Approximating multiple class queueing models with loss models

Multiple class queueing models arise in situations where some flexibility is sought through pooling of demands for different services. Earlier research has shown that most of the benefits of flexibility can be obtained with only a small proportion of cross-trained operators. Predicting the performance of a system with different types of demands and operator pools with different skills is very difficult. We present an approximation method that is based on equivalent loss systems. We successively develop approximations for the waiting probability, The average waiting time and the service level. Our approximations are validated using a series of simulations. Along the way we present some interesting insights into some similarities between queueing systems and equivalent loss systems that have to our knowledge never been reported in the literature.

Measuring the variability in supply chains with the peakedness

This paper introduces a novel way to measure the variability of order flows in supply chains, the peakedness. The peakedness can be used to measure the variability assuming the order flow is a general point pro- cess. We show basic properties of the peakedness, and demonstrate its computation from real-time continuous demand processes, and cumulative demand collected at fixed time intervals as well. We also show that the peakedness can be used to characterize demand, forecast, and inventory variables, to effectively manage the variability. Our results hold for both single stage and multistage inventory systems, and can further be extended to a tree-structured supply chain with a single supplier and multiple retailers. Furthermore, the peakedness can be applied to study traditional inventory problems such as quantifying bullwhip effects and determining safety stock levels. Finally, a numerical study based on real life Belgian supermarket data verifies the effectiveness of the peakedness for measuring the order flow variability, as well as estimating the bullwhip effects.variability, peakedness, supply chain

Planning drinking water for airplanes

The management of the Dutch national airline company KLM intends to bring a sufficient amount of water on board of all flights to fulfill customer’s demand. On the other hand, the surplus of water after a flight should be kept to a minimum to reduce fuel costs. The service to passengers is measured with a service level. The objective of this research is to develop models, which can be used to minimize the amount of water on board of flights such that a predefined service level is met. The difficulty that has to be overcome is the fact that most of the available data of water consumption on flights are rounded off to the nearest eighth of the water tank. For wide-body aircrafts this rounding may correspond to about two hundred litres of water. Part of the problem was also to define a good service level. The use of a service level as a model parameter would give KLM a better control of the water surplus. The available data have been analyzed to examine which aspects we had to take into consideration. Next, a general framework has been developed in which the service level has been defined as a Quality of Service for each flight: The probability that a sufficient amount of water is available on a given flight leg. Three approaches will be proposed to find a probability distribution function for the total water consumption on a flight. The first approach tries to fit a distribution for the water consumption based on the available data, without any assumptions on the underlying shape of the distribution. The second approach assumes normality for the total water consumption on a flight and the third approach uses a binomial distribution. All methods are validated and numerically illustrated. We recommend KLM to use the second approach, where the first approach can be used to determine an upper bound on the water level

Approximating multiple class queueing models

Multiple class queueing models arise in situations where some flexibility is sought through pooling of demands for different services. Earlier research has shown that most of the benefits of flexibility can be obtained with only a small proportion of cross-trained operators. Predicting the performance of a system with different types of demands and operator pools with different skills is very difficult. We present an approximation method that is based on equivalent loss systems. We successively develop approximations for the waiting probability, the average waiting time and the service level. Our approximations are validated using a series of simulations. Along the way we present some interesting insights into some similarities between queueing systems and equivalent loss systems that have to our knowledge never been reported in the literature

Multi-skill queueing models for call centers : approximations and performance optimization

