Inventory management for spare parts can be understood by nature, as risk management. The risk and associated cost of not having a spare part available when needed has to be balanced against the inventory cost for holding the part (Hagmark and Pernu 2007). Inventory control is a crucial part of operations management. Stocking spare parts ties up large amount of capital but too low inventory may lead to poor customer service or very expensive emergency actions (Aronis et al 2004).
Maintaining spare part aircraft is more or less unthinkable for airlines because of the high capital cost. To keep the aircraft in operating condition airlines need to plan for spare parts provisioning (Subramaniam 1978). Demand prediction of spare parts is considered to be the most critical aspect in Inventory
Management (El-Haram et al 2000); while one of the most frequently given reasons for delays in maintenance activities is the unavailability of spare parts (Siddique and Choudhary 2009).
The underlying assumption about the characteristics of demand for spare parts is crucial for selecting the inventory model (Razi and Tarn 2003).
In this study demand for spare parts is assumed lumpy, i.e. there are periods with no demand at all, as well as periods with high demand, so that the re-order quantity can differ significantly. This pattern is confirmed during the field work discussed in Chapter 4.3.
For modeling the demand pattern different parametric distributions are applied.
Hadley and Whitin (1963), Gelders and Van Looy (1978) as well as Schultz (1987) suggest the Poisson distribution that expresses the probability of a number of events occurring within a fixed period of time while assuming that these events occur with a known average rate and independently of the time elapsed since the most recent occurrence. The compound Poisson distribution as the probability distribution of the sum of Poisson-distributed numbers of independent identically-distributed random variables is applied by Feeney and Sherbrooke (1966) and Archibald and Silver (1978). Normal distribution is assumed by Croston (1972) and Bartakke (1981). Vereecke and Verstraeten (1994) introduce a package Poisson distribution. They combine demand occurrences characterised by a Poisson distribution with non-varying demand sizes. Snyder (1984), Dunsmuir and Snyder (1989), Segerstedt (1994) and Yeh (1997) recommend the gamma distribution for demand modeling. Sobel and Zhang (2001) apply a system where demand results simultaneously from both a deterministic and a random source.
These distributional functions have been criticised throughout literature not being suitable for describing the demand pattern of spare parts (Snyder 1984, Vereecke and Verstraeten 1994, Razi and Tarn 2003). These mathematical models can be too complex to be successfully implemented in Inventory Management systems (Razi and Tarn 2003). The use of Artificial Neural Networks approach is viewed to be a promising method in case the datasets are large enough to allow Artificial Neural Networks models pattern and trend detection (Razi and Tarn 2003).
To overcome complex theoretical distributions, Razi and Tarn (2003) propose pooled distribution, where items are grouped according to similarities in their demand histories and lead times.
The continuous operation of aircraft heavily depends on the availability of key spare parts. Stocking decisions based on inaccurate demand assumptions can result in very high costs (Razi and Tarn 2003). This perception is confirmed during the field work. The discussion in Chapter 4.3 will show that the airline faced a high cost exposure due to wrong inventory decisions.
Chang et al (2005) focus on spare parts criticality as the main aspect of demand forecasting. They propose a (r,r,Q) continuous review and constant reorder model where spare parts are as either critical or non-critical items. A fixed orders size Q is placed when the inventory level reaches r. The remaining stock is reserved for critical demand. All non-critical demand will be backordered until the stock level again exceeds r.
Beside the classic inventory theory with focus on consumable items, another branch of research deals with repairable inventory. These are typically high cost, long-life parts that can be repaired several times until repairing becomes more expensive than replacing. Repairable inventories are common in both military and civil aviation and in other commercial settings such as copying machines or transportation equipment (Guide and Srivastava 1997).
The repairable Inventory Management problem typically deals with the optimal stocking of parts at bases and a central depot facility where failed units returned from bases are repaired (Guide and Srivastava 1997). This problem has its origins in military applications (Sherbrooke 1968, Parsons and Goodwyn 1986, Humphrey et al 1998, Kang et al 1998, Raivio et al 2001). Here parts are stocked at bases that are capable to repair some, but not all items. A central depot serves all bases. Lack of spare parts in the event of component failure will prevent aircraft from fulfilling their mission. The objective therefore is to maximise aircraft availability, or minimise downtimes and numbers of grounded aircraft respectively, while meeting imposed budget constraints (Guide and Srivastava 1997).
Although repairable and spare parts inventories serve the same purpose, i.e.
ensuring equipment availability in the event of failures, they are not necessarily equal. Not all spare parts are repairable and return flows or repair of items are not categorical in spare parts settings (Guide and Srivastava 1997). Reviews on repairable item inventories can be found in Nahmias (1981), Mabini and
Gelders (1991) Guide and Srivastava (1997) and Diaz and Fu (2005) among others. Hereafter only models relevant within the context of this study will be detailed.
