تعمیر و نگهداری مشترک و سیستم های بهینه سازی موجودی : یک بررسی

During the past decades, several joint maintenance and inventory optimization systems have been studied in literature. Compared to the sequential optimization of both models, Kabir and Al-Olayan (1996) reported a remarkable influence on total cost due to their joint optimization method. This review focuses on models that include cost and optimization parameters related to both maintenance and inventory. The purpose of this paper is to review the pertinent literature on joint maintenance and inventory optimization models for non-repairable parts and suggest possible gaps. A classification based on the following seven sets of criteria is made: inventory policies, maintenance characteristics, delays, multi-echelon networks, single-unit versus multi-unit systems, objective function and optimization techniques.

The main reason a company keeps an inventory of spare parts is to perform maintenance in order to restore the system in such a way that it can perform its intended function. The number of spare parts in inventory is determined by the demand, caused by corrective as well as preventive maintenance, for each spare part. Maintenance relies on the availability of spare parts in order to reduce failure downtime and costs. It is clear that maintenance and inventory management are strongly interconnected and should both be considered simultaneously when optimizing a company's operations. During the past decades, several joint maintenance and inventory optimization systems have been studied in literature. Compared to the sequential optimization of both models, Kabir and Al-Olayan (1996) reported a remarkable improvement on total cost due to their joint optimization method. Several reasons can be found for this cost reduction. On the one hand, maintenance models often rely on the assumption of an inexhaustible number of available spare parts (e.g. Barlow and Hunter, 1960) and on the assumption that these are available without any lead time (Dohi et al., 1998). These assumptions are not always realistic and it would be too expensive for a company to sustain such a system. On the other hand, the unilateral focus on the inventory policy might result in higher costs for maintenance (Acharya et al., 1986). The joint optimization of spare parts and maintenance takes into account the trade-off between maintenance and inventory policies. This review focuses on papers that include costs (e.g. inventory and maintenance costs) and optimization parameters (e.g. ordering time, replacement time, etc.) related to both maintenance and inventory management. As far as the authors of this paper are aware, this is the first review paper on joint maintenance and inventory optimization taking into account both the costs and parameters related to maintenance and inventory. Another interesting review paper on the joint optimization of maintenance and inventory policies was written by Dohi et al. (1998), but in the end only inventory related costs were included in the models reviewed in their paper. Searching Web of Science and Google Scholar using the keywords ‘maintenance’, ‘inventory’, ‘replacement’ ‘joint’ and ‘ordering’ gave us the majority of the papers. The other papers were found by scanning the references and using the ‘cited by’ option. The scope of our paper is limited to models for non-repairables. If a non-repairable part breaks down, it is removed and replaced by a new part. These non-repairable parts are defined as a ‘unit’ throughout the entire paper. The reader interested in models for repairable spares is referred to e.g. Park and Park (1986); Chiang and Yuan (2001); Sarkar and Sarkar (2001) and de Smidt-Destombes et al. (2009). The purpose of this paper is to review the pertinent literature on joint maintenance and inventory models for non-repairables and to suggest possible gaps that could lead to interesting future work. A classification based on the following seven sets of criteria was made: inventory policies, maintenance characteristics, delays, multi-echelon networks, single-unit versus multi-unit systems, objective function and optimization techniques. Each of them is discussed in the second section. In the third section, the contribution of the existing papers is described. Finally, some major conclusions and ideas for future research are stated in the fourth section.