Our main objective in this thesis is to support the management of call centers by developing tools and methods to decide on the number of operators required in a call center. We use existing queueing theory models to analyze call centers with several types of calls. In this context the goal is to find the most efficient configurations, i.e. configurations that achieve the best performance at a minimum cost by combining different sorts of operators. Some can only answer calls of one type, others are skilled to treat calls of different types, but at a greater cost. We propose a Branch and Bound method to find the best combinations of operators while keeping the integrality constraints on the number of operators. The latter constraints matter in small-size call centers. Looking for efficient configurations requires assessing the performance in the models. We propose new methods to estimate the waiting probability, the average waiting time or the service level. These methods exploit the similarities observed in single-skill models between systems with no queue and the same systems with a queue of infinite size. Using Hayward's approximation, that permits to approximate the probability for a call to not be handled in a multi-skill system with no queues, we show how to estimate the performance of the same multi-skill system when blocked calls are put on hold. In the process we also present the peakedness functional. It is a measure of variability of the stochastic flows. We explain how to extract the peakedness from real-life data and to use it in our models. Different applications are proposed.La motivation première de cette thèse est d'aider à la gestion de centres d'appels en développant des outils et des méthodes pour décider du nombre d'agents nécessaires dans le centre d'appels. Concrètement, nous travaillons avec les modèles de théorie des files d'attente existants pour analyser les centres d'appels qui reçoivent des appels de plusieurs types. Dans ce cadre, l'objectif est de trouver les configurations qui permettent d'atteindre la meilleure performance à un moindre coût en combinant des operateurs de plusieurs sortes: certains ne traitent qu'un seul type d'appels, d'autres sont capables de répondre à des appels de plusieurs types. Nous proposons une méthode d'optimisation ``Branch and Bound'' qui conserve l'intégralité de la solution, contrainte importante pour les centres de petite taille. La recherche de configurations efficaces requiert d'être capable de mesurer la performance atteinte dans ces modèles. Nous proposons de nouvelles méthodes pour évaluer les mesures de performance classiques, comme la probabilité de devoir attendre, le temps moyen d'attente ou le niveau de service. Ces méthodes exploitent les similitudes observées dans les modèles avec un seul type d'appels entre les systèmes où il n'y a pas de file d'attente et les systèmes avec une file d'attente de longueur infinie. Grâce à l'approximation d'Hayward, qui permet d'estimer la probabilité qu'un appel ne reçoive pas de réponse quand il n'y a pas de file dans un système avec plusieurs types d'appels, il est possible d'estimer la performance du même système quand les appels bloqués sont mis en attente. Nous présentons aussi la peakedness. Il s'agit d'une mesure de variabilité des processus d'arrivée. Dans cette thèse, nous expliquons comment la peakedness peut être déterminée à partir d'un échantillon d'arrivées et nous montrons plusieurs usages qu'il peut être fait de cette mesure.(IAG 3) -- UCL, 201

Peakedness-based staffing for call center outsourcing

This study considers the staffing problem of a vendor call center in a co-sourcing setting. The aim is to take short-term variability and correlations in time for call arrivals at such a vendor call center into account. To do so, peakedness is proposed as a useful measure of the burstiness in the arrival stream. The study empirically demonstrates the presence of bursty arrivals at a call center and proposes an approach to the measurement of the peakedness of the arrival stream making use of standard call center data. The problematic nature of bursty arrivals in the context of call center co-sourcing is demonstrated along with an asymptotic result establishing that the problem persists in large call centers. The study then analyzes two peakedness-based staffing methods: one which is a well known extension of the square root staffing rule and another which makes use of the Hayward approximation principles. Both approaches are simple and enable the vendor to improve its staffing procedure with good accuracy

Measuring the variability in supply chains with the peakedness

This paper introduces a novel way to measure the variability of order flows in supply chains, the peakedness. The peakedness can be used to measure the variability assuming the order flow is a general point pro- cess. We show basic properties of the peakedness, and demonstrate its computation from real-time continuous demand processes, and cumulative demand collected at fixed time intervals as well. We also show that the peakedness can be used to characterize demand, forecast, and inventory variables, to effectively manage the variability. Our results hold for both single stage and multistage inventory systems, and can further be extended to a tree-structured supply chain with a single supplier and multiple retailers. Furthermore, the peakedness can be applied to study traditional inventory problems such as quantifying bullwhip effects and determining safety stock levels. Finally, a numerical study based on real life Belgian supermarket data verifies the effectiveness of the peakedness for measuring the order flow variability, as well as estimating the bullwhip effects