Supporting Maintenance Scheduling: a case Study
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| 2. Literature Review According to Noemi M. Paz [4], the maintenance scheduling problem can be modeled as a job shop scheduling problem where • a job in the job shop problem is the maintenance work order to process • an equipment in the job shop problem is a maintenance worker [4]. In this section the adequate objective functions for maintenance tasks scheduling and scheduling approaches are reviewed. 2.1 Objective Function According to Pinedo [3], due dates, deadlines and periodicity are important parameters on preventive maintenance tasks. These parameters should be respected to guarantee a proper functioning of production lines. The objective functions most related with maintenance task delays and due dates are the minimization of maximum lateness (L max ), minimization of number of tardy tasks (U j ) and minimization of total tardiness (ΣT j ) [3,5]. The minimization of maximum lateness is equivalent to minimizing the worst case of the schedule and it is expressed by L max = max (C j – d j ), where C j is the completion time of task j and d j is the due date of task j (Fig. 1 a. The minimization of number of tardy tasks (U j ) is another objective function which represents the number of tasks that were done after due date. However, minimizing the number of tardy tasks can result in a schedule with high delay. The total tardiness measure is another performance measure related with the delay expressed by ΣT j = Σ max {C j – d j ; 0} (Fig. b. It considers the sum of tardiness of all scheduled tasks. However, if it is intended, different tasks may carry different priority weights, where the most critical tasks have the higher weights (w j ). Apart from the tardiness penalization, the earliness completion (E j ) of tasks can be also penalized. The representation of cost functions that consider earliness and tardiness penalties (E j + T j ) is presented in Fig. 1 (c. 2125 Patrícia Senra et al. / Procedia Manufacturing 11 ( 2017 ) 2123 – 2130 Fig. 1 -Graphic of due date related objectives (a) the lateness L j of job j; (b) the tardiness T j of job j and (c) cost function in practice [4]. 2.2 Scheduling approaches Ebrahimipour et al. [2] proposes a scheduling model of preventive maintenance tasks in a series-parallel manufacturing system composed of multiple production lines. The proposed model considers reliability of the production line, maintenance costs, failure and downtime of system as multiple objectives. In this approach, different thresholds for available manpower, spare part inventory and periods under maintenance were applied. The authors consider two types of maintenance activities adjustment and replacement. A mixed-integer nonlinear multi- objective model was proposed for this problem. Duffua and Al- Sultan [6] present one of the first mathematical formulation of the stochastic programming for scheduling maintenance personnel. It incorporates deterministic and stochastic contributions. Samhouri [7] presents an intelligent method of how to decide whether a particular item requires opportunistic maintenance or not and if so, how cost-effective this opportunity-based maintenance will be when compared to a probable future grounding. Opportunistic Maintenance is a systematic method of collecting, investigating, preplanning and publishing a set of proposed maintenance tasks and acting on them when there is an unscheduled failure or a repair opportunity. The objective function of the method focuses on the total cost of maintenance that includes the remaining life cost, downtime cost, unplanned downtime cost, risk cost, Hazard function, secondary damage cost due to failure and unit price per finished product or service unit. Manzini et al. [8] present a resource-constraints mixed integer programming model that minimizes the total cost function which includes spare parts contributions, the cost of execution of the preventive actions, the cost of additional repair activity in case of unplanned failure, the cost of personnel of the producer and/or the maintenance provider. This model can be applied to a short-term plan (e.g. weekly) of preventive actions and resources (spare parts, equipment and personnel) necessary to conduct maintenance tasks. Each approach presented in this section aims to address specific cases, once each case requires different specifications. However, all the presented approaches have the same concern, scheduling the maintenance tasks required to keep items in a specified condition, guaranteeing a proper performance of equipment. These approaches were tested with small size instances. Though, our real world instances are very large, which demands a tailored constructive algorithm to provide effective solutions in real time. In this paper an initial approach of a scheduling algorithm will be presented and discussed based on a small instance. In order to validate and to compare the results obtained with the constructive algorithm, the small instance was also solved by a mixed-integer linear programming (MILP). Through the application of a MILP model, it is possible to obtain optimal plans considering small instances. Download 305.56 Kb. Share with your friends:
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