بهینه سازی برنامه زمانبندی تعمیر و نگهداری پیشگیرانه و حجم زیاد تولید

In this research, a developed mathematical model is proposed to optimize the preventive maintenance age and lot size for a single-unit production system producing a single item. The system is assumed to start in an in-control state producing items of acceptable quality and then after a period of production time the system may shift to an out-of-control state producing non-conforming items. The time for the system to shift is a random variable that is assumed to follow a general probability distribution. It is assumed that failure may occur at any time after the system shift to the out-of-control state. The system failure time is also assumed to follow a general probability distribution. The proposed model considers average total values of the maintenance, inventory holding, non-conforming items, and shortage costs. The results found indicated that the introduction of failure possibility decreased the production lot size for a specific preventive maintenance age. Sensitivity analysis is carried out to assess the effect of four cost parameters on model performance. Furthermore, the model is extended to consider the effects of: combining inspection with preventive maintenance; and introducing non-negligible preventive maintenance duration.

Maintenance accounts for a huge share of manpower and capital in every industrial firm. Nowadays, with the financial crisis attacking every industry, the importance of maintenance being effective and efficient is one of the top priorities for any firm. This can be achieved through proper maintenance management. One way of “managing maintenance” is through maintenance optimization models. Dekker (1996) reviewed and analyzed the subject of maintenance optimization models extensively. He tried to answer the questions of whether there has been a value of maintenance optimization models to maintenance management or not, how often these models have been applied successfully and in what sense. Lee and Rosenblatt (1987) addressed the problem of joint control of production cycles or manufacturing quantities and maintenance by inspection. They solved the problem of simultaneous determination of economic manufacturing quantity (EMQ) and the inspection schedule using an approximation to the cost function. The developed model is the first to address the problem of joint optimization of production lot size and maintenance. Ben-Daya and Makhdoum (1998) investigated the effect of various preventive maintenance policies on the joint optimization of the economic production quantity (EPQ) or economic manufacturing quantity (EMQ), the economic design of control charts, and the preventive maintenance level. They assumed that the level of the preventive maintenance activities reduces proportionally the shift rate to the out-of-control state. They found that performing preventive maintenance will always yield to reductions in the quality control costs. Ben-Daya and Hariga (2000) developed a mathematical model representing the effects of imperfect production processes on the economic lot scheduling problem (ELSP). The mathematical model is developed for ELSP taking into account the effect of imperfect quality and process restoration. They have showed that by using the developed model to solve for ELSP, the expected quality cost can be reduced by more than 50%. Chelbi and Ait-Kadi (2004) developed a mathematical model considering buffer stock size and preventive maintenance schedule of a production system with randomly failing production unit submitted to regular preventive maintenance. The optimum values of the decision variables, namely, buffer size and preventive maintenance schedule, are obtained by trading off the maintenance cost, the inventory holding cost, and the shortage cost such as their sum is minimized. Chakraborty et al. (2009) developed integrated production, inventory and maintenance models of a deteriorating production system in which the production facility may not only shift from an in-control state to an out-of-control state but also may break down at any random point in a production run. They assumed that in case of machine breakdown, production of the interrupted lot is aborted and a new production lot is started when the on-hand inventory is depleted after corrective repair. Chelbi et al. (2008) proposed and modeled an integrated production–maintenance strategy for unreliable production systems producing conforming and non-conforming items. In order to reduce the probability to shift to the out-of-control state, the system is subjected to age-based preventive maintenance strategy. When a shift to the out-of-control state is detected, a restoration action of the system is performed after a preparation period. While being in the out-of-control state, all the non-conforming items produced are rejected. The production cycle ends at the end of the preparation period. The authors assumed that failure may never occur during the preparation period. They focused on finding simultaneously the optimal values of the lot size and the age at which preventive maintenance should be performed. Maddah et al. (2010) developed two models to determine expected cost and optimal lot size. In one model, it was assumed that imperfect quality items were removed from inventory at no cost. Whereas, the second model assumed that batches of imperfect quality were consolidated and shipped together due to economies of sale in shipping. Pineyro and Viera (2010) investigated a lot-sizing problem with different demand streams for new and remanufactured items. They provided a mathematical model for the problem which proved to be NP-hard, even under particular cost structures. Aiming at a near optimal solution of the problem, a Tabu-search-based procedure was developed and evaluated. Rezaei and Davoodi (2011) presented two multi-objective mixed integer non-linear models for multi-period lot-sizing problems involving multiple products and multiple suppliers. Each model was based on three objective functions (cost, quality, and service level) and a set of constraints. Hongyan and Meissner (2011) looked into the dynamic lot-sizing and resource competition problem of an industry consisting of multiple firms. They developed a capacity model combining the complexity of time-varying demand with cost functions and economies of scale arising from dynamic lot-sizing costs. The competition model was solved, and the existence of capacity equilibrium over the firms and associated optimal dynamic lot-sizing plan for each firm was established. Within the context of this paper, the objective is to simultaneously determine the optimal values of preventive maintenance schedule and lot size of a single-unit production system which may randomly shift to an out-of-control state under the assumption that failure may occur during the preparation period for its restoration.

This paper presents a mathematical model to optimize the preventive maintenance age (time at which preventive maintenance should be performed for an age-based preventive maintenance policy) and lot size for a single-unit production system producing a single item. The possibility of system failure during any time after the system shift to the out-of-control state is introduced. A numerical example found in literature is solved using the proposed model. The results obtained shows the same behavior as that reported in literature. However, a decrease in the total expected cost and an increase of optimal preventive maintenance age was noticed. The reason behind this change is due to the effect of having fewer inventories. The introduction of failure possibility increased the level of model realism which decreased the optimal preventive maintenance age. The results of the given example show that Scenario 2 produced low preventive maintenance age for minimum total cost compared with Scenario 1. The sensitivity analysis of the different cost parameters on model performance shows that the maintenance age is sensitive to the preventive maintenance cost and inventory holding cost, less sensitive to the shortage cost, and nearly insensitive to corrective maintenance cost. Introduction of periodic inspection resulted into an increase in the total cost without an effect on the preventive maintenance age, while the introduction of non-negligible preventive maintenance duration leads to a increase in its age. For future research it is recommended to investigate the effect of: variable durations of preventive maintenance; non-periodic inspections; and remaining inventory at the end of a restoration cycle (in case of no shortage).