The classification of the existing literature according to the proposed framework of joint maintenance and inventory optimization models makes it possible to draw some major conclusions and suggest possible future work in this research area. The conclusions and future research are also subdivided based on the characteristics of the joint maintenance and inventory optimization models like described in this paper. 4.1. Inventory policy characteristics As can be concluded from Table 1, both periodic and continuous review policies are extensively investigated in the available literature. Both single-unit and multi-unit inventories are described as well in different publications. However, none of the reviewed joint optimization models consider obsolescence of spare parts, although this can have a major influence on inventory costs (Kennedy et al., 2002). 4.2. Maintenance characteristics The majority of the papers describe preventive maintenance policies (see Table 1, column II). However, only the most common preventive maintenance policies were examined, more specifically age-replacement and block-replacement policies. No papers seem to exist on the failure limit, repair limit and repair number counting policy. Moreover, only one paper (Elwany and Gebraeel, 2008) was published on predictive maintenance strategies which use prognostic information (i.e. remaining useful life) of components for optimizing the joint maintenance and inventory policy. All published papers consider the implementation of condition-based maintenance by taking into account the current level of degradation (i.e. control limit policy (CLP)), but no prediction of future degradation or prognostic information. This might be striking because of the increasing importance of predictive maintenance in industry. Furthermore, a reduction in spare parts and inventory cost is generally considered as one of the most important indirect benefits of a predictive maintenance strategy. Due to the available prognostic information, component replacement can be anticipated and spare parts can be ordered ‘just-in-time’. In the future, joint optimization of predictive maintenance and inventory should certainly be investigated more in detail in order to validate the impact of a predictive maintenance implementation and the use of prognostic information on the inventory costs. Only two papers (Armstrong and Atkins, 1998 and Nguyen and Bagajewicz, 2009) do not rely on the assumption of perfect maintenance or replacement, which makes the introduction of different degrees of maintenance into joint optimization models an opportunity for further investigation. 4.3. Logistics The downtime of the system might be influenced by several logistical delays. The production loss due to downtime of the system is certainly important to consider for bottleneck machines. Both constant and random lead times for spare parts are described in the reviewed publications. However, few papers take into account more specific time lags (e.g. response time of external technicians, failure diagnosis time). Although emergency orders are common in practice, few models take them into account. Another very interesting delay to include into the model is the mean time to corrective and preventive replacement/repair (Nosoohi and Hejazi, 2011). Although the use of a constant lead time in modeling is quite common, lead times in practice are (almost) never known exactly in advance, so one might want to use a statistical distribution to model these random lead times. Only a few papers take into account this randomness in their replenishment lead time (Table 1, Column III). Armstrong and Atkins (1998) and Sarker and Haque (2000) add a random replacement time. As maintenance actions are delayed until a labor resource is available, an implicit random technician response time is included in the models of Nguyen et al. (Nguyen and Bagajewicz, 2008, Nguyen and Bagajewicz, 2009 and Nguyen et al., 2008). Multi-echelon networks are not uncommon in industry. However, only one paper on joint maintenance and inventory was found that took into account the different echelons in a supply chain (Chen et al., 2006). Taking into account the interrelationship between the joint optimization problem (i.e. maintenance and inventory) and routing (e.g. mobile repairman) could be very interesting future work. Moreover, possibilities like outsourcing inventory and pooling are not considered in the available literature, although these are currently observed trends in inventory management (Kennedy et al., 2002). The effect of the recently arising concept of e-maintenance should be investigated, as the implementation of different e-maintenance concepts (e.g. remote maintenance, e-diagnostics, e-decision making) (Muller et al., 2008) will have a major impact on the joint maintenance and inventory models. By means of a collaborative environment, pertinent knowledge and intelligence become available at the right place and time, in order to facilitate reaching the best maintenance decisions. However, this knowledge should also be used to optimize the joint maintenance and inventory problem. Furthermore, new business models (e.g. product service systems (PSS)) (Meier et al., 2010) concerning maintenance and inventory management are arising fast in academics and industry. These new business models introduce a different problem environment and structure for optimizing joint maintenance and inventory systems and problems, as maintenance and inventory are controlled by an external company (i.e. the original equipment manufacturer (OEM)) rather than internally. The developed joint maintenance and inventory models should be adopted according to these current and future trends. 4.4. System characteristics Both single-unit and multi-unit systems are extensively studied in the reviewed literature as can be concluded from Table 1. None of these models, however, take into account multi-unit systems with non-identical or dependent units, units are always assumed to be independent and identically distributed. As a consequence, neither group maintenance nor opportunistic maintenance was investigated thus far. Future research should be on incorporating different levels of dependencies (structural, stochastic and economic) between units into the joint optimization models, like already done in several maintenance optimization models (Nicolai and Dekker, 2007). 4.5. Business objectives The objective taken into account in most of the joint optimization models is cost. In this cost function both maintenance and inventory related costs are defined. Armstrong and Atkins (1998) use an additional service constraint in their model, while Sergent et al. (2008) define an objective function to evaluate the risk of high costs. There are, however, other objectives that should or could be taken into account in certain business cases for both inventory (e.g. service levels) and maintenance (e.g. availability, reliability, maintainability and personnel management) management (Van Horenbeek et al., 2010). This makes multi-objective optimization for joint optimization models still an underexplored area of research. A possible opportunity where multi-objective optimization can be applied is in the models developed by Nguyen et al. (Nguyen and Bagajewicz, 2008, Nguyen and Bagajewicz, 2009 and Nguyen et al., 2008) which are applied to a chemical process plant (i.e. the “Tennessee Eastman plant” problem). As safety is a very important objective in chemical process plants, these models could be extended by for example incorporating safety as an objective in a multi-objective optimization problem. 4.6. Optimization techniques As a consequence of the complexity and the stochastic nature of the joint optimization problem, most papers base their research on simulation models or iterative solution procedures. Exact solutions are developed for relative simple models (e.g. single machine or single inventory systems). Moreover, some research on simulation in combination with alternative, more sophisticated, optimization techniques (e.g. genetic algorithms, simulated annealing) might further decrease the computational effort and provide superior results. Also some research on multi-objective optimization models (Section 4.5) including e.g. both availability and costs would be very interesting and valuable. In general, most papers on joint maintenance and inventory optimization are situated on the tactical level of decision making, although maintenance and inventory also have major strategic implications for a company. Papers focusing on joint optimization of maintenance and inventory with strategic implications deal with the choice between different maintenance policies (e.g. preventive maintenance and corrective maintenance) (Sergent et al., 2008), and the combination of these maintenance strategies with different inventory policies (Armstrong and Atkins, 1996). Nevertheless, papers on the strategic implications of joint maintenance and inventory models are scarce, and further research is necessary. It can be concluded that the joint optimization of inventory and maintenance seems to be beneficial compared to separate optimization. However, several aspects are still ill-researched, which are extensively outlined in this paper. Finally, a similar review paper on joint optimization including repairable spares would be very interesting.