Seismic loss assessment of the naval industry supply chain: a case study of italian navy warships

Among the logistical support activities of in-service ships, the process of resupplying failed parts to restore the efficiency of naval equipment is characterized by the highest level of importance. This is particularly true for warships due to the quantity and characteristics of the combat system items (i.e., complex electronics and high unit value) for which the repair or replacement process is typically characterized by long lead time (i.e., up to 1 year starting from the occurrence of the part failure). These delays affect the availability of warships, which cannot be used to respond to an emergency until the part is restored in the repair and replacement logistics cycle. In this context, an estimation of losses due to spare parts damage in warehouses after a seismic event is of crucial importance.

In the present study, a methodology for estimating indirect losses due to damage to warehouses and their contents after a strong earthquake is presented. Indirect losses are estimated in terms of the number of ships that will be unavailable due to the absence of spare parts after a seismic event. First, the distributions of failed items and expected values of backorders to warehouses are estimated. Then, the probability of loss of stock due to its seismic damage or due to the collapse of the structure in which the stock is located is taken into account. In addition, a methodology for estimating available ship loss curves due to seismic causes is proposed. As a numerical example, the estimation of losses related to the Italian Navy war- ships is described.

Italy is a maritime country that owes much of its prosperity, wellness and security to the sea. In this context, ensuring the efficiency of the naval industry assumes a key role. An in-service ship requires different logistical support activities which can be grouped into direct and indi- rect support for ships. For each type of support, different functions must be ensured. Berthing and ship services (i.e., water, electricity, sewage), are functions included in direct support. Indirect support consists of those activities performed ashore that, even without providing direct service to ships, affect their operational efficiency (e.g., command and control activities, telecommunications, material storage, housing and social support for personnel).

All functions, whether for direct or indirect support, are carried out by individual buildings or groups of buildings. Among the indirect support activities, the process of resupplying failed parts of a ship system is the one with the greatest impact on ship efficiency.

This is particularly relevant for warships in which Combat System (CdS) equipment is present. For such components, indeed, the supply of spare parts is more complex due to the high technological nature as well as the high production cost of CdS components, which lead to limiting their industrial production to a few pieces per year. In this case, the repair or replenishment process is characterised by high average lead times, up to 1 year starting from the occurrence of the part failure. These delays affect the readiness of ships, which will not be efficient until the part is restored in the repair and replacement logistics cycle.

Since the beginning of 2000, Italian Navy (IN) has adopted innovative processes for optimising stock levels by analysing the return data from the field during the TGS FREMM (Temporary Global Support of Fregate europee multi-missione) contract. These processes aim to identify of minimum stock levels and the adequate allocation of spare parts in different IN warehouses, to achieve a balance between warship life cycle cost and its availability.

The latter can be expressed as the probability that the system or equipment used under stated condition is in an operable state at any given time. In Sherbrooke (2004), different types of availability are defined: intrinsic, achieved and operational. Inherent availability is a function of the average time required for corrective maintenance of the system.

The achieved availability considers both the average corrective maintenance time and the average preventive maintenance time. Intrinsic availability and achieved availability are not a function of delays for spare parts. Such delays are considered in the more complete expression of operational availability. The latter can be defined as the product of achieved availability and supply availability. Once the maintenance manning, test equipment, and preventive maintenance policy have been defined, the achieved availability can be easily calculated. Supply availability is a function of the level of stock in the warehouse.

The aim of the present study is to estimate the loss of supply availability (herein referred to simply as availability) as a result of damage to warehouses and their contents after an earthquake. The first part of the work describes the estimation of backorders in accordance with approaches proposed in the literature. In the second part, approaches for estimating both the level of stock available after an event and availability loss curves due to earthquakes are proposed. The last part of the paper presents an illustrative example of the estimation of IN warships that will be unavailable due to a shortage of items after a seismic event.

Supply cicle

Spare parts inventory management starts with the analysis of bills of items. The technical systems installed on ships consist of numerous elements and different categories which, in most cases, can be further subdivided into sub-parts and sub-components. The spare parts are allocated in several warehouses, usually hierarchically structured, where each level is indi- cated with the term echelons.

