On the exact calculation of the fill rate in a periodic review inventory policy under discrete demand patterns

Abstract

ElsevierGuijarro Tarradellas, E.; Cardós, M.; Babiloni, E. (2012). On the exact calculation of the fill rate in a periodic review inventory policy under discrete demand patterns. European Journal of Operational Research. 218(2): 442-447. doi:10.1016/j.ejor.2011.11.025. On the exact calculation of the fill rate in a periodic review inventory policy under discrete demand patterns GUIJARRO, E., CARDÓS, M., BABILONI, E. Universidad Politécnica de Valencia AbstractThe primary goal of this paper is the development of a generalized method to compute the fill rate for any discrete demand distribution in a periodic review policy. The fill rate is defined as the fraction of demand that is satisfied directly from shelf. In the majority of related work, this service metric is computed by using what is known as the traditional approximation, which calculates the fill rate as the complement of the quotient between the expected unfulfilled demand and the expected demand per replenishment cycle, instead of focusing on the expected fraction of fulfilled demand. This paper shows the systematic underestimation of the fill rate when the traditional approximation is used, and revises both the foundations of the traditional approach and the definition of fill rate itself. As a result, this paper presents the following main contributions: (i) a new exact procedure to compute the traditional approximation for any discrete demand distribution; (ii) a more suitable definition of the fill rate in order to ignore those cycles without demand; and (iii) a new standard procedure to compute the fill rate that outperforms previous approaches, especially when the probability of zero demand is substantial. This paper focuses on the traditional periodic review, order up to level system under any uncorrelated, discrete and stationary demand pattern for the lost sales scenario.Keywords: inventory, fill rate, periodic review, discrete demand, lost sales. 2 Introduction and literature reviewOne of the service measures most commonly used in practice is the volume fill rate, defined as the fraction of demand that is immediately fulfilled from on hand stock (see Silver et al. (1998) or Axsäter (2000) among others). Therefore, in practice it also indicates the size of the backordering demand when this is allowed (Tempelmeier (2007)). The volume fill rate is also known as item fill rate, unit fill rate or just fill rate (denoted by β in the rest of this paper).Over the last sixty years, several works have suggested methods to estimate the fill rate in different contexts. However, to the best of our knowledge, there is not any exact and general method to estimate it under any discrete demand context. This paper focuses on the exact estimation of the fill rate for the periodic review, order up to level (base stock) system. This stock policy is commonly denoted by (R, S) and consists of examining the status of an item every R fixed time periods and launching a replenishment order which raises the inventory position to the order up to level S.Traditionally ...

Inventory management of spare parts in an energy company

“…As pointed out by Guijarro et al [12], while this expression is an approximation to the fill rate, it is the most common method to compute it. Based on simulation, their numerical experiments reveal that this traditional approximation underestimates the simulated fill rate and, therefore, in our purpose to set inventory control parameters it would lead to a more conservative approach.…”

Fill rate estimation in periodic review policies with lost sales using simple methods

“…Guijarro, Cardós and Babiloni (2012) compute the fill rate using a classical approach such as (1) However, we use the expression below because of its superior numerical stability and adherence to the fill rate definition itself (2)…”

Determining the fill rate for a periodic review inventory policy with capacitated replenishments, lost sales and zero lead time

“…In this paper however, periodic review inventory systems with a limited replenishment capacity are studied. Unlike [1], [2], [3], [4] and [5], in this paper the lead time is assumed to be negligible. In a part of [2], capacity is also considered, but in the context of multistage systems with process limitations.…”

“…In [2] and [3] general continuous demand and normal demand are considered, [1] and [4] focus on normal demand. Guijarro et al [5] discuss fill rate definitions and expressions for uncapacitated periodic review inventory systems with lost sales and discrete demand. In this paper however, periodic review inventory systems with a limited replenishment capacity are studied.…”

“…[5], in this paper the lead time is assumed to be negligible. In a part of [2], capacity is also considered, but in the context of multistage systems with process limitations.…”