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We consider a single stock-point for a repairable item facing Markov modulated Poisson demand. Repair of failed parts may be expedited at an additional cost to receive a shorter lead time. Demand that cannot be filled immediately is backordered and penalized. The manager decides on the number of spare repairables to purchase and on the expediting policy. We characterize the optimal expediting policy using a Markov decision process formulation and provide closed-form necessary and sufficient conditions that determine whether the optimal policy is a type of threshold policy or a no-expediting policy. We derive further asymptotic results as demand fluctuates arbitrarily slowly. In this regime, the cost of this system can be written as a weighted average of costs for systems facing Poisson demand. These asymptotics are leveraged to show that approximating Markov modulated Poisson demand by stationary Poisson demand can lead to arbitrarily poor results. We propose two heuristics based on our analytical results, and numerical tests show good performance with an average optimality gap of 0.11% and 0.33% respectively. Naive heuristics that ignore demand fluctuations have an average optimality gaps of more than 11%. This shows that there is great value in leveraging knowledge about demand fluctuations in making repairable expediting and stocking decisions.
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... They are used in after-sales services and in maintaining operating systems and capital goods within most companies, which renders their management an important lever to improve the service to customers and to reduce costs (Al Hanbali & van der Heijden 2013, Sleptchenko et al. 2018, Topan et al. 2020. The management of repairable spare parts inventory systems is challenging since it consists not only in controlling the inventories used to satisfy demand triggered by planned and unplanned maintenance activities but also in managing the repair shops that repair the spare parts often with a limited capacity and replenish the inventory points (Tiemessen & Van Houtum 2013, Arts et al. 2016, Drent & Arts 2021. The management of such systems require integrated design and control decisions. ...
... With regard to the literature that considers that the stock point can be supplied by a dual sourcing including a repair expediting, we refer to the research by Arts et al. (2016) and Drent & Arts (2021). This research builds on the early work on dual source inventory systems developed by Moinzadeh & Schmidt (1991), Song & Zipkin (2009) among others. ...
... A review on the inventory control of such multiple supply systems is provided by Svoboda et al. (2021). Arts et al. (2016) analyse a dual sourcing spare parts inventory system with an expedited sourcing. They make the assumption of a Markov modulated Poisson process and relax the assumptions that the demand process is a stationary Poisson process (often considered in the literature). ...
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... Estimating the HMM parameters is quite In natural sciences, it is used to model birthrelated events (Leroux & Puterman, 1992) and photon arrivals (Burzykowski et al., 2003). It has found relevance in inventory management (Arts et al., 2016;Ghanmi, 2016), communication networks (Heffes & Lucantoni, 1986;Kawashima & Saito, 1990;Muscariello et al., 2005), and insurance (Asmussen, 1989;Guillou et al., 2013;Wei et al., 2010). The MMNPP, which is a non-homogeneous MMPP, has also farreaching impact in various scientific undertakings. ...
... For example, Song and Zipkin (2009) use a queuing network representation to perform a closed-form performance analysis of an inventory system with two supply sources facing Poisson demand under the dual-index policy. This technique is extended to evaluate multi-echelon inventory networks with dual sourcing (Drent and Arts, 2021), also used when demand is a Markov-modulated Poisson process in asymptotic regimes of interest (Arts et al., 2016). For networks with emergency shipments that depend on the state in a complicated way, an exact analysis has also been obtained in some cases (e.g., ...
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... Due to the development of sensing technology, insitu degradation data are further considered in maintenance scheduling, and a substantial amount of works have been done that enrich the arsenal of CBM models. See Arts et al. (2016), Khojandi et al. (2018), Abbou and Makis (2019), Bensoussan et al. (2020), Zhu et al. (2021), Li and Tomlin (2022), Wang (2022), Zhao et al. (2022), for examples, and de Jonge and Scarf (2020) for reviews. Several maintenance models are further developed for production systems by considering restricted time windows for production, potential short of raw materials, or finite inventory capacity for finished goods (Iravani andDuenyas 2002, Drozdowski et al. 2017). ...
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