Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: the Infinite Horizon Case

We analyze an infinite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are identically distributed random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to maximize expected discounted, or expected average profit over the infinite planning horizon. We show that a stationary (s,S,p) policy is optimal for both the discounted and average profit models with general demand functions. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period.

Synapsing variable length crossover: An algorithm for crossing and comparing variable length genomes

The Synapsing Variable Length Crossover (SVLC) algorithm provides a biologically inspired method for performing meaningful crossover between variable length genomes. In addition to providing a rationale for variable length crossover it also provides a genotypic similarity metric for variable length genomes enabling standard niche formation techniques to be used with variable length genomes. Unlike other variable length crossover techniques which consider genomes to be rigid inflexible arrays and where some or all of the crossover points are randomly selected, the SVLC algorithm considers genomes to be flexible and chooses non-random crossover points based on the common parental sequence similarity. The SVLC Algorithm recurrently "glues" or synapses homogenous genetic sub-sequences together. This is done in such a way that common parental sequences are automatically preserved in the offspring with only the genetic differences being exchanged or removed, independent of the length of such differences. In a variable length test problem the SVLC algorithm is shown to outperform current variable length crossover techniques. The SVLC algorithm is also shown to work in a more realistic robot neural network controller evolution application.

Synapsing variable-length crossover: Meaningful crossover for variable-length genomes

The synapsing variable-length crossover (SVLC algorithm provides a biologically inspired method for performing meaningful crossover between variable-length genomes. In addition to providing a rationale for variable-length crossover, it also provides a genotypic similarity metric for variable-length genomes, enabling standard niche formation techniques to be used with variable-length genomes. Unlike other variable-length crossover techniques which consider genomes to be rigid inflexible arrays and where some or all of the crossover points are randomly selected, the SVLC algorithm considers genomes to be flexible and chooses non-random crossover points based on the common parental sequence similarity. The SVLC algorithm recurrently "glues" or synapses homogenous genetic subsequences together. This is done in such a way that common parental sequences are automatically preserved in the offspring with only the genetic differences being exchanged or removed, independent of the length of such differences. In a variable-length test problem, the SVLC algorithm compares favorably with current variable-length crossover techniques. The variable-length approach is further advocated by demonstrating how a variable-length genetic algorithm (GA) can obtain a high fitness solution in fewer iterations than a traditional fixed-length GA in a two-dimensional vector approximation task.

Simulating the interannual variability of major dust storms on Mars using variable lifting thresholds

The redistribution of a finite amount of martian surface dust during global dust storms and in the intervening periods has been modelled in a dust lifting version of the UK Mars General Circulation Model. When using a constant, uniform threshold in the model’s wind stress lifting parameterisation and assuming an unlimited supply of surface dust, multiannual simulations displayed some variability in dust lifting activity from year to year, arising from internal variability manifested in surface wind stress, but dust storms were limited in size and formed within a relatively short seasonal window. Lifting thresholds were then allowed to vary at each model gridpoint, dependent on the rates of emission or deposition of dust. This enhanced interannual variability in dust storm magnitude and timing, such that model storms covered most of the observed ranges in size and initiation date within a single multiannual simulation. Peak storm magnitude in a given year was primarily determined by the availability of surface dust at a number of key sites in the southern hemisphere. The observed global dust storm (GDS) frequency of roughly one in every 3 years was approximately reproduced, but the model failed to generate these GDSs spontaneously in the southern hemisphere, where they have typically been observed to initiate. After several years of simulation, the surface threshold field—a proxy for net change in surface dust density—showed good qualitative agreement with the observed pattern of martian surface dust cover. The model produced a net northward cross-equatorial dust mass flux, which necessitated the addition of an artificial threshold decrease rate in order to allow the continued generation of dust storms over the course of a multiannual simulation. At standard model resolution, for the southward mass flux due to cross-equatorial flushing storms to offset the northward flux due to GDSs on a timescale of ∼3 years would require an increase in the former by a factor of 3–4. Results at higher model resolution and uncertainties in dust vertical profiles mean that quasi-periodic redistribution of dust on such a timescale nevertheless appears to be a plausible explanation for the observed GDS frequency.

The potential of flood forecasting using a variable-resolution global Digital Terrain Model and flood extents from Synthetic Aperture Radar images

A basic data requirement of a river flood inundation model is a Digital Terrain Model (DTM) of the reach being studied. The scale at which modeling is required determines the accuracy required of the DTM. For modeling floods in urban areas, a high resolution DTM such as that produced by airborne LiDAR (Light Detection And Ranging) is most useful, and large parts of many developed countries have now been mapped using LiDAR. In remoter areas, it is possible to model flooding on a larger scale using a lower resolution DTM, and in the near future the DTM of choice is likely to be that derived from the TanDEM-X Digital Elevation Model (DEM). A variable-resolution global DTM obtained by combining existing high and low resolution data sets would be useful for modeling flood water dynamics globally, at high resolution wherever possible and at lower resolution over larger rivers in remote areas. A further important data resource used in flood modeling is the flood extent, commonly derived from Synthetic Aperture Radar (SAR) images. Flood extents become more useful if they are intersected with the DTM, when water level observations (WLOs) at the flood boundary can be estimated at various points along the river reach. To illustrate the utility of such a global DTM, two examples of recent research involving WLOs at opposite ends of the spatial scale are discussed. The first requires high resolution spatial data, and involves the assimilation of WLOs from a real sequence of high resolution SAR images into a flood model to update the model state with observations over time, and to estimate river discharge and model parameters, including river bathymetry and friction. The results indicate the feasibility of such an Earth Observation-based flood forecasting system. The second example is at a larger scale, and uses SAR-derived WLOs to improve the lower-resolution TanDEM-X DEM in the area covered by the flood extents. The resulting reduction in random height error is significant.

