Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations

In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements

Patterns of dissolved organic carbon and nitrogen fluxes in deciduous and coniferous forests under historic high nitrogen deposition

Numerous recent studies have indicated that dissolved organic carbon (DOC) and nitrogen (DON) play an important role in C and N cycling in natural ecosystems, and have shown that N deposition alters the concentrations and fluxes of dissolved organic substances and may increase leaching losses from forests. Our study was set up to accurately quantify concentrations and flux patterns of DOC, DON and dissolved inorganic nitrogen (DIN) in deciduous and coniferous forest in Flanders, Belgium, under historical high nitrogen deposition. We measured DOC, DON and DIN concentrations at two weekly intervals in a silver birch (SB) stand, a corsican pine (CP) stand and a pine stand with higher N deposition (CPN), and used the SWAP model (calibrated with PEST) for generating accurate water and matter fluxes. The input with precipitation was an important source of DON, but not for DOC. Release of DOC from the forest floor was minimally affected by forest type, but higher N deposition (CPN stand) caused an 82% increase of DOC release from the forest floor. Adsorption to mineral soil material rich in iron and/or aluminum oxyhydroxides was suggested to be the most important process removing DOC from the soil solution, responsible for substantial retention (67–84%) of DOC entering the mineral soil profile with forest floor leachate. Generally, DON was less reactive (i.e. less removal from the soil solution) than DOC, resulting in decreasing DOC/DON ratios with soil depth. We found increased DOC retention in the mineral soil as a result of higher N deposition (84 kg ha−1 yr−1 additional DOC retention in CPN compared to CP). Overall DON leaching losses were 2.2, 3.3 and 5.0 kg N yr−1 for SB, CP and CPN, respectively, contributing between 9–28% to total dissolved N (TDN) leaching. The relative contribution to TDN leaching from DON loss from SB and CP was mainly determined by (large) differences in DIN leaching. The large TDN leaching losses are alarming, especially in the CPN stand that was N saturated

Piecewise linear approximations of the standard normal first order loss function

The first order loss function and its complementary function are extensively used in practical settings. When the random variable of interest is normally distributed, the first order loss function can be easily expressed in terms of the standard normal cumulative distribution and probability density function. However, the standard normal cumulative distribution does not admit a closed form solution and cannot be easily linearised. Several works in the literature discuss approximations for either the standard normal cumulative distribution or the first order loss function and their inverse. However, a comprehensive study on piecewise linear upper and lower bounds for the first order loss function is still missing. In this work, we initially summarise a number of distribution independent results for the first order loss function and its complementary function. We then extend this discussion by focusing first on random variable featuring a symmetric distribution, and then on normally distributed random variables. For the latter, we develop effective piecewise linear upper and lower bounds that can be immediately embedded in MILP models. These linearisations rely on constant parameters that are independent of the mean and standard deviation of the normal distribution of interest. We finally discuss how to compute optimal linearisation parameters that minimise the maximum approximation error.Comment: 22 pages, 7 figures, working draf

Can the Solar Wind be Driven by Magnetic Reconnection in the Sun's Magnetic Carpet?

The physical processes that heat the solar corona and accelerate the solar wind remain unknown after many years of study. Some have suggested that the wind is driven by waves and turbulence in open magnetic flux tubes, and others have suggested that plasma is injected into the open tubes by magnetic reconnection with closed loops. In order to test the latter idea, we developed Monte Carlo simulations of the photospheric "magnetic carpet" and extrapolated the time-varying coronal field. These models were constructed for a range of different magnetic flux imbalance ratios. Completely balanced models represent quiet regions on the Sun and source regions of slow solar wind streams. Highly imbalanced models represent coronal holes and source regions of fast wind streams. The models agree with observed emergence rates, surface flux densities, and number distributions of magnetic elements. Despite having no imposed supergranular motions, a realistic network of magnetic "funnels" appeared spontaneously. We computed the rate at which closed field lines open up (i.e., recycling times for open flux), and we estimated the energy flux released in reconnection events involving the opening up of closed flux tubes. For quiet regions and mixed-polarity coronal holes, these energy fluxes were found to be much lower than required to accelerate the solar wind. For the most imbalanced coronal holes, the energy fluxes may be large enough to power the solar wind, but the recycling times are far longer than the time it takes the solar wind to accelerate into the low corona. Thus, it is unlikely that either the slow or fast solar wind is driven by reconnection and loop-opening processes in the magnetic carpet.Comment: 25 pages (emulateapj style), 13 figures, ApJ, in pres

Testing a Predictive Theoretical Model for the Mass Loss Rates of Cool Stars

The basic mechanisms responsible for producing winds from cool, late-type stars are still largely unknown. We take inspiration from recent progress in understanding solar wind acceleration to develop a physically motivated model of the time-steady mass loss rates of cool main-sequence stars and evolved giants. This model follows the energy flux of magnetohydrodynamic turbulence from a subsurface convection zone to its eventual dissipation and escape through open magnetic flux tubes. We show how Alfven waves and turbulence can produce winds in either a hot corona or a cool extended chromosphere, and we specify the conditions that determine whether or not coronal heating occurs. These models do not utilize arbitrary normalization factors, but instead predict the mass loss rate directly from a star's fundamental properties. We take account of stellar magnetic activity by extending standard age-activity-rotation indicators to include the evolution of the filling factor of strong photospheric magnetic fields. We compared the predicted mass loss rates with observed values for 47 stars and found significantly better agreement than was obtained from the popular scaling laws of Reimers, Schroeder, and Cuntz. The algorithm used to compute cool-star mass loss rates is provided as a self-contained and efficient computer code. We anticipate that the results from this kind of model can be incorporated straightforwardly into stellar evolution calculations and population synthesis techniques.Comment: 23 pages (emulateapj style), 14 figures, ApJ, in press. A brief IDL subroutine that implements the model described in this paper will be distributed as "online-only material," and this code is also available at http://www.cfa.harvard.edu/~scranmer/cranmer_data.htm