مقایسه روش بوت استرپ جدید با پارامتریک روش های برای تعیین سهام ایمنی در سیستم های موجودی بخش های خدمات

In this paper, we address the problem of forecasting and managing the inventory of service parts where the demand patterns are highly intermittent. Currently, there are two classes of methods for determining the safety stock for the intermittent item: the parametric and bootstrapping approaches. Viswanathan and Zhou (2008) developed an improved bootstrapping based method and showed through computational experiments that this is superior to the method by Willemain et al. (2004). In this paper, we compare this new bootstrapping method with the parametric methods of Babai and Syntetos (2007). Our computational results show that the bootstrapping method performs better with randomly generated data sets, where there is a large amount of (simulated) historical data to generate the distribution. On the other hand, with real industry data sets, the parametric method seems to perform better than the bootstrapping method.

In this paper, we address the problem of forecasting and managing the inventory of items for which the demand patterns are highly intermittent. An intermittent demand pattern is defined as one where a sequence of demand data contain a large percentage of zero values. One common example of items with intermittent demand is service (or spare) parts. It is believed that if this intermittent demand can be forecasted properly, it can result in significant improvement in managing the service parts inventories. The Croston (1972) method is considered to be the standard method for forecasting intermittent demand. This method has been shown to perform better than the single exponential smoothing (SES) technique and has been widely incorporated in commercial forecasting packages. Recently, many researchers have linked this method with inventory management. Some corrections or variations of Croston’s method are used to determine the average per period demand. Thereafter, the order quantity or order-up-to-levels are determined by calculating the safety stock required over the lead time (LT). Based on separate forecasts for the demand size of non-zero demands and the time-interval between non-zero demands, many researchers (e.g. Willemain et al., 1994, Johnston and Boylan, 1996, Levén and Segerstedt, 2004 and Babai and Syntetos, 2007) have used a parametric approach to derive the formula for the safety stock. See also chapter 16 of a recent book by Hyndman et al. (2008). Parametric methods typically assume that the demand per period follows a particular probability distribution. The parameters of the assumed distribution (such as mean and variance) are estimated using historical data and updated based on the latest demand value in every period. The safety stock or order-up-to-levels are then calculated using the estimated demand distribution parameters. The parametric approach has low computational overheads and is quite accurate. On the other hand, the bootstrapping method, a non-parametric approach, generates a large number of data points for the lead time demand by sampling from the historical demand data and demand interarrival data. By repeated sampling, a lead time distribution can be built (or at least the inventory position required for a certain service rate can be determined). Some researchers (e.g. Efron and Gong, 1983 and Willemain et al., 2004) have found bootstrapping to be efficient in dealing with intermittent demand items. The best known bootstrapping based method for determining the safety stock is by Willemain et al. (2004). In their method, the periods of positive demands are generated using a two-state Markov model and the actual demand sizes using past demand history. Their results show that the bootstrapping method produces more accurate forecasts of the distribution of demand over a fixed lead time than exponential smoothing and Croston’s method. Recently, Viswanathan and Zhou (2008) developed an improved bootstrapping based method and showed through computational experiments that this is superior to the method by Willemain et al. (2004) both in the context of computer generated demand data and industrial data. The key highlight of this improved bootstrapping method is that instead of a two-state Markov model, the positive demand arrivals are generated using the historical distribution of the inter-demand intervals (or intervals between non-zero demand). Viswanathan and Zhou (2008) compared their bootstrapping method with that of Willemain et al. (2004) using a computational study that was designed similar to the one used in this paper. Based on the distribution of the lead time demand generated using bootstrapping, the safety stock required was calculated under both methods for various service levels. The resulting total cost (comprised of holding and penalty cost) was calculated through a simulation experiment. For both the computer generated demand data and the real industrial data, the new method of Viswanathan and Zhou (2008) always obtained a lower average total cost. In this paper, we compare this new bootstrapping method with the parametric methods of Babai and Syntetos (2007) in two ways. First, we conduct a simulation study to compare the two approaches on randomly generated demand data sets with long demand history. We then conduct a numerical study to compare the two approaches with industrial demand data sets, where the length of the historical demand data available is relatively short. Our computational results show that the bootstrapping method of Viswanathan and Zhou (2008) performed better than the parametric approach with the randomly generated demand data sets. With industrial demand data sets which have only limited historical information, the parametric approach performed better than the bootstrapping method. The managerial insight from this research is that when sufficiently large amount of historical demand information is available, bootstrapping works well, but with limited historical information (as is most often the case when scientific forecasting approaches are initially applied in a company), parametric approaches such as the method of Babai and Syntetos produce better forecasts and are better at controlling the total inventory related costs. The rest of the paper is organized as follows. In Section 2, we provide a brief description of the methods being compared in this study. The design of the simulation experiments and the results are discussed in Sections 3 and 4. In Section 3, we discuss the simulation with randomly generated data and in Section 4, we discuss the simulation using industrial data sets. Finally, some concluding remarks are presented in Section 5.

In this paper, we address the problem of forecasting and managing the inventory of spare parts where the demand patterns are highly intermittent. We compare the newly developed bootstrapping method of Viswanathan and Zhou (2008) with the parametric method of Babai and Syntetos (2007). The computational results show that the bootstrapping method performs better with randomly generated demand data set, where there is a large amount of (simulated) historical data to generate the lead time demand distribution. On the other hand, for the real industry data set, the parametric methods seem to perform better than the bootstrapping method. An experiment which would be interesting to conduct would be to simulate shorter demand histories and find the point at which the bootstrapping method is no longer superior to the parametric method. This could be done either with simulated data or using industrial data with sufficiently long demand history in terms of number of periods. These are potential issues for future research.