کاهش موجودی در شبکه های قطعات یدکی با کاهش زمان کار گزینشی

We consider combined inventory control and throughput time reduction in multi-echelon, multi-indenture spare part networks for system upkeep of capital goods. We construct a model in which standard throughput times (TPTs) for repair and transportation can be reduced at additional costs. We first estimate the marginal impact of TPT reduction on the system availability. Next, we develop an optimization heuristic for the cost trade-off between TPT reduction and spare part inventories. In a case study at Thales Netherlands with limited options for TPT reduction, we find a net saving of 5.6% on spare part inventories. In an extensive numerical experiment, we find a 20% cost reduction on average compared to standard spare part inventory optimization. TPT reductions downstream in the spare part supply chain appear to be the most effective.

Manufacturers of advanced capital goods such as computer systems and medical systems tend to expand their business by offering service contracts for system upkeep during the life cycle (Cohen et al., 2006). Such service contracts typically contain quantified service levels, such as a maximum response time in the case of a failure or a minimum uptime per year. We encountered such contracts at Thales Netherlands, a supplier of naval radar and combat management systems. At the start of the contract, the supplier and/or the user invests in spare parts to facilitate fast repair by replacement of failed modules, the so-called Line Replaceable Units (LRUs). These (expensive) LRUs are often repaired rather than scrapped. Repair usually consists of diagnosis and replacement of a failed subcomponent, commonly referred to as Shop Replaceable Units (SRUs). Lack of spare SRUs leads to delay in LRU repairs, which increases the need for spare part inventories. Therefore, there is a trade-off between stocking LRUs and (cheaper) SRUs. Possibly, some SRUs are repairable themselves by replacing cheaper parts. So, we have a so-called multi-indenture product structure, see Fig. 1. We should decide about the stock levels of all items at all levels in the multi-indenture structure. In the remainder of this paper, we will use the phrases parent and child to refer to the relations in the multi-indenture structure: in Fig. 1, the supply cabinet is the parent of the power supply, and the power supply and air conditioning assembly are children of the supply cabinet. We use the term item for components at any level in the multi-indenture structure (LRUs, SRUs, parts). Full-size image (18 K) Fig. 1. A multi-indenture structure. Figure options Because the installed base is usually geographically dispersed, spare parts may be stocked at various locations. Stocks close to the sites where systems are installed are important for fast supply in case of a failure. This leads to several local stockpoints, each dedicated to a certain geographical area containing a part of the installed base. On the other hand, we may need central spare part stocks to take advantage of the risk pooling effect. Therefore, spare part supply systems usually have a multi-echelon structure as shown in Fig. 2. This is an example derived from a case study at Thales Netherlands, where we considered naval radars that are installed onboard of frigates. Spare parts may be stocked onboard, at the shore organization (close to a harbor), or at Thales Netherlands. In the remainder of this paper, we will use the common term base for a site where one or more systems are operational. We will use the phrases supplier and customer for the relations in the multi-echelon structure. In Fig. 2, Thales is the supplier of the Shore, and the Shore is a customer of Thales. Ready-for-use items are moved from the upstream part of the service supply chain (Thales) to the downstream part (ships). Full-size image (15 K) Fig. 2. A multi-echelon structure. Figure options To optimize the initial spare part inventories, Thales uses a commercial tool based on the VARI-METRIC method (Sherbrooke, 2004). If there is evidence during contract execution that the actual service levels are below target (e.g. in terms of downtime waiting for spare parts), the service provider intervenes. At a tactical level, options are among others (i) buying additional spare parts, (ii) reducing repair shop throughput times, and (iii) reducing transportation times of spare parts. In this research, we focus on throughput time (TPT) reduction (of repair and transportation) as alternatives to spare part investment for multi-indenture, multi-echelon spare part networks. At Thales Netherlands, such reductions are feasible at extra costs. It is well known that influencing repair TPT for specific items may have a large impact on the total costs (Sleptchenko et al., 2005 and Adan et al., 2009). To gain insight on the impact of TPT reductions, we first develop expressions for the marginal backorder reduction of LRUs at operating sites as a function of the marginal reduction in TPT of each repair and transport in the network. We use these expected backorders as criterion, because their minimization is approximately equivalent to maximizing operational availability (Sherbrooke, 2004). If pipelines are Poisson distributed, we need only the fill rates of all items in the multi-indenture structure at all locations in the multi-echelon networks for this purpose. Combining these marginal values with a certain discrete step size for the TPT reductions, we develop a heuristic optimization method to balance the investment in TPT reductions to investment in extra spares. In a numerical experiment, we show that a trade-off between spare part inventories and TPT reductions may yield considerable cost savings (20% on average). We find that TPT reductions downstream in the service supply chain are particularly interesting. TPT reductions of low level items (SRUs and subcomponents) upstream in the network make little sense. We illustrate our approach using a case study at Thales Netherlands. In this paper, we first discuss related literature and state our contribution (Section 2). We define our model in Section 3. Section 4 shows how we estimate the impact of TPT reduction for given spare part stock levels. This is input for our optimization heuristic (Section 5). In Section 6, we discuss numerical results from both the case study at Thales Netherlands and a large set of theoretical problem instances. We end up with conclusions and directions for further research in Section 7.

In this paper, we developed a heuristic for the joint optimization of spare part inventories and TPTs of repair and transportation based on pricing of TPT reductions for multi-item, multi-echelon, multi-indenture spare part networks. Our heuristic is easy to apply and yields significant cost reductions compared to the standard VARI-METRIC method for spare part optimization where TPTs are fixed. We find that it is particularly profitable to reduce TPTs downstream in the supply chain. Repair TPT reduction of lower indenture items upstream in the supply chain is the least useful. In a case study at Thales Netherlands, we find a cost reduction of 5.6%, which is somewhat low compared to our theoretical experiments. This is due to the fact that TPT reductions downstream in the Thales network are very expensive because of the special business characteristics (an installed base of radar onboard of frigates). Our approach is flexible and heavily relies upon the VARI-METRIC method for inventory optimization in multi-echelon, multi-indenture networks. As a consequence, we believe that known model extensions to VARI-METRIC can be included in our approach rather easily, thereby relaxing some model assumptions as mentioned in Section 3.1. For example, we can include the VARI-METRIC variants to deal with negative binominal demand (assumption 1), differences in item criticality (assumption 2), replenishment order quantities larger than 1 (assumption 8), and stochastic order-and-ship times (assumption 11) (Sherbrooke, 2004). Other model assumptions lead to considerably more complex models, in particular relaxing assumption 10 to include the use of lateral supply between stock points at the same level in the multi-echelon structure. Even disregarding throughput time reductions, a complete approach for lateral supply in general multi-echelon, multi-indenture networks is still missing. Most models are limited to single or two-echelon networks with a single indenture level only (Paterson et al., 2011). This is a topic for additional research. We also expect that the impact of repair throughput time reductions may be less under lateral transshipments, because we have additional flexibility for fast supply via the lateral channels. As other further research, we suggest developing a method for exact optimization of this model to provide a benchmark for the performance of our heuristic. The approach as applied by Basten et al. (under review b) for the joint optimization of the spare part provisioning and Level Of Repair Analysis (LORA) problem seems to be the most promising. However, we expect that an exact method requires more computation time, so that it will not be suitable to solve problem instances of practical size.