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

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

Cálculo de los niveles del stock disponible al inicio del ciclo mediante un formalismo fuzzy

[EN] Accurate inventory management is essential for the proper functioning of companies. Following a continuous review inventory policy under lost sales assumption, this paper proposes the estimation of on-hand stock levels at order delivery using fuzzy techniques that seek to obtain a reduction in computational costs and include demand uncertainty in the model. To this end, after describing the theoretical formalization, we design an experiment that shows the applicability and potentially of the proposed fuzzy method[ES] Una buena gestión de inventarios es fundamental para el funcionamiento de la empresa. Siguiendo una política de revisión continua y en un contexto de ventas perdidas, en este trabajo se propone el cálculo de los niveles de stock al inicio de ciclo usando técnicas fuzzy que buscan obtener una reducción de los costes computacionales e incluir en el modelo la incertidumbre sobre la demanda. Con este fin, después de describir la formalización teórica, se diseña un experimento con el que se muestra la aplicabilidad y potencialidad del método fuzzy propuestoEste trabajo ha sido financiado por la Generalitat Valenciana a través del proyecto con referencia GV/2017/032Guijarro, E.; Canós Darós, MJ.; Babiloni, E.; Canós-Darós, L. (2020). Cálculo de los niveles del stock disponible al inicio del ciclo mediante un formalismo fuzzy. Rect@. Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA. 21(1):151-159. https://doi.org/10.24309/recta.2020.21.2.04S15115921

Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

We consider the canonical periodic review lost sales inventory system with positive lead-times and stochastic i.i.d. demand under the average cost criterion. We introduce a new policy that places orders such that the expected inventory level at the time of arrival of an order is at a fixed level and call it the Projected Inventory Level (PIL) policy. We prove that this policy has a cost-rate superior to the equivalent system where excess demand is back-ordered instead of lost and is therefore asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions. We further show that this policy dominates the constant order policy for any finite lead-time and is therefore asymptotically optimal as the lead-time approaches infinity for the case of exponentially distributed demand per period. Numerical results show this policy also performs superior relative to other policies

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

Base-stock policies for lost-sales models: Aggregation and asymptotics

This paper considers the optimization of the base-stock level for the classical periodic review lost-sales inventory system. The optimal policy for this system is not fully understood and computationally expensive to obtain. Base-stock policies for this system are asymptotically optimal as lost-sales costs approach infinity, easy to implement and prevalent in practice. Unfortunately, the state space needed to evaluate a base-stock policy exactly grows exponentially in both the lead time and the base-stock level. We show that the dynamics of this system can be aggregated into a one-dimensional state space description that grows linearly in the base-stock level only by taking a non-traditional view of the dynamics. We provide asymptotics for the transition probabilities within this single dimensional state space and show that these asymptotics have good convergence properties that are independent of the lead time under mild conditions on the demand distribution. Furthermore, we show that these asymptotics satisfy a certain ow conservation property. These results lead to a new and computationally efficient heuristic to set base-stock levels in lost-sales systems. In a numerical study we demonstrate that this approach performs better than existing heuristics with an average gap with the best base-stock policy of 0.01% across a large test-bed

Optimization of Inventory and Capacity in Large-Scale Assembly Systems Using Extreme-Value Theory

High-tech systems are typically produced in two stages: (1) production of components using specialized equipment and staff and (2) system assembly/integration. Component production capacity is subject to fluctuations, causing a high risk of shortages of at least one component, which results in costly delays. Companies hedge this risk by strategic investments in excess production capacity and in buffer inventories of components. To optimize these, it is crucial to characterize the relation between component shortage risk and capacity and inventory investments. We suppose that component production capacity and produce demand are normally distributed over finite time intervals, and we accordingly model the production system as a symmetric fork-join queueing network with N statistically identical queues with a common arrival process and independent service processes. Assuming a symmetric cost structure, we subsequently apply extreme value theory to gain analytic insights into this optimization problem. We derive several new results for this queueing network, notably that the scaled maximum of N steady-state queue lengths converges in distribution to a Gaussian random variable. These results translate into asymptotically optimal methods to dimension the system. Tests on a range of problems reveal that these methods typically work well for systems of moderate size

Determinación de costo de ventas de la Empresa Inversiones Generales Arotaipe E.I.R.L. en el año 2019

