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

ABC classification of spare parts considering costs and service

[EN] This paper focuses on the multi-item problem where it is necessary to reach an overall stock availability of the spare parts while minimising involved costs. Over the last years, a number of authors have proposed a variety of approaches and provided different rules in order to classify items in ABC classes. An additional optimisation has to be performed in order to minimise the inventory cost while fulfilling a target service level. The proposed approach focuses on the characteristics of spare parts and optimises the inventory cost subject to the overall target fill rate by means of a closed form formula for calculating the fill rate of every item independently. This new method is validated with a dataset of spare parts of an airline company and clearly outperforms the alternative methods in terms of inventory cost reduction and ease of calculation. Extensions of our results are also indicated.S244255223-

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

Una metodología para la estimación eficiente del stock de referencia en políticas de revisión periódica con demanda discreta

El objetivo de la presente tesis es proponer una metodología para la estimación eficiente del stock de referencia en el diseño de políticas (R, S) cuando se utiliza en nivel de servicio de ciclo como restricción de diseño, asumiéndose que el proceso de demanda es estacionario con una función de probabilidad discreta, independiente, e idénticamente distribuida. Para ello se analiza el comportamiento de cuatro métodos de cálculo, tres aproximados y uno exacto. La aplicación del método exacto supone un elevado esfuerzo computacional cuyo coste no se justifica para cualquier ítem y cualquier circunstancia. Por ello es importante conocer el comportamiento de los métodos aproximados y los riesgos asociados a su utilización. En la práctica, el método más extendido para calcular el nivel de servicio de ciclo, denominado clásico, es una aproximación al cálculo exacto. Sin embargo, en la presente tesis se demuestra que su utilización para la determinación del stock de referencia no siempre asegura cumplir con el criterio de diseño de la política establecido como objetivo. Los métodos analizados son: (1) el método exacto propuesto por Cardós et al. (2006); (2) La aproximación PI derivada por Cardos y Babiloni (2008) a partir de hipótesis para simplificar el método exacto; (3) La aproximación PII derivada por Cardos y Babiloni (2008) a partir de hipótesis para simplificar el método exacto y la aproximación PI; y (4) el método clásico para el cálculo del stock de referencia [ver p. ej. Silver et al. (1998)], denominado aproximación clásica en la presente tesis, que resulta además al asumir hipótesis para simplificar el método exacto, la aproximación PI y la aproximación PII [Cardos y Babiloni (2008)]. La metodología propuesta se fundamenta en un experimento lo suficientemente amplio (115.941 casos) que justifica su validez.Babiloni Griñón, ME. (2009). Una metodología para la estimación eficiente del stock de referencia en políticas de revisión periódica con demanda discreta [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8322Palanci

On the exact calculation of the mean stock level in the base stock periodic review policy

Purpose: One of the most usual indicators to measure the performance of any inventory policy is the mean stock level. In the generalized base stock, periodic review policy, the expected mean stock during the replenishment cycle is usually estimated by practitioners and researchers with the traditional Hadley-Whitin approximation. However it is not accurate enough and exact methods suggested on the related literature focus on specific demand distributions. This paper proposes a generalized method to compute the exact value of the expected mean stock to be used when demand is modelled by any uncorrelated, discrete and stationary demand pattern. Design/methodology/approach: The suggested method is based on computing the probability of every stock level at every point of the replenishment cycle for which it is required to know the probability of any stock level at the beginning of the cycle and the probability transition matrix between two consecutive periods of time. Furthermore, the traditional Hadley-Whitin approximation is compared with the proposed exact method over different discrete demand distributions Findings: This paper points out the lack of accuracy that the Hadley-Whitin approximation shows over a wide range of service levels and discrete demand distributions. Research limitations/implications: The suggested method requires the availability of appropriate tools as well as a sound mathematical background. For this reason, approximations to it are the logical further research of this work. Practical implications: The use of the Hadley-Whitin approximation instead of an exact method can lead to underestimate systematically the expected mean stock level. This fact may increase total costs of the inventory system. Originality/value: The original derivation of an exact method to compute the expected mean stock level for the base stock, periodic review policy when demand is modelled by any discrete function and backlog is not allowed.Babiloni, E.; Cardós, M.; Guijarro Tarradellas, E. (2011). On the exact calculation of the mean stock level in the base stock periodic review policy. Journal of Industrial Engineering and Management. 4(2):194-205. doi:10.3926/jiem.2011.v4n2.p194-205S1942054

Stock control analytics: a data-driven approach to compute the fill rate for the (s, S) system considering undershoots

Inventory policies are traditionally characterized assuming several hypotheses that lead to commit important errors when are used in practical environments. This is the case when the inventory is continuously reviewed by means of the Order-Point, Order-Up-to-Level (s, S) system and undershoots, i.e. the difference between the order-point and the inventory position when it is reached, are neglected. This paper analyses conceptually and empirically the bias on the classic fill rate formula when neglecting undershoots. After that, we suggest a non-parametric approach based on a State Dependent Parameter algorithm to propose a new non-linear expression, named analytic fill rate that correct that bias. The proposed approach is developed under a data-driven perspective and is easily implementable in practice. This research is developed in a lost sales context with stochastic and i.i.d. discrete deman

Aplicación del puzzle de Aronson para trabajar el aprendizaje colaborativo y el desarrollo de competencias genéricas de los estudiantes

[ES] El puzzle de Aronson es una técnica de aprendizaje colaborativo cuya principal característica es que son los propios alumnos, trabajando en equipo, los que hacen de tutores del aprendizaje de sus compañeros siendo, a la vez, tutorizados por ellos. Este trabajo analiza la aplicación de esta técnica en la asignatura Gestión de Recursos Humanos del grado en Gestión y Administración Pública, así como los aprendizajes y resultados docentes obtenidos. La utilización del puzzle de Aronson fomenta el aprendizaje colaborativo de los alumnos, además de desarrollar competencias genéricas de la titulación tales como "demostrar compromiso ético en el trabajo" que difícilmente se pueden adquirir y/o evaluar con otras metodologías docentes.Guijarro, E.; Babiloni, E.; Fernández-Diego, M. (2014). Aplicación del puzzle de Aronson para trabajar el aprendizaje colaborativo y el desarrollo de competencias genéricas de los estudiantes. Editorial Universitat Politècnica de València. 496-505. http://hdl.handle.net/10251/82240S49650

On the Identification of the Key Factors for a Successful Use of Twitter as a Medium from a Social Marketing Perspective

[EN] Public administrations are organizations whose mission is to serve the interests of society by providing efficient and sustainable services. Much of the information received from public administrations uses social media due to their versatility and capacity to reach a large number of citizens. Among them, Twitter is the most widely used, especially to disseminate messages with a high social content. This type of messages falls within the discipline of social marketing. However, when public administrations use Twitter for social marketing communication, it is not known which factors are the most decisive to achieve the social objective for which they are issued. This article provides an answer to this question, using the Analytic Network Process Multicriteria method to determine which factors matter and how they are interrelated when issuing social marketing messages through Twitter. The result of this research reveals that from the 22 factors analyzed, the most influential from a social marketing point of view are the average age of population, the existence of a strategic communication plan, the number of tweets and the average number of tweets per day, the number of followers, retweets and mentions, as well as the efficiency of the account.Guijarro, E.; Santandreu Mascarell, C.; Blasco-Gallego, B.; Canós-Darós, L.; Babiloni, E. (2021). On the Identification of the Key Factors for a Successful Use of Twitter as a Medium from a Social Marketing Perspective. Sustainability. 13(12):1-15. https://doi.org/10.3390/su13126696S115131

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