Several types of repairable item inventory models can be recognised in literature.
Single-echelon models deal with the optimisation of a certain criterion, which typically is the determination of the optimal replacement quantity for a repairable item. Deterministic single-echelon models assume deterministic demand and known, constant recovery rates. They furthermore consider a single item only at the end item level. Stochastic single-echelon models deal with varying demand rates. They suffer from many of the limitations as the deterministic models.
They also ignore multi-indentured items. Independent repair times are assumed which would require sufficient capacity at repair facilities at any time. Both model types require the estimation of various cost parameters such as
backorder costs. These costs are very difficult to determine. In the commercial aviation context backorder costs are made up of lost revenues from the flight non-availability. These include costs for lost connections downstream, crew cancellation costs, intangible costs related to loss of goodwill from customers and also positive savings from such as no fuel expenditures (Guide and Srivastava 1997).
In multi-echelon models, the typical setting is a two-level system consisting of a number of bases served by a central depot. Failures of parts at base generate demand that may be satisfied from the stock at the base. At the same time, the failed item will be repaired at either the base or a central depot facility. In case stock is not available at base-level, a backorder occurs and demand has to be satisfied either from stock at the depot or from parts completing the repair process (Graves 1985, Sun and Zuo 2010). As long as no condemnation of items occurs, the system is a closed one. The objective lies in the determination of inventory levels at each base to meet a specified service level by taking into account set repair rates, transportation times and budget constraints. In case of condemnation procurement quantities and timing has to be considered as well.
Among other factors transshipments between bases, cannibalisation, and capacity constraints of repair facilities can induce additional complications in such multi-echelon models (Guide and Srivastava 1997). A successful
implementation of a multi-echelon inventory system can be found in the study from Cohen et al (1990) about IBM’s service business.
Sherbrooke (1968) first addressed the repairable inventory problem in the military context by applying the Multi-Echelon Technique for Recoverable Item Control within the United States Air Force. The Multi-Echelon Technique for Recoverable Item Control is a mathematical model translated into a computer program. It determines base and depot stock levels for a group of repairable items (Sheerbroke 1968). Contrary to an item approach where inventory levels for each individual part are set, here, the so-called system approach is applied by considering all parts in the system. Thonemann et al (2002) note, that the system approach outperforms the item approach but that its implementation is time consuming and costly. Cohen et al (1999) present a study in which
Sherbrooke’s approach is successfully applied to optimise the inventory system of a electronics manufacturer.
Critical assumptions underlying the Multi-Echelon Technique for Recoverable Item Control model are:
(1) infinite repair capacities at the base (Kim et al 1996, Diaz and Fu 1997, 2005, Kim et al 2000)
(2) successive replenishment processes at the bases are independent processes leading to Poisson distribution (Diaz and Fu 1997, 2005) (3) no lateral transshipments between bases
(Muckstadt 1973, Muckstadt and Thomas 1980).
The Multi-Echelon Technique for Recoverable Item Control has been modified by Muckstadt (1973, 1978). His MOD- Multi-Echelon Technique for Recoverable Item Control is a multi-indenture model which allows the explicit consideration of a hierarchical parts structure (Muckstadt 1973). The model assumes that the system is composed of main components which consist of subcomponents. A failed component is exchanged for a spare part unit supplied by the base or backordered if no spare part is on stock. The component is repaired either at the base or at the depot, depending on the type of failure. Here the
subcomponent is replaced or backordered. (Diaz 2003).
Slay (1984) developed the VARI- Multi-Echelon Technique for Recoverable Item Control to determine initial stock levels for multi-indenture items. Here, repair capacities are also assumed as infinite. Sleptchenko et al (2005) assume finite repair capacities and extend the VARI- Multi-Echelon Technique for Recoverable Item Control model with heuristics to assign repair priorities.
Cochran and Lewis (2002) claim that the Dyna- Multi-Echelon Technique for Recoverable Item Control model (Isaacson et al 1988) is currently the best analytical model to compute the aircraft spare parts provisioning model. They however note that it assumes a large number of aircraft. They propose an approach based on finite queuing theory for small fleets of three aircraft (sic).
Models assuming that repair capacity is finite, and thus parts queue at the depot have been developed e.g. by Gross et al (1987), Diaz and Fu (1997, 2005) and Ni et al (2008).
Wong et al (2005a, 2005b), Wong et al (2006) and Reijnen et al (2009)
introduce models that consider lateral transshipments. According to Reijnen et al (2009) planning with lateral transshipments can lead to significant cost savings with regard to inventory.