In this study, a multi-item two-echelon configuration with a central warehouse and multiple local warehouses was analysed (this configuration may approximate those used by IN for the supply cycle of CdS parts). In addition, a one-for-one replenishment policy was adopted, which is appropriate for components with high value and infrequent failures. One-for-one replenishment is a continuous review (s-1, s) inventory policy which means that whenever a demand for an arbitrary number of units is accepted, a reorder is placed immediately for that number of units. The Figure 1 shows an example of the supply cycle described.

When a ship item fails, three events occur simultaneously. First, the failed item is replaced with a spare item from the inventory of the local warehouse (LW), if one is available; other- wise, there is a backorder (i.e., a shortage) at the LW that will last until a replacement can arrive from the central warehouse (CW). Second, the failed item is sent to the CW for repair or ordering. Third, the CW ships a replacement item if it has available inventor; otherwise, the CW backorders the replacement request and will fill it when stock is available. When the failed item arrives at the CW, it enters the repair process; upon completion of the repair pro- cess, the item goes into the CW inventory or fills a backorder if any exist. A ship will not be available until the backorders of all elements of its equipment have been fulfilled.

Pre-event backorder distribution

The supply cycle described in Section 2 can be studied by means of the multi-echelon inven- tory model for a repairable item with one-for-one replenishment proposed in Graves (1985). For clarity, the symbology used in this study is presented in Figure 2 (right). Such symbology is derived from the existing literature and has been extended here to include the post-event condition (denoted by subscript E). In Graves (1985), the main objective of the model is to estimate for each item in the category ith, the outstanding orders (Qij) at LWj in a generic instant of time t, which are the replacement requests that have yet to be filled. If sij is the relative number of spare items stocked at LWj, then sij−Qij is the net spare inventory on hand at time t, where a negative value denotes a backorder at LWj. The model is an application of queuing theory to the study of queue systems, with customers, servants, waiting queues and incoming and outgoing traffic flows. For the supply cycle described in the previous section, the queue system consists of three sub-systems (Figure 2): 1) transferring items from LWs to CW; 2) repairing or reordering items at CW; 3) transferring items from CW to LWs.

The parameters governing the queue system are: i) arrival process (i.e., inter-arrival times of failed items); ii) service process (i.e., service times of each item; iii) number of servers (finite or infinite); iv) queue definition (finite or infinite); v) population (finite or infinite); vi) ser- vice discipline (e.g., first-come first-serve usually indicated as FCFS).
In the present study, it was assumed that all failures are Poisson processes, therefore the inter- arrival time is an exponential variable, and the failure processes are independent of the stock level at the warehouses. In addition, all service times were assumed to be deterministic, where the transfer times LW-to-CW and CW-to-LW are the same for all warehouses (Tij = T1), while the service time at CW is the lead time.

The number of servers, queue capacity and population were assumed to be infinite. Finally, FCFS is the service discipline considered in this study. Starting from the above assumptions, the process of estimating steady-state distributions of backorders to LWs proposed by Grave (1985) can be summarized into the following steps: i) estimation of aggregate outstanding orders (Qi) in the whole system; ii) estimation of out- standing orders (Qij) to each LW; iii) estimation of backorders to LWs. Qi is given by convo- lution of the distributions of the B(si0) (backorders to CW) and Di (aggregate items in transfer CW-to-LWs) variables, assumed stochastically independent. The distribution B(si0) = Qi0 - si0, with Qi0>si0, is estimated from those of outstanding orders at CW (Qi0), assuming that the stock level at CW (si0) in pre-event conditions is known. Qi0 are the items that may be in transit from local to the central warehouses (LW-to-CW sub-system) or in repair at the CW (repair to CW sub-system).

Therefore, Qi0 is distributed as a Poisson with rate equal to the sum of the rates of the overlapping (stochastically independent) Poisson variables: λ = λi0(T1+ Ti0), where λi0 = ∑ j λij with j=1,2,…,J. In the same way, Di distribution is Poisson with rate λi0(T1). The distribution of Qij is estimated through the total probability theorem, where the probability (conditioned) that part of Qi is from a particular LWj is distributed as a Binomial. Finally, the distribution of backorders at each LW is given by B(sij) = Qij-sij, with Qij>sij, where sij in pre-event conditions is considered deterministic and known.

...Continua a leggere nel PDF in allegato.