Fill rate: from its definition to its calculation for the continuous (s,Q) inventory system with discrete demands and lost sales

[EN] Customer service measures are traditionally used to determine the performance or/and the control parameters of any inventory system. Among them, the fill rate is one of the most widely used in practice and is defined as the fraction of demand that is immediately met from shelf i.e. from the available on-hand stock. However, this definition itself set out several problems that lead to consider two different approaches to compute the fill rate: the traditional, which computes the fill rate in terms of units short; and the standard, which directly computes the expected satisfied demand. This paper suggest two expressions, the traditional and the standard, to compute the fill rate in the continuous reorder point, order quantity (s, Q) policy following these approaches. Experimental results shows that the traditional approach is biased since underestimate the real fill rate whereas the standard computes it accurately and therefore both approaches cannot be treated as equivalent. This paper focuses on the lost sales context and discrete distributed demands.This work was supported by the European Regional Development Fund and Spanish Government (MINECO/FEDER, UE) under the Project with reference DPI2015-64133-R.Babiloni, E.; Guijarro, E. (2020). Fill rate: from its definition to its calculation for the continuous (s,Q) inventory system with discrete demands and lost sales. Central European Journal of Operations Research. 28(1):35-43. https://doi.org/10.1007/s10100-018-0546-7S3543281Agrawal V, Seshadri S (2000) Distribution free bounds for service constrained (Q, r) inventory systems. Nav Res Logist 47:635–656Axsäter S (2000) Inventory control. Kluwer Academic Publishers, NorwellAxsäter S (2006) A simple procedure for determining order quantities under a fill rate constraint and normally distributed lead-time demand. Eur J Oper Res 174:480–491Bijvank M, Vis IFA (2011) Lost-sales inventory theory: a review. Eur J Oper Res 215:1–13Bijvank M, Vis IFA (2012) Lost-sales inventory systems with a service level criterion. Eur J Oper Res 220:610–618Breugelmans E, Campo K, Gijsbrechts E (2006) Opportunities for active stock-out management in online stores: the impact of the stock-out policy on online stock-out reactions. J Retail 82:215–228Diels JL, Wiebach N (2011) Customer reactions in out-of-stock situations: Do promotion-induced phantom positions alleviate the similarity substitution hypothsis? Berlin: SFB 649 Discussion paper 2011-021Grinstead CM, Snell JL (1997) Introduction to probability. American Mathematical Society, ProvidenceGruen TW, Corsten D, Bharadwaj S (2002) Retail out-of-stocks: A worldwide examination of extent causes, rates and consumer responses. Grocery Manufacturers of America, WashingtonGuijarro E, Cardós M, Babiloni E (2012) On the exact calculation of the fill rate in a periodic review inventory policy under discrete demand patterns. Eur J Oper Res 218:442–447Platt DE, Robinson LW, Freund RB (1997) Tractable (Q, R) heuristic models for constrained service levels. Manag Sci 43:951–965Silver EA (1970) A modified formula for calculating customer service under continuous inventory review. AIIE T 2:241–245Silver EA, Pyke DF, Peterson R (1998) Inventory management and production planning and scheduling. Wiley, HobokenTempelmeier H (2007) On the stochastic uncapacitated dynamic single-item lotsizing problem with service level constraints. Eur J Oper Res 181:184–194Vincent P (1983) Practical methods for accurate fill rates. INFOR 21:109–120Zipkin P (2008a) Old and new methods for lost-sales inventory systems. Oper Res 56:1256–1263Zipkin P (2008b) On the structure of lost-sales inventory models. Oper Res 56:937–94

A periodic inventory system of intermittent demand items with fixed lifetimes

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