The scheduling of maintenance. A resource-constraints mixed integer linear programming model☆
Introduction
Literature classifies maintenance planning and scheduling into two major categories: the scheduled maintenance (1) and the unscheduled maintenance (2). The second deals with emergency breakdowns. The first includes preventive and routine maintenance (1.1), and the scheduled overhauls and corrective maintenance (1.2). The unscheduled maintenance is stochastic in nature. According to Duffuaa and Al-Sultan (1999) “this stochastic nature makes maintenance scheduling a challenging problem”.
Many companies produce and distribute worldwide complex production systems and machines. They also offer several maintenance services that include spare parts management, preventive maintenance actions, corrective maintenance actions, warranty management, and training of personnel. Maintenance service is a strategic activity to have a high level of productivity, quality, safety, and reliability of production systems. Furthermore, this can be a very expensive and labor-intensive service but also an opportunity for economic returns by post-sale services. The cost of maintenance can be also significantly affected by logistics decisions, including the number and location of service providers and regional offices, the inventory management of spare parts, and the organization of maintenance crews.
This paper illustrates an original cost-based, reliability-based and capacity-constraints optimization model for the scheduling of the maintenance and repair tasks within a maintenance plan (i.e., task plan).
The maintenance tasks refer to the set of activities necessary to replace a component or a group of components subjected to wear and tear within a generic plant or machine. The group of maintenance tasks including all the repairing and/or replacing activities that a generic machine or a plant require over its own life-cycle is named task plan. Each task to be scheduled usually involve spare parts, personnel (e.g., local personnel or service providers’ operators), resources and equipment. The frequency of each task is generally determined by the failure rates (i.e., the curve of failure probability to the machine up time) of the most critical component of the task. The general rule complied by the maintenance service provider in presence of complex components is assuming a constant failure rate (i.e., Assumption 1) corresponding to the average value suggested by the machine vendor. This assumption is critical in the presence of mechanical and mechatronic components that are mostly diffused in the modern automatic machines. However, Assumption 1 is often necessary due to the large amount of parts and components involved simultaneously and physically connected. Another assumption that frequently follows the constant failure rate is the constant frequency to execute preventive maintenance tasks (i.e., Assumption 2).
Furthermore, the provider commonly executes the preventive task on a component after a time equal to the mean time to failure (MTTF) of the task/component from the previous action and/or replacement (Assumption 3).
Unfortunately, when applied to real instances, these assumptions are not consistent, especially in presence of parts subject to “aging”, e.g., “early wear out” components or “old age and rapid wear out” components (Manzini, Regattieri, Pham, & Ferrari, 2010). Furthermore, the parts and components of a production system, e.g., a packaging machine, are not “as good as new” items after repairing or a preventive action, even in case of the part replacement.
To find more concrete and realistic solutions and go beyond to the illustrated assumptions, this paper presents an original mixed integer linear programming (MILP) model for the determination of the maintenance schedule that minimizes the total cost associated to the task plan. These costs include the preventive maintenance contributions, the corrective contributions (the so-called unplanned costs), the spare parts management, and the labor accounted by the maintenance operators.
The task plan scheduling is the result of the assignment and sequencing of different preventive maintenance tasks to a set of available service orders. This set is usually known in advance and results from a deal between the supplier of maintenance service, i.e., the previously defined “service provider”, and the client which requires for the maintenance of its plant. The generic service order corresponds to a time bucket located on a specific calendar date. This is the reason we adopt the terms time bucket to indicate a service order of a finite capacity.
The client purchases a calendar of preventive maintenance time buckets, and the service provider has to assign maintenance tasks to these buckets, controlling the availability of the system and reducing costs to realize a profitable service. In other words, the aim of the provider is to minimize the total cost of maintenance while guaranteeing a standard level of availability (i.e., up time) of the production system.
The remainder of this paper is organized as follows. Section 2 presents a literature review on the scheduling of the preventive maintenance. Section 3 illustrates the proposed maintenance planning model. Section 4 presents a significant case study which inspired the development of the proposed model. A sensitivity analysis is conducted to demonstrate the effectiveness of the proposed planning model. Finally, Section 5 discusses the conclusions and further research.
Section snippets
Literature review
The literature presents many contributions to preventive maintenance and scheduling issues for production systems with a special focus on operations. In particular, management science and operational research frequently discuss scheduling and optimization problems, but few studies deal with reliability and maintenance engineering (Manzini et al., 2010, Regattieri et al., 2010).
Sherwin (2000) presents a review and a discussion of the main issues in maintenance management. He also attributes
Maintenance planning model
This model deals with the scheduling of maintenance actions in a planning period of time made of pre-defined set of time buckets. The previously defined client purchases a calendar of preventive maintenance time buckets and the provider schedules the maintenance action in according with this calendar.
The problem object of this study is the planning and scheduling of maintenance tasks in the available time buckets corresponding to a set of planned stop periods and preventive maintenance actions.
Case study
This section presents a real case study of scheduling preventive maintenance actions for complex packaging machines. We decided to illustrate this case in a what-if environment in order to demonstrate the effectiveness of the proposed model when subject to different system configurations and instance dimensions.
This case deals with the maintenance scheduling of maintenance service provider of a leading company that manufactures automatic packaging systems and machines located in different
Conclusions and further research
This paper presents an original cost-based and reliability-based MILP model for scheduling preventive tasks on complex machines subject to failure. In particular, a set of tasks are available, and for each task, there is a nominal frequency of execution according to the MTTF of the parts and components involved. The aim is to define the best schedule that minimizes the global cost of maintenance due to the planned, i.e., preventive, and corrective maintenance cost, in agreement with the
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This manuscript was processed by Area Editor Maged M. Dessouky.