufacturer that aim to reduce the risk of system failure and total cost of maintaining the system. Preventive maintenance activities generally consist of inspection, cleaning, lubrication, adjustment, alignment, and/or replacement of sub-systems and sub-components that wear-out. Regardless of the specific system in question, preventive maintenance activities can be categorized in one of two ways, component maintenance or component replacement. An example of component maintenance would be maintaining proper air pressure in the tires of an automobile. Note that this activity changes the aging characteristics of the tires and, if done correctly, ultimately decreases their rate of occurrence of failure in the tires. An example of component replacement would be simply replacing one or more of the tires with new ones. Obviously, preventive maintenance involves a basic trade-off between the costs of conducting maintenance and replacement activities and the cost savings achieved by reducing the overall rate of occurrence of system failures. Designers of preventive maintenance schedules must weigh these individual costs in an attempt to minimize the overall cost of system operation. They may also be interested in maximizing the system reliability, subject to some sort of budgetary constraint. This paper presents mathematical models for planning preventive maintenance and replacement activities for a repairable and maintainable system with multiple components, each of which is subject to an increasing rate of occurrence of failure (ROCOF), also known as “deterioration”, over a discrete number of periods. In each period (which could be defined as an hour, a day, a week, a month, etc.) it is assumed that one of three distinct actions can be planned for each component in the system: (a) Do nothing – In this case, no action is to be taken on the component. This is often referred to as leaving a component in a state of “bad-as-old”, where the component of interest continues to age normally. (b) Maintenance – In this case the component is maintained, which places it into a state somewhere between “good-as-new” and “bad-as-old”. In this paper, the maintenance action reduces the effective age of the component by a stated percentage of its actual age. Because components subject to wear out experience an increasing ROCOF, this reduction in effective age results in a reduction in ROCOF as well. (c) Replacement – In this case, the component is to be replaced, immediately placing it in a state of “good-as-new”, i.e.., its age is effectively returned to time zero. The problem then becomes one of designing a sequence of actions (a), (b) or (c) for each component in the system for each period over the planning horizon such that overall costs are minimized or the reliability of the system is maximized. The motivation of this research comes from the complexity of finding optimal preventive maintenance policies in multi-component systems and the equipment replacement problem that have been separately studied so far. This research integrates the preventive maintenance optimization in the optimal reliability design area with the component replacement problem and employs a combination of dynamic programming and branch-and-bound method to find the global optimum solution. The organization of the paper is as follows: In Section 2, a brief review of existing literature in the various types of models and algorithms in preventive maintenance optimization and equipment replacement problem is presented and the contribution of the research is clarified. Section 3 presents the configuration of the system and formulation procedure of the optimization models. Section 4 provides the proposed optimization models and Section 5 presents a dynamic programming formulation of the optimization models and discuses the solution methodology to solve the proposed models. In Section 6, the developed models are applied to find the best preventive maintenance and replacement decisions of a numerical example to prove the effectiveness of the proposed model and the solution approach. Finally, Section 7 provides a conclusion of the research with summary and remarks.

In this paper, we present two non-linear mixed-integer optimization models for preventive maintenance and replacement scheduling of multi-component systems. These models seek to minimize the total cost subject to achieving some minimal reliability and maximize the total reliability of the system subject to a budgetary constraint. Such models should be useful to maintenance planners as they try to develop effective plans. While these results are promising, the complexity of the models will likely preclude solution of extremely large problems with hundreds of components and/or periods. In those cases, heuristic and metaheuristic solution procedures will be needed. Future work in this area is needed to investigate the use of heuristics, and metaheuristics, as well as techniques for estimating key model parameters, like the improvement factor, real large-scale systems. The developed models in this paper can be applied in a wide variety of industries such as semiconductor manufacturing, transportation, material handling, power generation, and healthcare systems. The developed models and solution methodology can be used to generate new preventive maintenance and replacement plans in complex systems even after unexpected failures occur. In such a situation, the original schedule should be updated and the new optimal schedule can be used over the remaining of the planning horizon. It can also be applied into condition-based simulation models as a real-time optimization procedure to refine and update maintenance plans during the simulation run. Prospective researchers can examine the effects of other constraints on system availability and demand for limited maintenance resources. In addition, more work is needed to apply more complex stochastic programming techniques for developing optimal preventive maintenance and replacement plans that better account for the stochastic nature of the problem.