La investigación titulada “Determinación de costos de ventas de la Empresa Inversiones Generales Arotaipe E.I.R.L. en el año 2019” tiene como objetivo analizar y determinar los costos de ventas la Empresa Inversiones Generales Arotaipe E.I.R.L. en el año 2019, se utilizó una metodología descriptiva de tipo aplicada no experimental con corte transaccional además se utilizó la técnica del tratamiento documental debido a que la información a la que se recurrió son documentos contables de la empresa, el estudio llegó a las siguientes conclusiones: De acuerdo a la investigación el análisis de costos de ventas de la empresa Inversiones Generales AROTAIPE E.I.R.L. en el año 2019, determinó que existen elementos tales como las adquisiciones, manejo de inventario inicial y final, costo de ventas propiamente dicho los cuales se encuentran con deficiencias afectando a la rentabilidad de la empresa

Analysing service level agreements with multiple customers.

Within numerous production and distribution environments, maintenance of effective customer service is central to securing competitive benefits. Globalised industries are becoming more commonplace as well, further increasing the competitive pressure. Companies, as a result, are forced to expand product availability and deliver to the demand on schedule. As part of a supply chain, service levels are an important measure of performance in operations management and are widely used to evaluate and manage supplier performance. This thesis examines the SLA for the supplier under two types of contracts to guarantee the agreed customer service level. Specifically, this dissertation will shed light on the two most important (SLA) measurements for inventory systems: fill rate and ready rate. Both SLA measurements are commonly used as performance measures in SLAs between customers and suppliers. Throughout this thesis, we examine performance-based contracts in which the supplier has either: a single customer with a large demand, or multiple customers with a smaller demand. Our experiments were designed so that the demand distribution for the single customer case was similar to the aggregated demand distribution in the multiple customer case. The thesis primarily focused on four main questions, with each question being examined in its own chapter. The first research problem is addressed in Chapter 3. Earlier studies of finite horizon fill rate only consider the situation in which there is a single customer in the supply chain. In Chapter 3, we develop a model to analyse the fill rate distributions for a supplier that has multiple customers, each with its own SLA. In particular, we examine the impacts of performance review period length and the correlation between customer demands on the average fill rate and the probability of overreaching the target fill rate when a supplier has multiple customers. Under the multiple customer contracts, two service policies for demand fulfilment. In the first policy, First-Come-First-Served (FCFS), demand is filled with no prioritization (e.g., in the case of two customers, there is a 50% chance that the first customer is served first). In the second policy, Prioritized Lowest Fill Rate (PLFR), customers are prioritized so that the customer with the highest negative deviation from its target fill rate in the current performance review period is served first. The results and findings in Chapter 3 provide insights that can assist suppliers in the design and negotiation of SLAs. The second research problem is addressed in Chapter 4. Previous studies on the finite horizon fill rate are limited and assume a zero lead time for the supplier. We create a model to examine the impact of different supplier lead times on the finite horizon fill rate, considering either single customer or multiple customers. As lead time exists in reallife supply chains, we explore the effect of various lead times on the fill rate distribution and required base stock over finite horizons with a variety of review period lengths. The results revealed that to fix the long-run fill rate, as the lead time increases, more stock is required; however, the probability of exceeding the target fill rate (the probability of success) increases as the lead time increases. The results indicate that the increase in the probability of success as the lead time increases is higher when the review period is shorter. For the third research problem Chapter 5 presents further results related to the fill rate, an important measure of supply chain performance, specifically ensuring that a customer’s service need is met with maximum reliability. These results mainly concentrate on variability, an aspect that is largely ignored in the literature on fill rate. Related results concerning consistency and asymptotic normality extend the range of application of the fill rate in evaluating reliability and determining the optimal stock level of a supply chain. Chapter 6 explores the fourth research problem which considers the ready rate, a widely used performance measure in SLAs. The ready rate considered in this study is defined as the long-run fraction of periods in which all customer demand is filled immediately from on-hand stock. Previous studies of SLAs have been solely concerned with one supplier serving one customer, whereas in practice, a supplier usually deals with more than one customer. In multiple customer cases, the supplier has an SLA with each customer, and a penalty is incurred whenever the agreement is violated. In this chapter, we create a model to examine the impacts of various factors such as the base-stock level, the type of penalty (lump-sum and linear penalty), and the review period duration on the supplier’s cost function when the supplier deals with multiple customers. The results show that dealing with more customers is preferable for a supplier (assuming the overall demand is the same) and that under a lump-sum penalty contract, a longer performance review is beneficial. Finally, Chapter 7 closes with a brief review, discussion on the models constructed and suggests areas for future studies