Design of a network of reusable logistic containers

In this paper, we consider the management of the return flows of empty logistic containers that accumulate at the customer’s sites. These containers must be brought back to the factories in order to sustain future expeditions. We consider a network composed of several factories and several customers in which the return flows are independent of the delivery flows. The models and their solutions aim at finding to which factory the contain- ers have to be brought back and at which frequency. These frequencies directly define the volume of logistic containers to hold in the network. We consider fixed transportation costs depending on the locations of the customers and of the factories and linear holding costs for the inventory of logistic containers. The analysis also provides insight on the benefit of pooling the containers among different customers and/or factories.supply chain management, returnable items, reverse logistic, economic order quantity, network design

A tight bound on the throughput of queueing networks with blocking

In this paper, we present a bounding methodology that allows to compute a tight lower bound on the cycle time of fork--join queueing networks with blocking and with general service time distributions. The methodology relies on two ideas. First, probability masses fitting (PMF) discretizes the service time distributions so that the evolution of the modified network can be modelled by a Markov chain. The PMF discretization is simple: the probability masses on regular intervals are computed and aggregated on a single value in the orresponding interval. Second, we take advantage of the concept of critical path, i.e. the sequence of jobs that covers a sample run. We show that the critical path can be computed with the discretized distributions and that the same sequence of jobs offers a lower bound on the original cycle time. The tightness of the bound is shown on computational experiments. Finally, we discuss the extension to split--and--merge networks and approximate estimations of the cycle time.queueing networks, blocking, throughput, bound, probability masses fitting, critical path.

Probability masses fitting in the analysis of manufacturing flow lines

A new alternative in the analysis of manufacturing systems with finite buffers is presented. We propose and study a new approach in order to build tractable phase-type distributions, which are required by state-of-the-art analytical models. Called "probability masses fitting" (PMF), the approach is quite simple: the probability masses on regular intervals are computed and aggregated on a single value in the corresponding interval, leading to a discrete distribution. PMF shows some interesting properties: it is bounding, monotonic and it conserves the shape of the distribution. After PMF, from the discrete phase-type distributions, state-of-the-art analytical models can be applied. Here, we choose the exactly model the evolution of the system by a Markov chain, and we focus on flow lines. The properties of the global modelling method can be discovered by extending the PMF properties, mainly leading to bounds on the throughput. Finally, the method is shown, by numerical experiments, to compute accurate estimations of the throughput and of various performance measures, reaching accuracy levels of a few tenths of percent.stochastic modelling, flow lines, probability masses fitting, discretization, bounds, performance measures, distributions.

Palaeogenomics of Upper Palaeolithic to Neolithic European hunter-gatherers

: Modern humans have populated Europe for more than 45,000 years1,2. Our knowledge of the genetic relatedness and structure of ancient hunter-gatherers is however limited, owing to the scarceness and poor molecular preservation of human remains from that period3. Here we analyse 356 ancient hunter-gatherer genomes, including new genomic data for 116 individuals from 14 countries in western and central Eurasia, spanning between 35,000 and 5,000 years ago. We identify a genetic ancestry profile in individuals associated with Upper Palaeolithic Gravettian assemblages from western Europe that is distinct from contemporaneous groups related to this archaeological culture in central and southern Europe4, but resembles that of preceding individuals associated with the Aurignacian culture. This ancestry profile survived during the Last Glacial Maximum (25,000 to 19,000 years ago) in human populations from southwestern Europe associated with the Solutrean culture, and with the following Magdalenian culture that re-expanded northeastward after the Last Glacial Maximum. Conversely, we reveal a genetic turnover in southern Europe suggesting a local replacement of human groups around the time of the Last Glacial Maximum, accompanied by a north-to-south dispersal of populations associated with the Epigravettian culture. From at least 14,000 years ago, an ancestry related to this culture spread from the south across the rest of Europe, largely replacing the Magdalenian-associated gene pool. After a period of limited admixture that spanned the beginning of the Mesolithic, we find genetic interactions between western and eastern European hunter-gatherers, who were also characterized by marked differences in phenotypically relevant variants

