تصمیمات بهینه تعمیر و نگهداری و جایگزین تحت تغییرات تکنولوژیکی با در نظر گرفتن موجودی قطعات یدکی

Classical spare parts inventory models assume that the same vintage of technology will be utilized throughout the planning horizon. However, asset replacement often occurs in the form of a new technology that renders existing spare parts inventories obsolete. This paper aims to study the impact of spare parts inventory on equipment maintenance and replacement decisions under technological change via a Markov decision process formulation. The replacement decision is complex in that one must decide with which technology available on the market to replace the current asset. Under technological change, it is shown that the do nothing and repair options have significantly more value as they allow waiting the appearance of even better technologies in the future.

Maintenance is a key for ensuring the efficient use of equipment as well as an efficient production process. Repetitive breakdowns or operating in bad condition may lead to lower product quality, increased energy consumption and reduced revenue. Therefore, the objective of maintenance is not simply to overcome failures, but also to predict and prevent revenue loss at the management level. Managers must analyze all relevant information to assess the profitability of equipment, give sound investment decisions, and consider possible cost saving. In particular, high spare parts inventory is one important factor in maintenance costs. Asset downtime may increase due to waiting time if necessary spare parts are not available due to poorly managed inventory levels. Hence, the consideration of the spare parts inventory problem is an essential task of managers. There has been intensive research to study the different aspects of spare parts inventory problems such as management issues, multi-echelon problems, age-based replacement, repairable spare parts, problems involving obsolescence, etc. A review of the spare parts inventory’s problems is presented in Kennedy et al. (2002). As the authors comment, spare parts inventories totally differ from other manufacturing inventories. Their function is to assist maintenance staff in keeping equipment in operating condition. The close relation between spare parts inventories and maintenance has been discussed in several articles. Kabir and Al-Olayan (1996) studies the joint-optimization of age-based replacement and spare parts inventory policy (s, S). Under a block replacement strategy, Vaughan (2005) utilizes dynamic programming to solve the spare parts ordering problem while Chelbi and Aït-Kadi (2001) and Saker and Haque (2000) present management policies for a manufacturing system, aiming to optimize jointly the maintenance strategy with continuous review spare items inventory. Chien (2009) and Sheu and Chien (2004) extend the problem by also studying minimal repair for minor failures while De Smidt-Destombes et al. (2006) considers repair capacity of degraded/failed units after they were replaced by spare parts. However, all of the above models are constructed on the assumption that the same vintage of technology will be utilized throughout the planning horizon. They do not take into account the appearance of new technology with performance improvement. This information is very important for managers who often confront the technology investment decision. They must weigh the benefits of utilizing the available equipment with their stock of spare parts and the revenues of investment in new technology. Nevertheless, there are few articles that take into account technological development in the spare parts inventory problem. They are generally based on the introduction of an economical loss when new technology appears by a cost of obsolescence. Kim et al. (1996) does not explicitly consider an obsolescence cost. They include it in the holding cost in a multi-echelon system. Cobbaert and Oudheusden (1996) develops models that can be seen as extensions of the EOQ formula for fast moving spare parts subject to sudden obsolescence risk. The authors examine the effects of obsolescence on costs under several different conditions: constant obsolescence risk and no shortages are allowed; varying obsolescence risk and no shortages are allowed and finally varying obsolescence risk with shortages. 7 parts inventory and maintenance strategy by considering a constant rate demand until the obsolescence time. On the end of the spectrum, models devoted to maintenance optimization involving technological change do not consider the spare part inventory impact (Borgonovo et al., 2000, Clavareau and Labeau, 2009a, Clavareau and Labeau, 2009b, Dogramaci and Fraiman, 2004, Hopp and Nair, 1994, Karsak and Tolga, 1998 and Mercier, 2008). This gap in the literature motivates us to develop an appropriate model to meet management’s requirements: optimization of maintenance cost while simultaneously updating information on technological development and considering the impact of spare parts inventory levels to make sound investment decisions. Our main objective is to examine how spare parts inventory levels will influence the replacement decision and also how much better a new technology must be in order to overcome the obsolescence of existing spare parts inventory. In order to focus on this objective, we do not consider spare parts management such as the inventory optimization problem and the potential repair of the spare parts. We formulate a discrete-time, non-stationary Markov decision process (MDP) to determine the optimal action plan. For modeling technological evolution, we combine the uncertain appearance model (wherein technology change is characterized by the uncertain arrival time of new technology) and the geometric model. The geometric model presented by Bethuyne (2002), Borgonovo et al. (2000), Karsak and Tolga (1998), Torpong and Smith (2003), Natali and Yatsenko, 2008b, Natali and Yatsenko, 2007, Natali and Yatsenko, 2008a and Natali and Yatsenko, 2008b is a model where geometric functions are utilized to characterize technology change, such as the maintenance/operation cost functions in vintage equipment or in time. Unlike these articles, we present technology change by the improvement of the expected deterioration rate and the expected profit function within a period. We also consider the non-stationary likelihood of new technology’s appearance over time. Thereby, we overcome the disadvantages of the geometric model proposed by Borgonovo et al. (2000). Recall Nair (1995), Nair (1997) also consider the non-stationary probability of the appearance of new technologies. However, their model is focused on the problem of capital investment decisions due to technological change rather than physical deterioration of equipment. To simplify its exposition, no salvage values are considered while we establish a reasonable salvage value function which is proportional to the current purchase price of the technology vintage, decreasing in the remaining lifetime and incurs an even greater reduction when it becomes obsolete due to new technology availability. The remainder of this paper is structured as follows. In Section 2, we present our mathematical formulation model and its assumptions. In Section 3, the performance of our model is discussed through numerical examples. Finally, conclusions and future work are discussed in Section 4.

In this paper, we proposed a model that takes into account the spare part inventory in the maintenance/replacement problem of a stochastically deteriorating system under technological change. It determines the maintenance/replacement strategy based on the parametric performance of the system and the technological environment. We have combined several aspects never seen before in the same model: equipment replacement, maintenance optimization, technological evolution, and spare parts inventory. However, the application of such model in practice remains difficult both for the characterization of many parameters presented and the integration of new hypotheses that would make a not solvable model. Through our numerical examples we have shown the influence of the spare parts inventory level and technological change on the maintenance/replacement strategy. In the non-obsolescence case, it is obvious that replacement is done only at low stock levels; on the contrary, at high stock levels, the maintenance options demonstrate their dominance. In the obsolescence case, the replacement option with new technology is motivated, but the trade-off between the benefits of utilizing spare parts in store and the revenues of investment in new technology is also considered. Therefore, replacement is not done when the stock level is in the interval that is determined by the parameters of the model. The better the technological improvement is the greater value the replacement option has. However, in the case of rapid technological change, the do nothing and repair options have significantly more value as they allow the appearance of even better technologies in the future. These findings can greatly aid equipment managers in their maintenance and replacement decisions. Some proposed assumptions can be seen as limitations of our model such as the expectation of purchase price and improvement of new technology. In fact, these can be stochastic and difficult to capture. An extension of our model could reflect the stochastic characteristics of these parameters. Furthermore, the stochastic efficiency of the imperfect maintenance action could also be included in our model or the non-stationary properties of the deterioration. The principal objective of this paper is to consider simultaneously the influences of technological evolution and spare parts levels on the optimal maintenance/replacement strategy. Thus we have simplified the inventory problem by assuming that spare parts stock cannot be replenished without purchasing a new asset and that the quantity of spare parts supplied is determined by the manufacturer. In further research, we could take into account the ability to replenish the current spare parts and also examine the optimal inventory policy.