Non-random reef use by fishes at two dominant zones in a tropical, algal-dominated coastal reef

Habitat use and the processes which determine fish distribution were evaluated at the reef flat and reef crest zones of a tropical, algal-dominated reef. Our comparisons indicated significant differences in the majority of the evaluated environmental characteristics between zones. Also, significant differences in the abundances of twelve, from thirteen analyzed species, were observed within and between-sites. According to null models, non-random patterns of species co-occurrences were significant, suggesting that fish guilds in both zones were non-randomly structured. Unexpectedly, structural complexity negatively affected overall species richness, but had a major positive influence on highly site-attached species such as a damselfish. Depth and substrate composition, particularly macroalgae cover, were positive determinants for the fish assemblage structure in the studied reef, prevailing over factors such as structural complexity and live coral cover. Our results are conflicting with other studies carried out in coral-dominated reefs of the Caribbean and Pacific, therefore supporting the idea that the factors which may potentially influence reef fish composition are highly site-dependent and variable.

Disentangling static and dynamic effects of low breakup threshold in fusion reactions

A new technique to analyze fusion data is developed. From experimental cross sections and results of coupled-channel calculations a dimensionless function is constructed. In collisions of strongly bound nuclei this quantity is very close to a universal function of a variable related to the collision energy, whereas for weakly bound projectiles the effects of breakup coupling are measured by the deviations with respect to this universal function. This technique is applied to collisions of stable and unstable weakly bound isotopes.

Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009

A data driven approach for automating vehicle activated signs

Vehicle activated signs (VAS) display a warning message when drivers exceed a particular threshold. VAS are often installed on local roads to display a warning message depending on the speed of the approaching vehicles. VAS are usually powered by electricity; however, battery and solar powered VAS are also commonplace. This thesis investigated devel-opment of an automatic trigger speed of vehicle activated signs in order to influence driver behaviour, the effect of which has been measured in terms of reduced mean speed and low standard deviation. A comprehen-sive understanding of the effectiveness of the trigger speed of the VAS on driver behaviour was established by systematically collecting data. Specif-ically, data on time of day, speed, length and direction of the vehicle have been collected for the purpose, using Doppler radar installed at the road. A data driven calibration method for the radar used in the experiment has also been developed and evaluated. Results indicate that trigger speed of the VAS had variable effect on driv-ers’ speed at different sites and at different times of the day. It is evident that the optimal trigger speed should be set near the 85th percentile speed, to be able to lower the standard deviation. In the case of battery and solar powered VAS, trigger speeds between the 50th and 85th per-centile offered the best compromise between safety and power consump-tion. Results also indicate that different classes of vehicles report differ-ences in mean speed and standard deviation; on a highway, the mean speed of cars differs slightly from the mean speed of trucks, whereas a significant difference was observed between the classes of vehicles on lo-cal roads. A differential trigger speed was therefore investigated for the sake of completion. A data driven approach using Random forest was found to be appropriate in predicting trigger speeds respective to types of vehicles and traffic conditions. The fact that the predicted trigger speed was found to be consistently around the 85th percentile speed justifies the choice of the automatic model.

Mapping an uncertainty zone between interpolated types of a categorical variable

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

AATS for the (X)over-bar chart with variable parameters

A Fortran computer program is given for the computation of the adjusted average time to signal, or AATS, for adaptive (X) over bar charts with one, two, or all three design parameters variable: the sample size, n, the sampling interval, h, and the factor k used in determining the width of the action limits. The program calculates the threshold limit to switch the adaptive design parameters and also provides the in-control average time to signal, or ATS.

X̄ charts with variable sample size

The usual practice in using a control chart to monitor a process is to take samples of size n from the process every h hours. This article considers the properties of the X̄ chart when the size of each sample depends on what is observed in the preceding sample. The idea is that the sample should be large if the sample point of the preceding sample is close to but not actually outside the control limits and small if the sample point is close to the target. The properties of the variable sample size (VSS) X̄ chart are obtained using Markov chains. The VSS X̄ chart is substantially quicker than the traditional X̄ chart in detecting moderate shifts in the process.

AATS for the X̄ Chart with Variable Parameters

A Fortran computer program is given for the computation of the adjusted average time to signal, or AATS, for adaptive X̄ charts with one, two, or all three design parameters variable: the sample size, n, the sampling interval, h, and the factor k used in determining the width of the action limits. The program calculates the threshold limit to switch the adaptive design parameters and also provides the in-control average time to signal, or ATS.

Upconversion ultraviolet random lasing in Nd 3+ doped fluoroindate glass powder

An upconversion random laser (RL) operating in the ultraviolet is reported for Nd 3+ doped fluoroindate glass powder pumped at 575 nm. The RL is obtained by the resonant excitation of the Nd 3+ state 2G 7/2 followed by energy transfer among two excited ions such that one ion in the pair decays to a lower energy state and the other is promoted to state 4D 7/2 from where it decays emitting light at 381 nm. The RL threshold of 30 kW/cm 2 was determined by monitoring the photoluminescence intensity as a function of the pump laser intensity. The RL pulses have time duration of 29 ns that is 50 times smaller than the decay time of the upconversion signal when the sample is pumped with intensities below the RL laser threshold. © 2011 Optical Society of America.

Random laser action from flexible biocellulose-based device

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)