Analysis of Some Single and Two Commodity Inventory Problems

This thesis is devoted to the study of some stochastic models in inventories. An inventory system is a facility at which items of materials are stocked. In order to promote smooth and efficient running of business, and to provide adequate service to the customers, an inventory materials is essential for any enterprise. When uncertainty is present, inventories are used as a protection against risk of stock out. It is advantageous to procure the item before it is needed at a lower marginal cost. Again, by bulk purchasing, the advantage of price discounts can be availed. All these contribute to the formation of inventory. Maintaining inventories is a major expenditure for any organization. For each inventory, the fundamental question is how much new stock should be ordered and when should the orders are replaced. In the present study, considered several models for single and two commodity stochastic inventory problems. The thesis discusses two models. In the first model, examined the case in which the time elapsed between two consecutive demand points are independent and identically distributed with common distribution function F(.) with mean  (assumed finite) and in which demand magnitude depends only on the time elapsed since the previous demand epoch. The time between disasters has an exponential distribution with parameter . In Model II, the inter arrival time of disasters have general distribution (F.) with mean  ( ) and the quantity destructed depends on the time elapsed between disasters. Demands form compound poison processes with inter arrival times of demands having mean 1/. It deals with linearly correlated bulk demand two Commodity inventory problem, where each arrival demands a random number of items of each commodity C1 and C2, the maximum quantity demanded being a (< S1) and b(

Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Legal Control of Industrial Pollution

Industries constitute the main spring of development. Without industrial development no country could reach a stage in which a decent living for its citizens would be achieved. Increasing production to meet the basic needs of society augmented scientific invention and machine oriented industrial order.Environmental pollution ls a burning global issue. It is more serious and dangerous than terrorism. Started with the discovery of fire and development of civilization. Pollution went unnoticed throughout the centuries of human growth until its adverse effects on human environment become explicit.National concern tor environment started in our country only atter the cause of protection of environment received global attention. At present legal control ot industrial pollution is in a scattered framework of piece meal processes with overlapping provisions and authorities.Environmental protection- should be an item not only in the concurrent list of schedule 7 to the Constitution but also in the list of matters entrusted to the panchayati institutions in the Schedule 11. It is heartening to note that so far as municipalities are concerned the Constitution of India lives up to the expectation. In the wake of New Industrial Policy based on liberalisation a long list of small scale industries fall outside the purview of environmental clearance. The Indian concept of environmental im»act assessment introduced under the Environment Act by notification excludes the entire gamut of small scale industries and r.elates only to scheduled industries covered by the notifica~ion. Most of them are subjected to ETA only it the investment goes above ~.50 crores. This provision dilutes the impact assessment considerably A mandatory impact assessment with public partiCipation and with provision for a review by specialized environmental courts will eliminate the possible evils of this judicial passiveness.

Thermohaline variability in the upper layers of the Arabian Sea

The Arabian Sea is an area of complex air-sea interaction processes with seasonal reversing monsoons. The associated thermohaline variability in the upper layers appears to control the large scale monsoon flow which is not yet completely understood. The variability in the thermohaline fields is known to occur in temporal domain ranging from intra-diurnal to inter-annual time scales and on spatial domains of few tens of kilometers to few thousands of kilometers. In the Arabian Sea though the surface temperature was routinely measured by both conventional measurements and satellites, the corresponding information on the subsurface thermohaline field is very sparse due to the lack cw adequate measurements. In such cases the numerical models offer promise in providing information on the subsurface features given an initial thermohaline field and surface heat flux boundary conditions. This thesis is an outcome of investigations carried out on the various aspects of the thermohaline variability on different time scales. In addition to the description of the mean annual cycle. the one dimensional numerical models of Miller (1976) and Price et a1 (1986) are utilised to simulate the observed mixed layer characteristics at selected locations in the Arabian Sea on time scales ranging from intra-diurnal to synoptic scales under variable atmospheric forcing.

Stratosphere Troposphere Interactions Associated With the Dynamical Processes in the Atmosphere

The aim of the present study is to understand the biennial scale stratosphere-troposphere interactions over India, and synoptic to interannual timescale meridional stratosphere-troposhere exchanges caused by upper tropospheric/lower stratospheric longwaves using NCEP/NCAR reanalysis data and satellite measured total ozone data. The biennial timescale interaction between lower stratosphere and troposphere over Thumba is analysed using high-resolution radiosonde data. The results suggest that TBO and QBO are two different phenomena with nearly biennial periodicity. Interannual timescale meridional stratosphere-troposphere exchanges caused by the newly documented Asia Pacific Wave (APW) were analysed using ozone as tracer of atmospheric motion. Synoptic timescale meridional stratosphere-troposhere exchanges caused by subtropical upper tropospheric long waves over Asia were studied using global total ozone measurements from TOMS. This research work can be extended to study the influence of decadal scale epochal nature in Indian summer monsoon activity on the APW generated total ozone anomalies around the globe and the trend estimates in total ozone

Queueing Theory And Other Applications Of Stochastic Processes Queueing And Inventory Models With Rest Periods

In this thesis we study the effect of rest periods in queueing systems without exhaustive service and inventory systems with rest to the server. Most of the works in the vacation models deal with exhaustive service. Recently some results have appeared for the systems without exhaustive service.