Ester Guijarro

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

The 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.

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

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.

On the Impact of Undershoots at Order Point in the Fill Rate Estimation in Continuous Review Policies for the Lost Sales Case

The fill rate is usually computed by using the traditional approach, which calculates it as the complement of the quotient between the expected unfulfilled demand and the expected demand per replenishment cycle. However, when dealing with continuous review the common derivation of the order point, order quantity (s, Q) policy simplify the computation of the expected unfulfilled demand per replenishment cycle by means of neglecting undershoots at order point s. This paper shows, by means of some illustrative examples and using simulation, how neglecting undershoots at s introduces a significant bias on the estimation of the fill rate. The fill rate is systematically overestimated by the traditional approach. Practical implication of this performance leads to design policies that are less protected than managers may expect. This paper focuses on the lost sales case and discrete demands.

Transversal Competences Acquisition by Assigning Collaborative Work Group Roles

Valencia Polytechnic University (UPV) is innovative as far as its training and evaluation considerations are concerned. It has introduced the project “Incorporating transversal competences into UPV graduates’ curriculum” as a strategic challenge, which promotes the training and assessment of transversal competences in several UPV degrees. This work presents an innovative group work experience by assigning roles in preparing a portfolio. Students participate in team work by playing a role whose tasks and competences are previously determined by the teacher, who also describes the role and its competency profile. Students participate in the portfolio by playing the role that they are committed to and co-assess it by a performance assessment system designed in the group. The main work conclusions drawn are that this innovative classroom-based strategy motivates students, helps organise group work and encourages collaborative learning.

A Reference Framework to Design Inventory Policies Using a Fill Rate Criterion in Lost Sales Contexts

This paper suggests a reference framework to decide the best method to compute the base stock level in a lost sales and discrete demand context given a target fill rate. Under this context, only (Guijarro et al. in Eur J Oper Res 218(2):442–447, 2012a) propose an exact fill rate expression, but it requires a huge computational effort. However, the literature shows several approximations which are simpler and easier to implement in practical environments. In this paper, we design a large experiment and analyze by means of data mining techniques under which conditions approximate expressions can provide an accurate enough approximation to the base stock level for the lost sales case. As a result, we propose a reference framework that allows the selection of the most suitable method to compute the base stock depending on the characteristics of the item.

An Experience in Teaching Innovation Based on Collaborative Learning and the Aronson Jigsaw Technique

Jigsaw technique is a collaborative learning technique that can be used as an alternative to conventional teaching methods. Basically this technique boosts group work cohesion since each member of the group is in charge of one part of the learning objective of the whole group. This work shows the experience of using the jigsaw technique in an undergraduate course named “Innovation and Competitiveness”. The learning objective of the activity consists of highlighting the most important ideas of the “Oslo Manual” which is a reference manual in innovation concepts. The process is divided into five steps: (1) initial groups of five students are formed; (2) professor gives five parts of the “Oslo Manual” and the group decides which member will be the “expert” of each part; (3) experts of each part work together to understand and summarize main concepts; (4) experts come back to the initial group and transmit their expertise to the rest of the group; (5) professor asks for a “one minute question” regarding one concept or idea of the Manual. Results from this experience show that students feel that they are not only responsible for their own learning but also for the learning of the rest of the group. The inclusion of the “one minute question” after the process further enhances this feeling. Furthermore, it is known that sharing our knowledge with other people requires a deep understanding of the topic. As a conclusion, this experience improves not only the self-confidence of the student, but also the communicative competence and group work performance whilst students work and assess important concepts related to the course.

ABC classification of spare parts considering costs and service

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.

Optimal multi-item fill rate determination for spare parts

We consider four existing methods in order to determine individual fill rates when a global target fill rate has been established. Given the drawbacks of these approaches, needing numerical optimization and especially unsuitable in the context of spare parts, we present a new approach which provide a closed form formula more focused on the characteristics of these items. This novel approach is validated with a dataset of spare parts of an airline company and outperforms the previous methods. Extensions of our results are also indicated.

On the selection of fill rate estimation method to determine the optimal base stock in periodic review systems

The fill rate is defined as the fraction of demand that is directly satisfied with the on-hand stock. Despite its definition is apparently simple, in the literature we find different interpretations and consequently different methods to compute it. In the majority of related works, the fill rate is computed by using the traditional approximation, which calculates the fill rate in terms of units short instead of computing directly the satisfied demand. However, the traditional approximation can lead to underestimate the real value of the fill rate under some conditions. The underestimation behaviour has important consequences when the optimal parameters of the policy are determined applying the traditional approach. However, in the literature the majority of authors derive approximate expressions to compute the fill rate based on it. This paper assesses when approximate methods provide accurate results when the stock level is defined given a target fill rate in periodic review systems. We design a large experiment and analyze the results using statistical techniques. The main result of this work can be used as a reference framework to help managers to decide the most efficient method to determine the stock level given a target fill rate.

Fill Rate in a Periodic Review Base Stock System Under Discrete Distributed Demand for the Backordering Case

The fill rate is the fraction of demand that is satisfied directly from shelf. In the literature, this service metric is usually computed by using the traditional approach, 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 directly the expected fraction of fulfilled demand. Furthermore the available methods to estimate the fill rate apply only under specific demand conditions. This paper shows the research gap regarding the estimation procedures to compute the fill rate and suggests: (1) a new exact procedure to compute the traditional approximation for any discrete demand distribution; and (2) a new method to compute the fill rate directly as the fraction of fulfilled demand for any discrete demand distribution. Simulation results show that the latter methods outperform the traditional approach, which underestimates the simulated fill rate, over different demand patterns. This paper focuses on the traditional periodic review, base stock system when backlogged demands are allowed.