Single-Machine Scheduling with Fixed Periodic Preventive Maintenance to Minimise the Total Weighted Completion Times

The single-machine scheduling problem with fixed periodic preventive maintenance, in which preventive maintenance is implemented periodically to maintain good machine operational status and decrease the cost caused by sudden machine failure, is studied in this paper. The adopted objective function is to minimise the total weighted completion time, which is representative of the minimisation of the global holding/inventory cost in the system. This problem is proven to be NP-hard; a position-based mixed integer programming model and an efficient heuristic algorithm with local improvement strategy are developed for the total weighted completion time problem. To evaluate the performances of the proposed heuristic algorithms, two new lower bounds are further developed. Computational experiments show that the proposed heuristic can rapidly achieve optimal results for small-sized problems and obtain near-optimal solutions with tight average relative percentage deviation for large-sized problems.

Joint design of control chart, production and maintenance policy for unreliable manufacturing systems

PurposeThe purpose of this study is to develop a joint production, maintenance and quality control strategy involving a periodic preventive maintenance policy.Design/methodology/approachThe proposed integrated policy is defined and modeled mathematically.FindingsThe paper focuses on finding simultaneously the optimal values of the preventive maintenance period, the buffer stock size, the sample size, the sampling interval and the control chart limits, such that the expected total cost per time unit is minimized.Practical implicationsThe paper attempts to integrate in a single model the three main aspects of any manufacturing system: production, maintenance and quality. The considered system consists of one machine subject to a degradation process that directly affects the quality of products. The process and product quality control is carried out using an “x-bar” control chart. In the proposed model, a preventive maintenance action is performed every α inspections of product quality in order to reduce the shift rate to the “out-of-control” state. A corrective maintenance action is undertaken once the control limits are exceeded. In order to palliate perturbations caused by the stopping of the machine to undergo maintenance actions, a buffer stock is built up to ensure the continuous supply of the subsequent machine. The main goal of this work is to develop a model that captures the underlying link between the preventive maintenance policy, the buffer stock size and the parameters of an “x-bar” control chart used to control the quality of the product. Numerical experiments and a study of the effects of the input parameters variation on the obtained results are performed.Originality/valueThe existing models that simultaneously consider maintenance, inventory and control charts consist of a condition-based maintenance (CBM) policy. Periodic preventive maintenance (PM) has not been considered in such models. The proposed integrated model is original, in that it links production through buffer stocks, quality through a control chart and maintenance through periodic preventive maintenance (different practical settings and modeling approach than when CBM is used). Hence, this paper addresses practical situations where, for economic or technical reasons, only systematic periodic preventive maintenance is possible.

Improved Approaches to Minimize the Makespan on Single-Machine Scheduling with Periodic Preventive Maintenance Activities

This paper addresses a single-machine scheduling problem with periodic preventive maintenance activities that are predeterministic so that the machine is not available all the time, and jobs have to be processed between two consecutive maintenance periods. We propose a mixed integer programming (MIP) model and two heuristics to minimize the makespan. With more constraints in our model, the model is more efficient than the recent model of Perez-Gonzalez and Framinan , and our model could solve problems with up to fifty jobs. Two heuristic algorithms, namely, H (MW) and H (LB∗), are also proposed, in which two bin-packing policies of the minimum waste and minimum lower bound are used, respectively. Furthermore, we also proposed an improvement procedure. The results showed that the heuristic H (MW) outperformed other heuristics of the paper, indicating that the bin-packing policy of the minimum waste is more effective than well-known ones such as full batch and best fit. Additionally, all the heuristic algorithms addressed in this paper combined with the improvement procedure could achieve a similar and high quality of solutions with a very tiny increase in computational expense.