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(

Systematics, Life history traits, abundance andstock assessment of cobia, Rachycentron canadum ( Linnaeus, 1766) occurring in Indian waters with special reference to the north west coast in India

This thesis entitled Systematics,life history traits ,abundance and stock assessment of cobia rachycentron canadum (linnaeus ,1766) occurring in indian waters with special reference to the northwest coast of india.Cobia, Rachycentron canadum is a fast growing pelagic fish belonging to the monotypic family Rachycentridae. They show worldwide distribution in tropical and sub tropical waters. Cobia is exploited commercially in various countries like Taiwan, Pakistan, India, United State of America, Australia, Gulf of Mexico and the Caribbean. Recreational fishery of Cobia exists in different parts of the world. In India Cobia is caught as bycatch of trawlers, gillnet and hook and line fishery.This study also focuses on to bring out the distribution pattern and also to assess the biomass and estimate sustainable yield of Cobia inhabiting in Indian EEZ. In addition to above, present study standardised live collection methods and also reviewed culture prospects.Results of osteological study and morphological studies indicate its close resemblance to Remora and support the view that Cobia was evolved from Dolphin fishes and remoras followed it. Study also confirmed that Cobia does not have any relative or similar species and is a monotypic species belonging to the family Rachycentridae. Re description of the species was done based on the characters identified. In this study, feeding intensity was also assessed following methods like Gastrosomatic index, Mean index of feeding intensity and Index of fullness. Sex wise, month wise and length group wise fluctuations in the feeding intensity also were studied. Cobia actively fed during post monsoon period. In general, adult fed actively than the juveniles. Trophic level value estimated (4.36) indicates that Cobia occupy top level position in the food chain.

On Queueinginventory Models – product form solution; reservation, Cancellation and common life time

Queueing theory is the mathematical study of ‘queue’ or ‘waiting lines’ where an item from inventory is provided to the customer on completion of service. A typical queueing system consists of a queue and a server. Customers arrive in the system from outside and join the queue in a certain way. The server picks up customers and serves them according to certain service discipline. Customers leave the system immediately after their service is completed. For queueing systems, queue length, waiting time and busy period are of primary interest to applications. The theory permits the derivation and calculation of several performance measures including the average waiting time in the queue or the system, mean queue length, traffic intensity, the expected number waiting or receiving service, mean busy period, distribution of queue length, and the probability of encountering the system in certain states, such as empty, full, having an available server or having to wait a certain time to be served.

Environmental Influences on the Frequency and Intensity of North Indian Ocean Tropical Cyclones

Tropical cyclones genesis, movement and intensification are highly dependent on its environment both oceanic and atmospheric. This thesis has made a detailed study on the environmental factors related to tropical cyclones of North Indian Ocean basin. This ocean basin has produced only 6% of the global tropical cyclones annually but it has caused maximum loss of human life associated with the strong winds, heavy rain and particularly storm surges that accompany severe cyclones as they strike the heavily populated coastal areas. Atmospheric factors studied in the thesis are the moisture content of the atmosphere, instability of the atmosphere that produces thunderstorms which are the main source of energy for the tropical cyclone, vertical wind shear to which cyclones are highly sensitive and the Sub-Tropical westerly Jetsteram and its Asian high speed center. The oceanic parameters studied are sea surface temperature and heat storage in the top layer of the ocean. A major portion of the thesis has dealt with the three temporal variabilities of tropical cyclone frequency namely intra-seasonal (mainly the influence of Madden Julian Oscillation), inter- annual (the relation with El Nino Southern Oscillation) and decadal variabilities. Regarding decadal variability, a prominent four decade oscillation in the frequency of both tropical cyclones and monsoon depressions unique to the Indian Ocean basin has been brought out. The thesis consists of 9 chapters.

Long term trends of seasonal and monthly rainfall in different intensity ranges over Indian subcontinent

In general Indian summer monsoon rainfall did not show any significant trend in all Indian summer monsoon rainfall series, however, it was reported that the ISMR is subjected to spatial trends. This paper made an attempt to bring out long term trends of different intensity classes of summer monsoon rainfall in different regions of Indian subcontinent. The long term trend of seasonal and monthly rainfall were also made using the India Meteorological Department gridded daily rainfall data with a spatial resolution of 1° × 1° latitude-longitude grid for the period from 1st January, 1901 to 31st December, 2003. The summer monsoon rainfall shows an increasing trend in southeast, northwest and northeast regions, whereas decreasing trend in the central and west coastal regions. In monthly scale, July rainfall shows decreasing trend over west coastal and central Indian regions and significant increasing trend over northeast region at 0.1% significant level. During the month August, decreasing trend is observed in the west coastal stations at 10% significant level. In most of the stations, mean daily rainfall shows an increasing trend for low and very high intense rainfall. For the moderate rainfall, the trend is different for different regions. In the central and southern regions the trend of moderate and moderately high classes show increasing trend. And for the high and very high intensity classes, the trend is decreasing significantly. In the northeastern regions, above 10 mm/day rainfall shows significantly increasing trend with 0.1% significant level.

Queues with inter- ruption in Random/ Markovian Environment

In many situations probability models are more realistic than deterministic models. Several phenomena occurring in physics are studied as random phenomena changing with time and space. Stochastic processes originated from the needs of physicists.Let X(t) be a random variable where t is a parameter assuming values from the set T. Then the collection of random variables {X(t), t ∈ T} is called a stochastic process. We denote the state of the process at time t by X(t) and the collection of all possible values X(t) can assume, is called state space