This paper models a call center as a Markovian queue with multiple servers, where customer balking, impatience, and retrials are modeled explicitly. The resulting queue is analyzed both in a stationary and non-stationary setting. For the stationary setting a fluid approximation is proposed, which overcomes the computational burden of the continuous time markov chain analysis, and which is shown to provide an accurate representation of the system for large call centers with high system load. An insensitivity property of the retrial rate to key system parameters is established. The fluid approximation is shown to work equally well for the nonstationary setting with time varying arrival rates. Using the fluid approximation, the paper explores the retrial phenomenon for a real call center. The model is used to estimate the real arrival rates based on demand data where retrials cannot be distinguished from first time calls. This is a common problem encountered in call centers. Through numerical examples, it is shown that disregarding the retrial phenomenon in call centers can lead to huge distortions in subsequent forecasting and staffing analysis.

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Accurate demand forecasts are essential to the inventory control of spare parts. There is a plethora of statistical methods developed in the academic literature to deal with the forecasting of spare parts demand. These methods belong to the parametric and the non-parametric approaches. Within the second approach, the bootstrapping methods are the most considered ones. Despite that bootstrapping methods have shown a good empirical performance in comparison with their parametric counterparts, none of the available studies highlight the necessity to bring together its related state of knowledge and critically review the relevant research advancements. The present paper bridges this gap by reviewing the literature that deals with the bootstrapping approach and by discussing some of its statistical properties. This yields a better understanding of its framework, and hence, retrieves more robust explanations of the observed mixed-performances of the available bootstrap-based forecasting methods. This paper reviews as well the service level models associated with the bootstrapping approach with an emphasis on the fill rate models.