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

On the estimation of on-hand stocks for base-stock policies and lost sales systems and its impact on service measures

[EN] This paper focuses on computing on-hand stock levels at the beginning of a replenishment cycle for a lost sales inventory system with periodic reviews and discrete demand. A base-stock policy is used for replenishments. The literature provides an Exact method which requires a huge computational effort, and two closed-form approximate methods that arise from the backordering case, the Non-stockout and the Bijvank & Johansen. In this paper we propose three new and closed-form approaches that explicitly consider the lost sales assumptions: the Adjusted Non-stockout, the Polar Opposite and the 1-Step methods. Existing and proposed methods are evaluated in terms of their accuracy when computing the cycle service level and the fill rate. In this sense, results show that the Bijvank & Johansen and 1-Step methods provide similar performance but present different behaviours in terms of under or over estimating service measures that have different implications on the design of stock policies.This work was supported by the European Regional Development Fund and Spanish Government (MINECO/FEDER, UE) under the project with reference [DPI2015-64,133-R].Cardós, M.; Guijarro, E.; Babiloni, E. (2017). On the estimation of on-hand stocks for base-stock policies and lost sales systems and its impact on service measures. International Journal of Production Research. 55(16):4680-4694. https://doi.org/10.1080/00207543.2017.1279759S46804694551

Fill Rate Estimation in Periodic Review Policies with Lost Sales Using Simple Methods

[EN] Purpose: The exact estimation of the fill rate in the lost sales case is complex and time consuming. However, simple and suitable methods are needed for its estimation so that inventory managers could use them. Design/methodology/approach: Instead of trying to compute the fill rate in one step, this paper focuses first on estimating the probabilities of different on-hand stock levels so that the fill rate is computed later. Findings: As a result, the performance of a novel proposed method overcomes the other methods and is relatively simple to compute. Originality/value: Existing methods for estimating stock levels are examined, new procedures are proposed and their performance is assessed.This work was supported by the European Regional Development Fund and Spanish Government (MINECO/FEDER, UE) under the project with reference DPI2015-64133-R.Cardós, M.; Guijarro, E.; Babiloni, E. (2016). Fill Rate Estimation in Periodic Review Policies with Lost Sales Using Simple Methods. Journal of Industrial Engineering and Management. 9(5):73-89. https://doi.org/10.3926/jiem.2063S73899

Fuzzy Modeling Approach to On-Hand Stock Levels Estimation in (R, S) Inventory Systems with Lost Sales

[EN] Purpose: One challenge in inventory control models is to know the stock available at the beginning of the cycle to satisfy future demands, i.e. to know the on-hand stock levels at order delivery. For inventory managers, this knowledge is necessary to both determine service levels and establish the control parameters of the inventory policy. However, the calculation of on-hand stock levels when unfilled demand is lost is mathematically complex since on-hand stock cannot be negative by definition. The purpose of this paper is to propose a new approach to estimate on-hand stock levels when the inventory is periodically reviewed and unfilled demand is lost, through the use of fuzzy techniques. Design/methodology/approach: This paper applies fuzzy set techniques for the calculation of the on-hand stock levels at order delivery in the lost sales context, based on the uncertainty that real demand introduces. To this end, we propose a new approach based on modeling the on-hand stock as an imprecise Markov chain using possibility functions, which reduces significantly the computational effort required to obtain the on-hand stock levels. Findings: To illustrate the performance of the proposed method, two experiments are carried out. The first experiment shows that the proposed fuzzy method correctly calculates on-hand stock levels with insignificant deviation with respect the exact vector. Additionally, the results illustrate that the fuzzy method simplifies the calculation and highly reduces the computational efforts. The second experiment shows the performance of the fuzzy method when it is used to estimate service levels by means of the fill rate. The results show that the proposed method accurately estimates the fill rate with average deviations lower than 0.00015. Practical implications: Knowing the on-hand stock vector is important for inventory managers to establish the control parameters of the system, i.e. to determine the minimum base stock level, S, that guarantees the achievement of a target service level. The difficulty of this estimation is that to obtain the on-hand stock vector in a lost sales context requires a huge computational effort and it is difficult to implement in companies' information systems. However, the proposed fuzzy method leads to a very accurate calculation of the on-hand stock vector significantly reducing the computational costs, which makes this method easily implementable in practical environments. Originality/value: Fuzzy set techniques have been widely used in inventory models to introduce the uncertainty of demand, costs or shortage. However, to the best of our knowledge, this is the first paper which deals directly with fuzzy estimation of on-hand levels.This work was supported by Generalitat Valenciana under the project with reference GV/2017/032.Guijarro, E.; Babiloni, E.; Canós-Darós, MJ.; Canós-Darós, L.; Estelles Miguel, S. (2020). Fuzzy Modeling Approach to On-Hand Stock Levels Estimation in (R, S) Inventory Systems with Lost Sales. Journal of Industrial Engineering and Management. 13(2):464-474. https://doi.org/10.3926/jiem.3071S46447413