Palaeogenomics of Upper Palaeolithic to Neolithic European hunter-gatherers

Publisher Copyright: © 2023, The Author(s).Modern humans have populated Europe for more than 45,000 years1,2. Our knowledge of the genetic relatedness and structure of ancient hunter-gatherers is however limited, owing to the scarceness and poor molecular preservation of human remains from that period3. Here we analyse 356 ancient hunter-gatherer genomes, including new genomic data for 116 individuals from 14 countries in western and central Eurasia, spanning between 35,000 and 5,000 years ago. We identify a genetic ancestry profile in individuals associated with Upper Palaeolithic Gravettian assemblages from western Europe that is distinct from contemporaneous groups related to this archaeological culture in central and southern Europe4, but resembles that of preceding individuals associated with the Aurignacian culture. This ancestry profile survived during the Last Glacial Maximum (25,000 to 19,000 years ago) in human populations from southwestern Europe associated with the Solutrean culture, and with the following Magdalenian culture that re-expanded northeastward after the Last Glacial Maximum. Conversely, we reveal a genetic turnover in southern Europe suggesting a local replacement of human groups around the time of the Last Glacial Maximum, accompanied by a north-to-south dispersal of populations associated with the Epigravettian culture. From at least 14,000 years ago, an ancestry related to this culture spread from the south across the rest of Europe, largely replacing the Magdalenian-associated gene pool. After a period of limited admixture that spanned the beginning of the Mesolithic, we find genetic interactions between western and eastern European hunter-gatherers, who were also characterized by marked differences in phenotypically relevant variants.Peer reviewe

The bounding discrete phase-type method

Models of production systems have always been essential. They are needed at a strategic level in order to guide the design of production systems but also at an operational level when, for example, the daily load and staffing have to be chosen. Models can be classified into three categories: analytical, simulative and approximate. In this paper, we propose an approximation approach that works as follows. Each arrival or service distribution is discretized using the same time step. The evolution of the production system can then be described by a Markov chain. The performances of the production system can then be estimated from the analysis of the Markov chain. The way the discretization is carried on determines the properties of the results. In this paper, we investigate the 'grouping at the end' discretization method and, in order to fix ideas, in the context of production lines. In this case, upper and lower bounds on the throughput can be derived. Furthermore, the distance between these bounds is proved to be related to the time step used in the discretization. They are thus refinable and their precision can be evaluated a priori. All these results are proved using the concept of critical path of a production run. Beside the conceptual contribution of this paper, the method has been successfully applied to a line with three stations in which three buffer spaces have to be allocated. Nevertheless, the complexity and solution aspects will require further attention before making the method eligible for real largescale problems

Iterative Algorithms for Large Stochastic Matrices

Markov chains have always constituted an efficient tool to model discrete systems. Many performance criteria for discrete systems can be derived from the steady-state probability vector of the associated Markov chain. However, the large size of the state space of the Markov chain often allows this vector to be determined by iterative methods only. Various iterative methods exist, but none can be proved a priori to be the best. In this paper, we propose a practical measure which allows the convergence rate of the various existing methods to be compared. This measure is an approximation of the modulus of the second largest eigenvalue of the iteration matrix and can be determined a priori. The model of a queueing network is used as an example to compare the convergence of several iterative methods and to show the accuracy of the measure

Monotone Iterative Methods for Markov-chains

This paper deals with monotone iterative methods for the computation of the steady-state probability vector of irreducible Markov chains. The emphasis is laid on verification techniques aiming at deriving, from an approximation, true bounds on the solution

Refinable Bounds for Large Markov-chains

A method to bound the steady-state solution of large Markov chains is presented. It integrates the concepts of eigenvector polyhedron and of aggregation and is iterative in nature. The bounds are obtained by considering a subset only of the system state space. This makes the method specially attractive for problems which are too large to be dealt with by traditional methods. The quality of the bounds depends on the locality of the system which is studied: when the system spends most of its time in a small subset of states, tight bounds can be obtained by considering this subset only. Finally, the bounds are refinable in the sense that the tightness of the bounds can be improved by enlarging the subset of states which is considered. The method is illustrated on a model of a repairable fault-tolerant system with 16 million states. Tight bounds on its availability are obtained by considering less than 0.1 percent of its state space

Probability masses fitting in the analysis of manufacturing flow lines

A new alternative in the analysis of manufacturing systems with finite buffers is presented. We propose and study a new approach in order to build tractable phase-type distributions, which are required by state-of the- art analytical models. Called "probability masses fitting" (PMF), the approach is quite simple: the probability masses on regular intervals are computed and aggregated on a single value in the corresponding interval, leading to a discrete distribution. PMF shows some interesting properties: it is bounding, monotonic and it conserves the shape of the distribution. After PMF, from the discrete phase-type distributions, state-of-the-art analytical models can be applied. Here, we choose the exactly model the evolution of the system by a Markov chain, and we focus on flow lines. The properties of the global modelling method can be discovered by extending the PMF properties, mainly leading to bounds on the throughput. Finally, the method is shown, by numerical experiments, to compute accurate estimations of the throughput and of various performance measures, reaching accuracy levels of a few tenths of percent