محاسبه دقیق و تقریبی سطح خدمات چرخه ای در سیاست های موجودی بررسی دوره ای
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|20628||2011||6 صفحه PDF||سفارش دهید||محاسبه نشده|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : International Journal of Production Economics, Volume 131, Issue 1, May 2011, Pages 63–68
The parameters of stock policies are usually determined to minimize costs while satisfying a target service level. In a periodic review policy the time between reviews can be selected to minimize costs while the order-up-to-level is based on the fulfilment of a target service level. Generally, the calculation of this service measurement is obtained using approximations based on an additional hypothesis related to the demand pattern. Previous research has shown that there is a substantial difference between exact and approximate calculations in some general circumstances, so in these cases the service level is not accomplished or the stock level is overestimated. Although an exact calculation of CSL was developed in previous work, the computational effort required to apply it in practical environments leads to the proposal of two approximate methods (PI and PII) that, with the classic approximation, are analysed and evaluated in this paper. This analysis points out the risks of using the classic approximation and leads one to suggest PII as the most suitable and accurate enough procedure to compute the CSL straightforwardly in practice. Additionally, a heuristic approach based on PII is proposed to accept or reject an inventory policy in terms of fulfilling a given target CSL. This paper focuses on uncorrelated, discrete and stationary demand with a known distribution pattern and without backlog.
The estimation of the cycle service level, CSL, in the traditional periodic review, order-up-to-level (R, S) system is based on the assumptions detailed by Silver et al. (1998) that are inappropriate when managing intermittent and slow movement demand items. It is especially relevant for the purpose of this paper that one of the main underlying assumptions related to the (R, S) formulation is the negligible chance of no demand between two consecutive reviews. This is because in an intermittent demand context: (i) the probability of no demand when the physical stock is equal to zero is not negligible and (ii) there is a chance of no demand during the replenishment cycle. However, despite the violation of this hypothesis the traditional (R, S) policy is applied in an intermittent demand context such as the model suggested by Syntetos and Boylan (2006) which is based on Sani and Kingsman (1997), where demand during the lead time is modelled using the negative binomial distribution or the model proposed by Leven and Segerstedt (2004), which uses the Erlang distribution. According to Cardós et al. (2006), when the demand pattern does not meet the hypotheses mentioned above, the procedure used to estimate the service level is only approximate and eventually may show large deviations. The CSL is defined by Chopra and Meindl (2004) as “the probability of not stocking out in a replenishment cycle”. Silver et al. (1998) defines the stockout as “an occasion when the available physical stock drops to the zero level”. Therefore, CSL is defined as the fraction of cycles in which the physical stock does not drop to the zero level. Surprisingly, this definition, called classic in this paper, does not take into account demand fulfilment. Furthermore, if the system is managed using a (R, S) policy, the classic definition leads one to consider that the CSL is equal to one if there is no demand during the replenishment cycle. For these reasons Cardós et al. (2006) suggest a more standard and useful definition capable of dealing with any type of stationary, discrete and independent and identically distributed (i.i.d.) demand pattern as the fraction of cycles in which non-zero demand is completely met by the physical stock. In this definition, the fulfilment of demand is explicitly considered and it works properly even if there is no demand during the replenishment cycle. According to this standard definition, with the physical stock at the beginning of the replenishment cycle being z0 and DR the demand during this cycle, the exact CSL value is calculated as equation(1) View the MathML sourceCSL(z0)=P(DR≤z0|DR>0)=P(0<DR≤z0)P(DR>0) Turn MathJax on However, to compute the exact CSL when the physical stock at the beginning of the replenishment cycle is not known a priori is quite complex, requiring the availability of appropriate tools as well as a sound mathematical background and eventually it may also be time consuming. Therefore, the exact method to compute the CSL is not an appropriate procedure to be widely used in a business context. This fact justifies the twofold objectives of this paper. Firstly, it points out the risks of using the classic CSL definition and secondly, this paper proposes two new approximations, PI and PII, in order to provide a suitable and accurate approximate procedure to compute the CSL but which is computationally simple enough to be used straightforwardly in practice. This paper is organized as follows. Section 2 is dedicated to describing the derivation of the exact method to compute the CSL for the (R, S) policy derived by Cardós et al. (2006), since this is the starting point of this paper. Section 3 proposes approximations PI, PII and the classic one. Section 4 presents a comparison between the exact and the approximate methods to compute the CSL and the discussion of the results from it. Section 5 compares the performance of the approximations based on their ability to provide the exact inventory policy and shows the risks involved. Finally, conclusions and further research are briefly pointed out in Section 6.
نتیجه گیری انگلیسی
This paper develops two new approximations, PI and PII, to compute the cycle service level for a periodic review policy subject to two conditions: (1) easy to compute so it could be applicable in operations management in practice and (2) more accurate than the classic approximation since the latter presents a substantial bias as pointed out in this paper. Approximation PII, which is defined by the ease of computing the expression (19), is selected as the most suitable approximation since PII presents a very similar performance to PI, being more appropriate than the classic one, as shown in Section 4 and Section 5. Furthermore, this paper points out the risks of using the classic approximation since, unlike PI and PII, it may overestimate the CSL, which implies that when using the classic approximation to design the (R, S) policy given a target cycle service level, the system may not achieve the target, thereby being less protected than expected. Additionally, a heuristic approach based on PII has been suggested in Section 5 to accept or reject an inventory policy in terms of fulfilling a given target CSL. The percentage of misclassified cases has been used as a measurement of the risk of taking a wrong decision. From this point of view, the heuristic approximation outperforms the classic one, which increases the misclassified risk for CSL values greater than 0.70 ( Fig. 3). Given the impact and the practical implications for the operational research and management of the results of this paper, further research will focus on developing a similar approach for the continuous review policy.