Production inventory with service time and interruptions

This paper considers an (s,S) production inventory system with positive service time, with time for producing each item following Erlang distribution. Customers arrive according to a Poisson process. A customer who arrives when there is no inventory in the system is considered lost. On the other hand, a customer who finds a busy server with at least one inventory in the system joins a queue of infinite capacity. When the inventory level falls to s, production process is switched on, and it is switched off when the inventory level reaches back to S. Service time to each customer also follows an Erlang distribution. The service of a customer may be interrupted, where the time for such a phenomenon follows an exponential distribution, whenever it occurs. An interrupted service, after repair, resumes from where it was stopped. The correction/repair time follows an exponential distribution. We assume that the service of a single customer may encounter any number of interruptions and that the customer being served waits there until his service is completed. Moreover, at a time the server is subject to at most one interruption. We also assume that no inventory is lost due to a service interruption. Like the service process, the production process also is subject to interruptions, where the duration to an interruption follows an exponential distribution. However, in contrast to the service interruption, in the case of interruption to production process, we assume that the item being processed is lost because of interruption. That is, the production process, on being interrupted, restarts from the beginning, after repair. The repair time of an interrupted production process follows exponential distribution. Few of the last service phases are assumed to be protected in the sense that the service will not be interrupted while being in these phases. The same is assumed for the production process also.

The model is analysed as a level-independent quasi-birth–death process. We apply a novel method to obtain an explicit expression for the necessary and sufficient condition for the stability of the system under study. This method works even if we assume general phase-type distributions for the production as well as the service processes, and hence can be used to characterise the stability of inventory systems where the assumption of disallowing the customers to join the system, when there is a shortage of inventory has been made. Under stability, we apply matrix analytic methods to compute the system state distribution. In consequence to that, several system performance measures have been derived, and their dependence on the system parameters has been studied numerically.     

Separation of water–isopropyl alcohol mixtures with novel hybrid composite membranes

New‐fangled hybrid composite membranes were prepared by the incorporation of 5, 10, and 15 mass % NaY–zeolite particles into blend membranes of carboxymethyl cellulose (CMC)‐g‐acrylamide/sodium alginate (NaAlg) and crosslinked with glutaraldehyde. The pervaporation (PV) separation performance of the hybrid composite membranes was explored for the dehydration of isopropyl alcohol from their aqueous solutions at 30°C. The effect of NaY–zeolite in these blend membranes was investigated in PV dehydration. From the experimental results, we found that NaY particles could be intercalated in the aqueous polymer solution. The obtained results show that both the flux and selectivity increased simultaneously with increasing zeolite content in the membrane. This was explained on the basis of an enhancement of the hydrophilicity, selective adsorption, and molecular sieving action by the creation of pores in the membrane matrix. The membranes were characterized by differential scanning calorimetry, scanning electron microscopy, and Fourier transform infrared spectroscopy. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2012     

Degradation of poly(methyl methacrylate) (PMMA) with aluminum nitride and alumina

This paper deals with the thermal and thermal-oxidative degradation of pure poly(methyl methacrylate) (PMMA), PMMA/A1N and PMMA/Al₂O₃ composites. Kinetic parameters were determined from the weight loss data using non-isothermal Thermogravimetric Analysis (TGA). The amount and morphology of the carbon residue in the burnt samples under N₂ and air atmospheres were also investigated using a Leco combustion analyzer. This study also showed that the normally accepted three-stage polymer thermal degradation, and hence three regions of Arrhenius linearity, can be treated with one value of activation energy. This is a basic departure from the normally accepted three different regions and applying the same diffusion equation (such as Jander diffusion) separately to each region. In nitrogen atmosphere, the activation energy of pure PMMA was 129.4 kJ/mol; however, the activation energies of 14% PMMA/AlN and PMMA/Al₂O₃ were found to be 119.5 and 118.2 kJ/mol, respectively.     

Experimental and numerical investigation of the gas‐phase effectiveness of phosphorus compounds

The effectiveness of phosphorus‐containing compounds as gas‐phase combustion inhibitors varies widely with flame type. To understand this behavior, experiments are performed with dimethyl methylphosphonate (DMMP) added to the oxidizer stream of methane–air co‐flow diffusion flames (cup‐burner configuration). At low volume fraction, phosphorus (via DMMP addition) is shown to be about four times as effective as bromine (via Br₂ addition) at reducing the amount of CO₂ required for extinguishment; however, above about 3000 μL/L to 6000 μL/L, the marginal effectiveness of DMMP is approximately zero. In contrast, the diminished effectiveness does not occur for Br₂ addition. To explore the role of condensation of active phosphorus‐containing compounds to the particles, laser‐scattering measurements are performed. Finally, to examine the behavior of the flame stabilization region (which is responsible for extinguishment), premixed burning velocity simulations with detailed kinetics are performed for DMMP addition to methane–air flames. Analyses of the numerical results are performed to understand the variation in the inhibition mechanism with temperature, agent loading, and stoichiometry, to interpret the loss of effectiveness for DMMP in the present experiments. Copyright © 2015 John Wiley & Sons, Ltd.     

Approximation Algorithms for Requirement Cut on Graphs

In this paper, we unify several graph partitioning problems including multicut, multiway cut, and k-cut, into a single problem. The input to the requirement cut problem is an undirected edge-weighted graph G=(V,E), and g groups of vertices X ₁,…,X _g ⊆V, with each group X _i having a requirement r _i between 0 and |X _i |. The goal is to find a minimum cost set of edges whose removal separates each group X _i into at least r _i disconnected components. We give an O(log n⋅log (gR)) approximation algorithm for the requirement cut problem, where n is the total number of vertices, g is the number of groups, and R is the maximum requirement. We also show that the integrality gap of a natural LP relaxation for this problem is bounded by O(log n⋅log (gR)). On trees, we obtain an improved guarantee of O(log (gR)). There is an Ω(log g) hardness of approximation for the requirement cut problem, even on trees.     

Stirred reactor calculations to understand unwanted combustion enhancement by potential halon replacements

Several agents are under consideration to replace CF₃Br for use in suppressing fires in aircraft cargo bays. In a Federal Aviation Administration performance test simulating the explosion of an aerosol can, however, the replacements, when added at sub-inerting concentrations, have all been found to create higher pressure rise than with no agent, hence failing the test. Thermodynamic equilibrium calculations as well as perfectly-stirred reactor simulations with detailed reaction kinetics, are performed to understand the reasons for the unexpected enhanced combustion rather than suppression. The high pressure rise with added C₂HF₅ or C₃H₂F₃Br is shown to be dependent upon the amount of added agent, and can only occur if a large fraction of the available oxidizer in the chamber is consumed, corresponding to stoichiometric proportions of fuel, oxygen, and agent. Conversely, due to the unique stoichiometry of CF₃Br, this agent is predicted to cause no increase in pressure, even in the absence of chemical inhibition. The stirred-reactor simulations predict that the inhibition effectiveness of CF₃Br is highly dependent upon the mixing conditions of the reactants (which affects the local stoichiometry and hence the overall reaction rate). For C₂HF₅, however, the overall reaction rate was only weakly dependent upon stoichiometry, so the fuel–oxidizer mixing state has less effect on the suppression effectiveness.     

Hydrothermal Growth of Undoped and Zn-Doped SnO Nanocrystals: A Frequency Dependence of AC Conductivity and Dielectric Response Studies

Semiconductors - The aim of this work is to investigate the dielectric properties of undoped and Zn-doped Tin monoxide (SnO) nanocrystals synthesized by the hydrothermal technique. The prepared...