Optimal maintenance and replacement decisions under technological change with consideration of spare parts inventories

Classical spare parts inventory models assume that the same vintage of technology will be utilized throughout the planning horizon. However, replacement often occurs in the form of a new technology. A consequence of such replacements is the rendering of existing spare parts inventories obsolete and the necessity to purchase a new set. This paper aims to study the impact of spare parts inventory on maintenance and replacement decisions under technological change. We model this problem as a Markov decision process where the decisions are made as a function of the state of the asset itself, the technological environment, and the current spare parts inventory. The actions available to the decision maker are to do nothing, imperfectly or perfectly maintain the system, or replace the asset. The replacement decision is complex in that one must be decide with which technology available on the market to replace the current asset. Under technological change, the do nothing and repair options have significantly more value as they allow for the appearance of even better technologies in the future. Our model yields policies that demonstrate how replacement and maintenance strategies should be adjusted due to considerations of technological evolution spare parts inventory levels. technology. Nevertheless, there are few articles that take into account the technological development in the spare parts inventory problem. Those that do are generally based on the introduction of an economical loss when new technology appears by a cost of obsolescence. [14] does not explicitly consider obsolete cost. They include it in the holding cost in a multi-echelon system. [7] 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, no shortages allowed; varying obsolescence risk, no shortages allowed and varying obsolescence risk, shortages allowed. However, they relax the interactive relation of spare parts inventory and maintenance strategy by considering a constant rate demand until the moment of obsolescence. On the end of the spectrum, models devoted to maintenance optimization involving technological change do not consider the spare part inventory impact [2, 5, 6, 9, 10, 12, 15]. 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 the technological development and considering the impact of spare parts inventory levels to make sound investment decisions. With such a model, we can examine how spare parts inventory levels will influence the replacement decision and how much better a new technology must be in order to overcome the obsolescence of existing spare parts inventory. We formulate a discrete-time, non-stationary Markov decision process (MDP) to determine the optimal action plan. To model the technological evolution, we combine the geometric model and uncertain apparition model of technology. The geometric technological evolution model is presented by [1, 2, 12, 21, 18, 19, 20]. They utilize the geometric model to form the 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. In addition, we also consider non-stationary likelihood of new technology’s apparition over time. Thereby, we overcome the disadvantages of the geometric model proposed by [2]. Recall [16, 17] also consider the non-stationary probability of the appearance of new technologies. But in their model, Nair focuses on the problem of capital investment decisions due to technological change rather than physical deterioration of equipment. To simplify its exposition, he also does not consider salvage values while we establish a reasonable salvage value function which is proportional to the purchase price of technology at that time, decreasing in the remaining lifetime and incurs an even greater reduction when it becomes obsolete due to new technology appearances. The remainder of this paper is structured as follows: In Section 2, we present our mathematical formulation model and its assumptions. Next, in Section 3, the performance of our model is discussed through numerical examples. Finally, conclusions and future work are discussed in Section 4. 2 MODEL AND ASSUMPTIONS 2.1 Problem Statement Consider a repairable asset which is accompanied by a cargo of n spare parts. They are utilized for the maintenance of the asset and are not sold separately in the market, i.e., we cannot replenish the spare parts store when it is empty. This is a common assumption for special spare parts because it can be difficult and costly to find original and compatible spare units. In making this assumption we de not consider the optimization of the inventory policy. Our primary goal is to study the impact of the spare parts inventory level on maintenance and replacement decisions under technological change rather than determining what should be the optimal order level/order quantity for the spare parts. The asset operates continuously from the new state X = 0 and is characterized by its expected deterioration rate. In the failure state, denoted m, the asset continues to operate but unprofitably. To reveal the deterioration and the spare parts inventory level, periodic inspections are performed. The interinspection interval, τ, defines the decision epochs. We assume that only one new technology can appear in a decision interval, τ. We introduce 1