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.

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.

How stochasticity and emergencies disrupt the surgical schedule

In health care system, the operating theatre is recognized as having an important role, notably in terms of generated income and cost. Its management, and in particular its scheduling, is thus a critical activity, and has been the sub ject of many studies. However, the stochasticity of the operating theatre environment is rarely considered while it has considerable effect on the actual working of a surgical unit. In practice, the planners keep a safety margin, let’s say 15% of the capacity, in order to absorb the effect of unpredictable events. However, this safety margin is most often chosen sub jectively, from experience. In this paper, our goal is to rationalize this process. We want to give insights to managers in order to deal with the stochasticity of their environment, at a tactical–strategic decision level. For this, we propose an analytical approach that takes account of the stochastic operating times as well as the disruptions caused by emergency arrivals. From our model, various performance measures can be computed: the emergency disruption rate, the waiting time for an emergency, the distribution of the working time, the probability of overtime, the average overtime, etc. In particular, our tool is able to tell how many operations can be scheduled per day in order to keep the overtime limited.health care, surgical schedule, emergencies, Markov chain.

Programming Integrated Surgical Operations and Preventive Maintenance Activities

Part 2: Knowledge-Based ServicesInternational audienceThe operating theatre (OT) represents a significant component of the technical means centre. This facility is the largest cost and revenue centre. To be efficient, it needs an optimal operational pro- gramme, which takes into account maintenance activi- ties and not only surgical operations. To build such a programme, various methods have been used: mixed integer programming (MIP), three classic heuristics for Bin-Packing and a coupling of the first alterna- tive with a stochastic descent (SD). Then we compare the obtained results from generated data

Balancing partner preferences for logistics costs and carbon footprint in a horizontal cooperation

Horizontal cooperation in logistics has gathered momentum in the last decade as a way to reach economic as well as environmental benefits. In the literature, these benefits are most often assessed through aggregation of demand and supply chain optimization of the partnership as a whole. However, such an approach ignores the individual preferences of the participating companies and forces them to agree on a unique coalition objective. Companies with different (potentially conflicting) preferences could improve their individual outcome by diverging from this joint solution. To account for companies preferences, we propose an optimization framework that integrates the individual partners’ interests directly in a cooperative model. The partners specify their preferences regarding the decrease of logistical costs versus reduced CO2 emissions. Doing so, all stakeholders are more likely to accept the solution, and the long-term viability of the collaboration is improved. First, we formulate a multi-objective, multi-partner location-inventory model. Second, we distinguish two approaches for solving it, each focusing primarily on one of these two dimensions. The result is a set of Pareto-optimal solutions that support the decision and negotiation process. Third, we propose and compare three different approaches to construct a unique solution which is fair and efficient for the coalition. Extensive numerical results not only confirm the potential of collaboration but, more importantly, also reveal valuable managerial insights on the effect of dissimilarities between partners with respect to size, geographical overlap and operational preferences

Tricaesium tris­(pyridine-2,6-dicarboxyl­ato-κ3 O 2,N,O 6)lutetium(III) octa­hydrate

Colourless block crystals of the title compound, Cs3[Lu(dipic)3]·8H2O [dipic is dipicolinate or pyridine-2,6-dicarboxyl­ate, C7H3NO4] were synthesized by slow evaporation of the solvent. The crystal structure of this LuIII-complex, isostructural with the DyIII and EuIII complexes, was determined from a crystal twinned by inversion and consists of discrete [Lu(dipic)3]3− anions, Cs+ cations and water mol­ecules involving hydrogen bonding. The Lu atom lies on a twofold rotation axis and is coordinated by six O atoms and three N atoms of three dipicolinate ligands. One Cs atom is also on a twofold axis. The unit cell can be regarded as successive layers along the crystallographic c-axis formed by [Lu(dipic)3]3− anionic planes and [Cs+, H2O] cationic planes. In the crystal structure, although the H atoms attached to water mol­ecules could not be located, short O—O contacts clearly indicate the occurrence of an intricate hydrogen-bonded network through contacts with other water mol­ecules, Cs cations or with the O atoms of the dipicolinate ligands

Analysis of the influence of different real flow effects on computational fluid dynamics boundary conditions based on the method of characteristics

Nowadays, turbocharged internal combustion engines (ICEs) are very common in automotive powerplants, monopolizing the Diesel sector and having a steadily increasing percentage in the gasoline one. In this frame, the interest in modeling the behavior of the turbomachinery components involved, with the ultimate goal of characterizing the performance of the turbocharged ICE, seems clear. A turbomachine can be simulated using 3D-CFD software, but its computational cost does not allow to reproduce the whole turbocharger test rig. Moreover, the existence of long ducts requires a considerable computational time until the pressure reflections at the boundaries dissipate in order to reach a periodic solution. The use of non-reflecting boundary conditions reduces the needed length of ducts without introducing spurious wave reflections. An anechoic boundary condition (BC) based on the Method of Characteristics has been previously developed, considering the case of an inviscid and adiabatic 1D flow of a perfect gas. However, real flows do not behave in such ideal manner. In this paper, the extension of the scope of the previous BC is sought. In this way, a methodology to evaluate the performance of the anechoic BC under these real flow situations is shown. The consideration of ideal gas instead of perfect gas, the flow viscosity and the non-homentropic flow makes it necessary to modify the Method of Characteristics, since the Riemann Invariants are not constant any more. In this frame they are referred to as Riemann Variables. An additional issue that has been considered is the effect of swirl flow, as the one in the turbine outlet, on the anechoic BC. Some improvements to be implemented in the BC are proposed in order to have a better performance in these real flow situations.Galindo, J.; Tiseira Izaguirre, AO.; Fajardo, P.; Navarro García, R. (2013). Analysis of the influence of different real flow effects on computational fluid dynamics boundary conditions based on the method of characteristics. Mathematical and Computer Modelling. 57(7-8):1957-1964. doi:10.1016/j.mcm.2012.01.016S19571964577-

Uncertainties in power computations in a turbocharger test bench

A specific study of the uncertainties of turbine power output measured in turbocharger test benches is presented using the law of uncertainty propagation and the influence of the different terms that contribute to it is shown. Then, non-linear mixed integer mathematical programming algorithms used with the turbine power uncertainty expression become an essential tool to overcome the problem of selection new sensors to improve an existing test rig or to contribute to a new one. A method of optimisation is presented for two different scenarios: first, where the maximum cost is a constraint; second where the maximum uncertainty is a constraint and the total cost is minimised. When using a large transducers database, computational efforts may be reduced by solving the relaxed non-integer problem by means of sequential quadratic programming and then probing the ceilings and floors of the parameters to get an optimum approximation with low costs. A comparison between the linear uncertainty propagation model and Monte Carlo simulations is also presented, only showing benefits of the later method when computing high order statistical moments of the turbine power output probability distribution.This work has been partially supported by the Spanish Ministerio de Ciencia e Innovacion through Grant No. DPI2010-20891-C02-02 and by the Spanish Ministerio de Economia y Competitividad through Grant No. TRA2012-36954.Olmeda González, PC.; Tiseira Izaguirre, AO.; Dolz Ruiz, V.; García-Cuevas González, LM. (2015). Uncertainties in power computations in a turbocharger test bench. Measurement. 59:363-371. https://doi.org/10.1016/j.measurement.2014.09.055S3633715